From a1b63f2f5deb8b86fc97bb5665bd7dc28ea15211 Mon Sep 17 00:00:00 2001 From: josd Date: Fri, 20 Dec 2024 20:18:53 +0100 Subject: [PATCH] adding list:quicksort built-in which is not removing duplicates --- RELEASE | 1 + VERSION | 2 +- eye-builtins.n3 | 4 + eye.pl | 27 +- eye.zip | Bin 108460 -> 108541 bytes .../proof-by-recursion/example2-answer.n3 | 1999 +- .../proof-by-recursion/example2-proof.n3 | 142332 ++++----------- .../proof-by-recursion/example2-query.n3 | 5 +- reasoning/proof-by-recursion/example2.n3 | 60 +- 9 files changed, 37635 insertions(+), 106795 deletions(-) diff --git a/RELEASE b/RELEASE index b9e57e45b..e8d8311f7 100644 --- a/RELEASE +++ b/RELEASE @@ -1,5 +1,6 @@ EYE release +v11.1.1 (2024-12-20) adding list:quicksort built-in which is not removing duplicates v11.1.0 (2024-12-18) reverting to rdfsurfaces implementation in eye v10 v11.0.2 (2024-12-17) adding log:callWithDisjunction built-in v11.0.1 (2024-12-15) adding list:intersection back diff --git a/VERSION b/VERSION index 68d8f15e2..668182d21 100644 --- a/VERSION +++ b/VERSION @@ -1 +1 @@ -11.1.0 +11.1.1 diff --git a/eye-builtins.n3 b/eye-builtins.n3 index ef8df290f..3a13d8309 100644 --- a/eye-builtins.n3 +++ b/eye-builtins.n3 @@ -110,6 +110,7 @@ list:append a e:Builtin. list:first a e:Builtin. list:firstRest a e:Builtin. list:in a e:Builtin. +list:intersection a e:Builtin. list:isList a e:Builtin. list:iterate a e:Builtin. list:last a e:Builtin. @@ -120,6 +121,7 @@ list:memberAt a e:Builtin. list:multisetEqualTo a e:Builtin. list:multisetNotEqualTo a e:Builtin. list:notMember a e:Builtin. +list:quicksort a e:Builtin. list:remove a e:Builtin. list:removeAt a e:Builtin. list:removeDuplicates a e:Builtin. @@ -140,6 +142,7 @@ log:call a e:Builtin. log:callNotBind a e:Builtin. log:callWithCleanup a e:Builtin. log:callWithCut a e:Builtin. +log:callWithDisjunction a e:Builtin. log:callWithOptional a e:Builtin. log:collectAllIn a e:Builtin. log:conclusion a e:Builtin. @@ -176,6 +179,7 @@ log:query a e:Builtin. log:racine a e:Builtin. log:rawType a e:Builtin. log:repeat a e:Builtin. +log:satisfiable a e:Builtin. log:semantics a e:Builtin. log:semanticsOrError a e:Builtin. log:shell a e:Builtin. diff --git a/eye.pl b/eye.pl index 2b7552680..c21cdea12 100644 --- a/eye.pl +++ b/eye.pl @@ -22,7 +22,7 @@ :- catch(use_module(library(process)), _, true). :- catch(use_module(library(http/http_open)), _, true). -version_info('EYE v11.1.0 (2024-12-18)'). +version_info('EYE v11.1.1 (2024-12-20)'). license_info('MIT License @@ -6943,6 +6943,17 @@ ) ). +''([A, B], C) :- + when( + ( nonvar(A), + nonvar(B) + ), + ( getlist(A, D), + getlist(B, E), + intersection(D, E, C) + ) + ). + ''(A, B) :- ( getlist(A, _) -> B = true @@ -7041,6 +7052,15 @@ ) ). +''(A, B) :- + when( + ( nonvar(A) + ), + ( getlist(A, C), + quicksort(C, B) + ) + ). + ''([A, B], C) :- when( ( nonvar(A), @@ -7253,6 +7273,11 @@ istep('<>', C, ''(A, B), D) ). +''(A, B) :- + ( catch(call(A), _, fail) + ; catch(call(B), _, fail) + ). + ''(A, B) :- call(A), ( \+catch(call(B), _, fail) diff --git a/eye.zip b/eye.zip index cdd9589d1d10f075e1b0eda9dabb5ab10e4ce354..b6587d12a637512c0470fe88ceefc046f68c2f21 100644 GIT binary patch delta 103506 zcmV)1K+V6b&j$U^1`SY40|W{H00000TcVVa4H^d>!)0e3!)1{!LIYApW3h8V0t1;v zWs|o8b^}sIW0Nog{R5aqWwS5@gaIlRqLf*T9r)Ae&;S4r%LM=m02}~id1WtUd1Wqe zY*kbV00W!CWoMhhWwYJ|I01hj{$s|`!O@HE;ZgVKV6Tm!j%|T?a0PlboUlvT(rWen z;4!q9tB4ua9y>ZX_!+Q{j`POex&_;?1rEk+!C-0d*&|zqrWf&fhb=;|Y*;901xpV6 z`LKc>Spe(-f~bY>#1I(#6)Wvivw=As10-TS%kBY|nDyIr5NnJGN`9 z5fGgOAX-2al+YnQI}CJTFYukyw1RjBOK{a;a~ny|;s_cAHj*SeIFFtmGQl0E1r%)H zo93EvM=;2GfC7z_hy;JOtXIBUoQW-3i#YUPNKQC&A4EnY{=uyXTM&HVJC47`sad`^ zw{b?|q}7^0mpSwAIn71t7rYv7hT}nposWiN6v*q*%~hv`;sk$;8zKUD*8@ofMa>Et0TBHD zZahc{vWvm_CD0lpGEOl8-X{;T;!dF4$2(yz`3Zx~ik|R839)@}RuH{8r;=}ra2Fs7Z4ThqI+#I*1 z9mrk$V>lVs(6ZgY!DYBDtpr|AEx31gn&|EOE12w@SIBV+mg-*oA#hCPrDdRl&MFr8 z7q;ya*c0!$P^8exYAJzx^4E+&kgWv8HLdPv{>Xn$;m=tay)g;;kBqv?h 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:recursionsNeeded 6 . -(2021 6174) :recursionsNeeded 3 . -(2022 6174) :recursionsNeeded 4 . -(2023 6174) :recursionsNeeded 6 . -(2024 6174) :recursionsNeeded 4 . -(2025 6174) :recursionsNeeded 6 . -(2026 6174) :recursionsNeeded 6 . -(2027 6174) :recursionsNeeded 4 . -(2028 6174) :recursionsNeeded 6 . -(2029 6174) :recursionsNeeded 4 . -(2030 6174) :recursionsNeeded 5 . -(2031 6174) :recursionsNeeded 3 . -(2032 6174) :recursionsNeeded 6 . -(2033 6174) :recursionsNeeded 3 . -(2034 6174) :recursionsNeeded 7 . -(2035 6174) :recursionsNeeded 7 . -(2036 6174) :recursionsNeeded 7 . -(2037 6174) :recursionsNeeded 3 . -(2038 6174) :recursionsNeeded 3 . -(2039 6174) :recursionsNeeded 4 . -(2040 6174) :recursionsNeeded 2 . -(2041 6174) :recursionsNeeded 7 . -(2042 6174) :recursionsNeeded 4 . -(2043 6174) :recursionsNeeded 7 . -(2044 6174) :recursionsNeeded 2 . -(2045 6174) :recursionsNeeded 7 . -(2046 6174) :recursionsNeeded 1 . -(2047 6174) :recursionsNeeded 5 . -(2048 6174) :recursionsNeeded 6 . -(2049 6174) :recursionsNeeded 3 . -(2050 6174) :recursionsNeeded 7 . -(2051 6174) :recursionsNeeded 7 . -(2052 6174) :recursionsNeeded 6 . -(2053 6174) :recursionsNeeded 7 . -(2054 6174) :recursionsNeeded 7 . -(2055 6174) :recursionsNeeded 5 . -(2056 6174) :recursionsNeeded 3 . -(2057 6174) :recursionsNeeded 6 . -(2058 6174) :recursionsNeeded 5 . -(2059 6174) :recursionsNeeded 3 . -(2060 6174) :recursionsNeeded 1 . -(2061 6174) :recursionsNeeded 7 . -(2062 6174) :recursionsNeeded 6 . -(2063 6174) :recursionsNeeded 7 . -(2064 6174) :recursionsNeeded 1 . -(2065 6174) :recursionsNeeded 3 . -(2066 6174) :recursionsNeeded 4 . -(2067 6174) :recursionsNeeded 3 . -(2068 6174) :recursionsNeeded 2 . -(2069 6174) :recursionsNeeded 7 . -(2070 6174) :recursionsNeeded 5 . -(2071 6174) :recursionsNeeded 3 . -(2072 6174) :recursionsNeeded 4 . -(2073 6174) :recursionsNeeded 3 . -(2074 6174) :recursionsNeeded 5 . -(2075 6174) :recursionsNeeded 6 . -(2076 6174) :recursionsNeeded 3 . -(2077 6174) :recursionsNeeded 5 . -(2078 6174) :recursionsNeeded 7 . -(2079 6174) :recursionsNeeded 7 . -(2080 6174) :recursionsNeeded 6 . -(2081 6174) :recursionsNeeded 3 . -(2082 6174) :recursionsNeeded 6 . -(2083 6174) :recursionsNeeded 3 . -(2084 6174) :recursionsNeeded 6 . -(2085 6174) :recursionsNeeded 5 . -(2086 6174) :recursionsNeeded 2 . -(2087 6174) :recursionsNeeded 7 . -(2088 6174) :recursionsNeeded 2 . -(2089 6174) :recursionsNeeded 7 . -(2090 6174) :recursionsNeeded 3 . -(2091 6174) :recursionsNeeded 4 . -(2092 6174) :recursionsNeeded 4 . -(2093 6174) :recursionsNeeded 4 . -(2094 6174) :recursionsNeeded 3 . -(2095 6174) :recursionsNeeded 3 . -(2096 6174) :recursionsNeeded 7 . -(2097 6174) :recursionsNeeded 7 . -(2098 6174) :recursionsNeeded 7 . -(2099 6174) :recursionsNeeded 3 . -(2100 6174) :recursionsNeeded 3 . -(2101 6174) :recursionsNeeded 4 . -(2102 6174) :recursionsNeeded 3 . -(2103 6174) :recursionsNeeded 3 . -(2104 6174) :recursionsNeeded 7 . -(2105 6174) :recursionsNeeded 7 . -(2106 6174) :recursionsNeeded 7 . -(2107 6174) :recursionsNeeded 3 . -(2108 6174) :recursionsNeeded 3 . -(2109 6174) :recursionsNeeded 4 . -(2110 6174) :recursionsNeeded 4 . -(2111 6174) :recursionsNeeded 5 . -(2112 6174) :recursionsNeeded 4 . -(2113 6174) :recursionsNeeded 3 . -(2114 6174) :recursionsNeeded 3 . -(2115 6174) :recursionsNeeded 7 . -(2116 6174) :recursionsNeeded 7 . -(2117 6174) :recursionsNeeded 7 . -(2118 6174) :recursionsNeeded 3 . -(2119 6174) :recursionsNeeded 3 . -(2120 6174) :recursionsNeeded 3 . -(2121 6174) :recursionsNeeded 4 . -(2122 6174) :recursionsNeeded 5 . -(2123 6174) :recursionsNeeded 4 . -(2124 6174) :recursionsNeeded 6 . -(2125 6174) :recursionsNeeded 4 . -(2126 6174) :recursionsNeeded 6 . -(2127 6174) :recursionsNeeded 6 . -(2128 6174) :recursionsNeeded 4 . -(2129 6174) :recursionsNeeded 6 . -(2130 6174) :recursionsNeeded 3 . -(2131 6174) :recursionsNeeded 3 . -(2132 6174) :recursionsNeeded 4 . -(2133 6174) :recursionsNeeded 3 . -(2134 6174) :recursionsNeeded 3 . -(2135 6174) :recursionsNeeded 7 . -(2136 6174) :recursionsNeeded 7 . -(2137 6174) :recursionsNeeded 7 . -(2138 6174) :recursionsNeeded 3 . -(2139 6174) :recursionsNeeded 3 . -(2140 6174) :recursionsNeeded 7 . -(2141 6174) :recursionsNeeded 3 . -(2142 6174) :recursionsNeeded 6 . -(2143 6174) :recursionsNeeded 3 . -(2144 6174) :recursionsNeeded 5 . -(2145 6174) :recursionsNeeded 2 . -(2146 6174) :recursionsNeeded 7 . -(2147 6174) :recursionsNeeded 1 . -(2148 6174) :recursionsNeeded 5 . -(2149 6174) :recursionsNeeded 6 . -(2150 6174) :recursionsNeeded 7 . -(2151 6174) :recursionsNeeded 7 . -(2152 6174) :recursionsNeeded 4 . -(2153 6174) :recursionsNeeded 7 . -(2154 6174) :recursionsNeeded 2 . -(2155 6174) :recursionsNeeded 3 . -(2156 6174) :recursionsNeeded 5 . -(2157 6174) :recursionsNeeded 3 . -(2158 6174) :recursionsNeeded 6 . -(2159 6174) :recursionsNeeded 5 . -(2160 6174) :recursionsNeeded 7 . -(2161 6174) :recursionsNeeded 7 . -(2162 6174) :recursionsNeeded 6 . -(2163 6174) :recursionsNeeded 7 . -(2164 6174) :recursionsNeeded 7 . -(2165 6174) :recursionsNeeded 5 . -(2166 6174) :recursionsNeeded 5 . -(2167 6174) :recursionsNeeded 4 . -(2168 6174) :recursionsNeeded 3 . -(2169 6174) :recursionsNeeded 2 . -(2170 6174) :recursionsNeeded 3 . -(2171 6174) :recursionsNeeded 7 . -(2172 6174) :recursionsNeeded 6 . -(2173 6174) :recursionsNeeded 7 . -(2174 6174) :recursionsNeeded 1 . -(2175 6174) :recursionsNeeded 3 . -(2176 6174) :recursionsNeeded 4 . -(2177 6174) :recursionsNeeded 5 . -(2178 6174) :recursionsNeeded 5 . -(2179 6174) :recursionsNeeded 7 . -(2180 6174) :recursionsNeeded 3 . -(2181 6174) :recursionsNeeded 3 . -(2182 6174) :recursionsNeeded 4 . -(2183 6174) :recursionsNeeded 3 . -(2184 6174) :recursionsNeeded 5 . -(2185 6174) :recursionsNeeded 6 . -(2186 6174) :recursionsNeeded 3 . -(2187 6174) :recursionsNeeded 5 . -(2188 6174) :recursionsNeeded 3 . -(2189 6174) :recursionsNeeded 2 . -(2190 6174) :recursionsNeeded 4 . -(2191 6174) 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:recursionCount 5 . +2976 :recursionCount 3 . +2977 :recursionCount 4 . +2978 :recursionCount 3 . +2979 :recursionCount 5 . +2980 :recursionCount 7 . +2981 :recursionCount 2 . +2982 :recursionCount 3 . +2983 :recursionCount 5 . +2984 :recursionCount 3 . +2985 :recursionCount 6 . +2986 :recursionCount 5 . +2987 :recursionCount 3 . +2988 :recursionCount 4 . +2989 :recursionCount 3 . +2990 :recursionCount 3 . +2991 :recursionCount 5 . +2992 :recursionCount 6 . +2993 :recursionCount 3 . +2994 :recursionCount 5 . +2995 :recursionCount 3 . +2996 :recursionCount 6 . +2997 :recursionCount 5 . +2998 :recursionCount 3 . +2999 :recursionCount 4 . diff --git a/reasoning/proof-by-recursion/example2-proof.n3 b/reasoning/proof-by-recursion/example2-proof.n3 index f757f3830..013b8e848 100644 --- a/reasoning/proof-by-recursion/example2-proof.n3 +++ b/reasoning/proof-by-recursion/example2-proof.n3 @@ -1007,53068 +1007,48973 @@ skolem:proof a r:Proof, r:Conjunction; r:component skolem:lemma997; r:component skolem:lemma998; r:component skolem:lemma999; - r:component skolem:lemma1000; - r:gives { - (2000 6174) :recursionsNeeded 4 . - (2001 6174) :recursionsNeeded 3 . - (2002 6174) :recursionsNeeded 6 . - (2003 6174) :recursionsNeeded 5 . - (2004 6174) :recursionsNeeded 2 . - (2005 6174) :recursionsNeeded 7 . - (2006 6174) :recursionsNeeded 1 . - (2007 6174) :recursionsNeeded 5 . - (2008 6174) :recursionsNeeded 6 . - (2009 6174) :recursionsNeeded 3 . - (2010 6174) :recursionsNeeded 3 . - (2011 6174) :recursionsNeeded 4 . - (2012 6174) :recursionsNeeded 3 . - (2013 6174) :recursionsNeeded 3 . - (2014 6174) :recursionsNeeded 7 . - (2015 6174) :recursionsNeeded 7 . - (2016 6174) :recursionsNeeded 7 . - (2017 6174) :recursionsNeeded 3 . - (2018 6174) :recursionsNeeded 3 . - (2019 6174) :recursionsNeeded 4 . - (2020 6174) :recursionsNeeded 6 . - (2021 6174) :recursionsNeeded 3 . - (2022 6174) :recursionsNeeded 4 . - (2023 6174) :recursionsNeeded 6 . - (2024 6174) :recursionsNeeded 4 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(2080 6174) :recursionsNeeded 6 . - (2081 6174) :recursionsNeeded 3 . - (2082 6174) :recursionsNeeded 6 . - (2083 6174) :recursionsNeeded 3 . - (2084 6174) :recursionsNeeded 6 . - (2085 6174) :recursionsNeeded 5 . - (2086 6174) :recursionsNeeded 2 . - (2087 6174) :recursionsNeeded 7 . - (2088 6174) :recursionsNeeded 2 . - (2089 6174) :recursionsNeeded 7 . - (2090 6174) :recursionsNeeded 3 . - (2091 6174) :recursionsNeeded 4 . - (2092 6174) :recursionsNeeded 4 . - (2093 6174) :recursionsNeeded 4 . - (2094 6174) :recursionsNeeded 3 . - (2095 6174) :recursionsNeeded 3 . - (2096 6174) :recursionsNeeded 7 . - (2097 6174) :recursionsNeeded 7 . - (2098 6174) :recursionsNeeded 7 . - (2099 6174) :recursionsNeeded 3 . - (2100 6174) :recursionsNeeded 3 . - (2101 6174) :recursionsNeeded 4 . - (2102 6174) :recursionsNeeded 3 . - (2103 6174) :recursionsNeeded 3 . - (2104 6174) :recursionsNeeded 7 . - (2105 6174) :recursionsNeeded 7 . - (2106 6174) :recursionsNeeded 7 . - (2107 6174) :recursionsNeeded 3 . - (2108 6174) :recursionsNeeded 3 . - (2109 6174) :recursionsNeeded 4 . - (2110 6174) :recursionsNeeded 4 . - (2111 6174) :recursionsNeeded 5 . - (2112 6174) :recursionsNeeded 4 . - (2113 6174) :recursionsNeeded 3 . - (2114 6174) :recursionsNeeded 3 . - (2115 6174) :recursionsNeeded 7 . - (2116 6174) :recursionsNeeded 7 . - (2117 6174) :recursionsNeeded 7 . - (2118 6174) :recursionsNeeded 3 . - (2119 6174) :recursionsNeeded 3 . - (2120 6174) :recursionsNeeded 3 . - (2121 6174) :recursionsNeeded 4 . - (2122 6174) :recursionsNeeded 5 . - (2123 6174) :recursionsNeeded 4 . - (2124 6174) :recursionsNeeded 6 . - (2125 6174) :recursionsNeeded 4 . - (2126 6174) :recursionsNeeded 6 . - (2127 6174) :recursionsNeeded 6 . - (2128 6174) :recursionsNeeded 4 . - (2129 6174) :recursionsNeeded 6 . - (2130 6174) :recursionsNeeded 3 . - (2131 6174) :recursionsNeeded 3 . - (2132 6174) :recursionsNeeded 4 . - (2133 6174) :recursionsNeeded 3 . - (2134 6174) :recursionsNeeded 3 . - 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:recursionCount 5 . + 2984 :recursionCount 3 . + 2985 :recursionCount 6 . + 2986 :recursionCount 5 . + 2987 :recursionCount 3 . + 2988 :recursionCount 4 . + 2989 :recursionCount 3 . + 2990 :recursionCount 3 . + 2991 :recursionCount 5 . + 2992 :recursionCount 6 . + 2993 :recursionCount 3 . + 2994 :recursionCount 5 . + 2995 :recursionCount 3 . + 2996 :recursionCount 6 . + 2997 :recursionCount 5 . + 2998 :recursionCount 3 . + 2999 :recursionCount 4 . }. skolem:lemma1 a r:Inference; r:gives { - (2000 6174) :recursionsNeeded 4 . + 2000 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 0}] [ a r:Fact; r:gives {(0 2000) math:sum 2000}] - skolem:lemma1001 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1000 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma2 a r:Inference; r:gives { - (2001 6174) :recursionsNeeded 3 . + 2001 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 1}] [ a r:Fact; r:gives {(1 2000) math:sum 2001}] - skolem:lemma1003 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1002 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma3 a r:Inference; r:gives { - (2002 6174) :recursionsNeeded 6 . + 2002 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 2}] [ a r:Fact; r:gives {(2 2000) math:sum 2002}] - skolem:lemma1004 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1003 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma4 a r:Inference; r:gives { - (2003 6174) :recursionsNeeded 5 . + 2003 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 3}] [ a r:Fact; r:gives {(3 2000) math:sum 2003}] - skolem:lemma1005 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1004 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma5 a r:Inference; r:gives { - (2004 6174) :recursionsNeeded 2 . + 2004 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 4}] [ a r:Fact; r:gives {(4 2000) math:sum 2004}] - skolem:lemma1006 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1005 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma6 a r:Inference; r:gives { - (2005 6174) :recursionsNeeded 7 . + 2005 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 5}] [ a r:Fact; r:gives {(5 2000) math:sum 2005}] - skolem:lemma1007 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1006 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma7 a r:Inference; r:gives { - (2006 6174) :recursionsNeeded 1 . + 2006 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 6}] [ a r:Fact; r:gives {(6 2000) math:sum 2006}] - skolem:lemma1008 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1007 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. skolem:lemma8 a r:Inference; r:gives { - (2007 6174) :recursionsNeeded 5 . + 2007 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 7}] [ a r:Fact; r:gives {(7 2000) math:sum 2007}] - skolem:lemma1009 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1008 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma9 a r:Inference; r:gives { - (2008 6174) :recursionsNeeded 6 . + 2008 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 8}] [ a r:Fact; r:gives {(8 2000) math:sum 2008}] - skolem:lemma1010 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1009 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma10 a r:Inference; r:gives { - (2009 6174) :recursionsNeeded 3 . + 2009 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 9}] [ a r:Fact; r:gives {(9 2000) math:sum 2009}] - skolem:lemma1011 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1010 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma11 a r:Inference; r:gives { - (2010 6174) :recursionsNeeded 3 . + 2010 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 10}] [ a r:Fact; r:gives {(10 2000) math:sum 2010}] - skolem:lemma1012 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1011 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma12 a r:Inference; r:gives { - (2011 6174) :recursionsNeeded 4 . + 2011 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 11}] [ a r:Fact; r:gives {(11 2000) math:sum 2011}] - skolem:lemma1013 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1012 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma13 a r:Inference; r:gives { - (2012 6174) :recursionsNeeded 3 . + 2012 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 12}] [ a r:Fact; r:gives {(12 2000) math:sum 2012}] - skolem:lemma1014 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1013 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma14 a r:Inference; r:gives { - (2013 6174) :recursionsNeeded 3 . + 2013 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 13}] [ a r:Fact; r:gives {(13 2000) math:sum 2013}] - skolem:lemma1015 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1014 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma15 a r:Inference; r:gives { - (2014 6174) :recursionsNeeded 7 . + 2014 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 14}] [ a r:Fact; r:gives {(14 2000) math:sum 2014}] - skolem:lemma1016 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1015 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma16 a r:Inference; r:gives { - (2015 6174) :recursionsNeeded 7 . + 2015 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 15}] [ a r:Fact; r:gives {(15 2000) math:sum 2015}] - skolem:lemma1017 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1016 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma17 a r:Inference; r:gives { - (2016 6174) :recursionsNeeded 7 . + 2016 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 16}] [ a r:Fact; r:gives {(16 2000) math:sum 2016}] - skolem:lemma1018 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1017 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma18 a r:Inference; r:gives { - (2017 6174) :recursionsNeeded 3 . + 2017 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 17}] [ a r:Fact; r:gives {(17 2000) math:sum 2017}] - skolem:lemma1019 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1018 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma19 a r:Inference; r:gives { - (2018 6174) :recursionsNeeded 3 . + 2018 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 18}] [ a r:Fact; r:gives {(18 2000) math:sum 2018}] - skolem:lemma1020 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1019 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma20 a r:Inference; r:gives { - (2019 6174) :recursionsNeeded 4 . + 2019 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 19}] [ a r:Fact; r:gives {(19 2000) math:sum 2019}] - skolem:lemma1021 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1020 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma21 a r:Inference; r:gives { - (2020 6174) :recursionsNeeded 6 . + 2020 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 20}] [ a r:Fact; r:gives {(20 2000) math:sum 2020}] - skolem:lemma1022 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1021 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma22 a r:Inference; r:gives { - (2021 6174) :recursionsNeeded 3 . + 2021 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 21}] [ a r:Fact; r:gives {(21 2000) math:sum 2021}] - skolem:lemma1023 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1022 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma23 a r:Inference; r:gives { - (2022 6174) :recursionsNeeded 4 . + 2022 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 22}] [ a r:Fact; r:gives {(22 2000) math:sum 2022}] - skolem:lemma1024 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1023 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma24 a r:Inference; r:gives { - (2023 6174) :recursionsNeeded 6 . + 2023 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 23}] [ a r:Fact; r:gives {(23 2000) math:sum 2023}] - skolem:lemma1025 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1024 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma25 a r:Inference; r:gives { - (2024 6174) :recursionsNeeded 4 . + 2024 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 24}] [ a r:Fact; r:gives {(24 2000) math:sum 2024}] - skolem:lemma1026 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1025 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma26 a r:Inference; r:gives { - (2025 6174) :recursionsNeeded 6 . + 2025 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 25}] [ a r:Fact; r:gives {(25 2000) math:sum 2025}] - skolem:lemma1027 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1026 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma27 a r:Inference; r:gives { - (2026 6174) :recursionsNeeded 6 . + 2026 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 26}] [ a r:Fact; r:gives {(26 2000) math:sum 2026}] - skolem:lemma1028 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1027 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma28 a r:Inference; r:gives { - (2027 6174) :recursionsNeeded 4 . + 2027 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 27}] [ a r:Fact; r:gives {(27 2000) math:sum 2027}] - skolem:lemma1029 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1028 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma29 a r:Inference; r:gives { - (2028 6174) :recursionsNeeded 6 . + 2028 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 28}] [ a r:Fact; r:gives {(28 2000) math:sum 2028}] - skolem:lemma1030 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1029 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma30 a r:Inference; r:gives { - (2029 6174) :recursionsNeeded 4 . + 2029 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 29}] [ a r:Fact; r:gives {(29 2000) math:sum 2029}] - skolem:lemma1031 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1030 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma31 a r:Inference; r:gives { - (2030 6174) :recursionsNeeded 5 . + 2030 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 30}] [ a r:Fact; r:gives {(30 2000) math:sum 2030}] - skolem:lemma1032 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1031 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma32 a r:Inference; r:gives { - (2031 6174) :recursionsNeeded 3 . + 2031 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 31}] [ a r:Fact; r:gives {(31 2000) math:sum 2031}] - skolem:lemma1033 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1032 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma33 a r:Inference; r:gives { - (2032 6174) :recursionsNeeded 6 . + 2032 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 32}] [ a r:Fact; r:gives {(32 2000) math:sum 2032}] - skolem:lemma1034 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1033 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma34 a r:Inference; r:gives { - (2033 6174) :recursionsNeeded 3 . + 2033 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 33}] [ a r:Fact; r:gives {(33 2000) math:sum 2033}] - skolem:lemma1035 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1034 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma35 a r:Inference; r:gives { - (2034 6174) :recursionsNeeded 7 . + 2034 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 34}] [ a r:Fact; r:gives {(34 2000) math:sum 2034}] - skolem:lemma1036 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1035 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma36 a r:Inference; r:gives { - (2035 6174) :recursionsNeeded 7 . + 2035 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 35}] [ a r:Fact; r:gives {(35 2000) math:sum 2035}] - skolem:lemma1037 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1036 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma37 a r:Inference; r:gives { - (2036 6174) :recursionsNeeded 7 . + 2036 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 36}] [ a r:Fact; r:gives {(36 2000) math:sum 2036}] - skolem:lemma1038 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1037 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma38 a r:Inference; r:gives { - (2037 6174) :recursionsNeeded 3 . + 2037 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 37}] [ a r:Fact; r:gives {(37 2000) math:sum 2037}] - skolem:lemma1039 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1038 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma39 a r:Inference; r:gives { - (2038 6174) :recursionsNeeded 3 . + 2038 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 38}] [ a r:Fact; r:gives {(38 2000) math:sum 2038}] - skolem:lemma1040 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1039 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma40 a r:Inference; r:gives { - (2039 6174) :recursionsNeeded 4 . + 2039 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 39}] [ a r:Fact; r:gives {(39 2000) math:sum 2039}] - skolem:lemma1041 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1040 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma41 a r:Inference; r:gives { - (2040 6174) :recursionsNeeded 2 . + 2040 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 40}] [ a r:Fact; r:gives {(40 2000) math:sum 2040}] - skolem:lemma1042 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1041 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma42 a r:Inference; r:gives { - (2041 6174) :recursionsNeeded 7 . + 2041 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 41}] [ a r:Fact; r:gives {(41 2000) math:sum 2041}] - skolem:lemma1043 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1042 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma43 a r:Inference; r:gives { - (2042 6174) :recursionsNeeded 4 . + 2042 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 42}] [ a r:Fact; r:gives {(42 2000) math:sum 2042}] - skolem:lemma1044 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1043 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma44 a r:Inference; r:gives { - (2043 6174) :recursionsNeeded 7 . + 2043 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 43}] [ a r:Fact; r:gives {(43 2000) math:sum 2043}] - skolem:lemma1045 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1044 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma45 a r:Inference; r:gives { - (2044 6174) :recursionsNeeded 2 . + 2044 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 44}] [ a r:Fact; r:gives {(44 2000) math:sum 2044}] - skolem:lemma1046 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1045 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma46 a r:Inference; r:gives { - (2045 6174) :recursionsNeeded 7 . + 2045 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 45}] [ a r:Fact; r:gives {(45 2000) math:sum 2045}] - skolem:lemma1047 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1046 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma47 a r:Inference; r:gives { - (2046 6174) :recursionsNeeded 1 . + 2046 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 46}] [ a r:Fact; r:gives {(46 2000) math:sum 2046}] - skolem:lemma1048 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1047 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. skolem:lemma48 a r:Inference; r:gives { - (2047 6174) :recursionsNeeded 5 . + 2047 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 47}] [ a r:Fact; r:gives {(47 2000) math:sum 2047}] - skolem:lemma1049 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1048 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma49 a r:Inference; r:gives { - (2048 6174) :recursionsNeeded 6 . + 2048 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 48}] [ a r:Fact; r:gives {(48 2000) math:sum 2048}] - skolem:lemma1050 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1049 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma50 a r:Inference; r:gives { - (2049 6174) :recursionsNeeded 3 . + 2049 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 49}] [ a r:Fact; r:gives {(49 2000) math:sum 2049}] - skolem:lemma1051 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1050 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma51 a r:Inference; r:gives { - (2050 6174) :recursionsNeeded 7 . + 2050 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 50}] [ a r:Fact; r:gives {(50 2000) math:sum 2050}] - skolem:lemma1052 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1051 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma52 a r:Inference; r:gives { - (2051 6174) :recursionsNeeded 7 . + 2051 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 51}] [ a r:Fact; r:gives {(51 2000) math:sum 2051}] - skolem:lemma1053 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1052 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma53 a r:Inference; r:gives { - (2052 6174) :recursionsNeeded 6 . + 2052 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 52}] [ a r:Fact; r:gives {(52 2000) math:sum 2052}] - skolem:lemma1054 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1053 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma54 a r:Inference; r:gives { - (2053 6174) :recursionsNeeded 7 . + 2053 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 53}] [ a r:Fact; r:gives {(53 2000) math:sum 2053}] - skolem:lemma1055 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1054 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma55 a r:Inference; r:gives { - (2054 6174) :recursionsNeeded 7 . + 2054 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 54}] [ a r:Fact; r:gives {(54 2000) math:sum 2054}] - skolem:lemma1056 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1055 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma56 a r:Inference; r:gives { - (2055 6174) :recursionsNeeded 5 . + 2055 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 55}] [ a r:Fact; r:gives {(55 2000) math:sum 2055}] - skolem:lemma1057 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1056 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma57 a r:Inference; r:gives { - (2056 6174) :recursionsNeeded 3 . + 2056 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 56}] [ a r:Fact; r:gives {(56 2000) math:sum 2056}] - skolem:lemma1058 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1057 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma58 a r:Inference; r:gives { - (2057 6174) :recursionsNeeded 6 . + 2057 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 57}] [ a r:Fact; r:gives {(57 2000) math:sum 2057}] - skolem:lemma1059 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1058 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma59 a r:Inference; r:gives { - (2058 6174) :recursionsNeeded 5 . + 2058 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 58}] [ a r:Fact; r:gives {(58 2000) math:sum 2058}] - skolem:lemma1060 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1059 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma60 a r:Inference; r:gives { - (2059 6174) :recursionsNeeded 3 . + 2059 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 59}] [ a r:Fact; r:gives {(59 2000) math:sum 2059}] - skolem:lemma1061 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1060 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma61 a r:Inference; r:gives { - (2060 6174) :recursionsNeeded 1 . + 2060 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 60}] [ a r:Fact; r:gives {(60 2000) math:sum 2060}] - skolem:lemma1062 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1061 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. skolem:lemma62 a r:Inference; r:gives { - (2061 6174) :recursionsNeeded 7 . + 2061 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 61}] [ a r:Fact; r:gives {(61 2000) math:sum 2061}] - skolem:lemma1063 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1062 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma63 a r:Inference; r:gives { - (2062 6174) :recursionsNeeded 6 . + 2062 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 62}] [ a r:Fact; r:gives {(62 2000) math:sum 2062}] - skolem:lemma1064 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1063 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma64 a r:Inference; r:gives { - (2063 6174) :recursionsNeeded 7 . + 2063 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 63}] [ a r:Fact; r:gives {(63 2000) math:sum 2063}] - skolem:lemma1065 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1064 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma65 a r:Inference; r:gives { - (2064 6174) :recursionsNeeded 1 . + 2064 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 64}] [ a r:Fact; r:gives {(64 2000) math:sum 2064}] - skolem:lemma1066 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1065 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. skolem:lemma66 a r:Inference; r:gives { - (2065 6174) :recursionsNeeded 3 . + 2065 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 65}] [ a r:Fact; r:gives {(65 2000) math:sum 2065}] - skolem:lemma1067 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1066 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma67 a r:Inference; r:gives { - (2066 6174) :recursionsNeeded 4 . + 2066 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 66}] [ a r:Fact; r:gives {(66 2000) math:sum 2066}] - skolem:lemma1068 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1067 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma68 a r:Inference; r:gives { - (2067 6174) :recursionsNeeded 3 . + 2067 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 67}] [ a r:Fact; r:gives {(67 2000) math:sum 2067}] - skolem:lemma1069 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1068 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma69 a r:Inference; r:gives { - (2068 6174) :recursionsNeeded 2 . + 2068 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 68}] [ a r:Fact; r:gives {(68 2000) math:sum 2068}] - skolem:lemma1070 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1069 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma70 a r:Inference; r:gives { - (2069 6174) :recursionsNeeded 7 . + 2069 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 69}] [ a r:Fact; r:gives {(69 2000) math:sum 2069}] - skolem:lemma1071 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1070 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma71 a r:Inference; r:gives { - (2070 6174) :recursionsNeeded 5 . + 2070 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 70}] [ a r:Fact; r:gives {(70 2000) math:sum 2070}] - skolem:lemma1072 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1071 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma72 a r:Inference; r:gives { - (2071 6174) :recursionsNeeded 3 . + 2071 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 71}] [ a r:Fact; r:gives {(71 2000) math:sum 2071}] - skolem:lemma1073 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1072 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma73 a r:Inference; r:gives { - (2072 6174) :recursionsNeeded 4 . + 2072 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 72}] [ a r:Fact; r:gives {(72 2000) math:sum 2072}] - skolem:lemma1074 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1073 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma74 a r:Inference; r:gives { - (2073 6174) :recursionsNeeded 3 . + 2073 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 73}] [ a r:Fact; r:gives {(73 2000) math:sum 2073}] - skolem:lemma1075 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1074 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma75 a r:Inference; r:gives { - (2074 6174) :recursionsNeeded 5 . + 2074 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 74}] [ a r:Fact; r:gives {(74 2000) math:sum 2074}] - skolem:lemma1076 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1075 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma76 a r:Inference; r:gives { - (2075 6174) :recursionsNeeded 6 . + 2075 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 75}] [ a r:Fact; r:gives {(75 2000) math:sum 2075}] - skolem:lemma1077 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1076 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma77 a r:Inference; r:gives { - (2076 6174) :recursionsNeeded 3 . + 2076 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 76}] [ a r:Fact; r:gives {(76 2000) math:sum 2076}] - skolem:lemma1078 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1077 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma78 a r:Inference; r:gives { - (2077 6174) :recursionsNeeded 5 . + 2077 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 77}] [ a r:Fact; r:gives {(77 2000) math:sum 2077}] - skolem:lemma1079 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1078 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma79 a r:Inference; r:gives { - (2078 6174) :recursionsNeeded 7 . + 2078 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 78}] [ a r:Fact; r:gives {(78 2000) math:sum 2078}] - skolem:lemma1080 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1079 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma80 a r:Inference; r:gives { - (2079 6174) :recursionsNeeded 7 . + 2079 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 79}] [ a r:Fact; r:gives {(79 2000) math:sum 2079}] - skolem:lemma1081 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1080 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma81 a r:Inference; r:gives { - (2080 6174) :recursionsNeeded 6 . + 2080 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 80}] [ a r:Fact; r:gives {(80 2000) math:sum 2080}] - skolem:lemma1082 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1081 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma82 a r:Inference; r:gives { - (2081 6174) :recursionsNeeded 3 . + 2081 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 81}] [ a r:Fact; r:gives {(81 2000) math:sum 2081}] - skolem:lemma1083 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1082 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma83 a r:Inference; r:gives { - (2082 6174) :recursionsNeeded 6 . + 2082 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 82}] [ a r:Fact; r:gives {(82 2000) math:sum 2082}] - skolem:lemma1084 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1083 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma84 a r:Inference; r:gives { - (2083 6174) :recursionsNeeded 3 . + 2083 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 83}] [ a r:Fact; r:gives {(83 2000) math:sum 2083}] - skolem:lemma1085 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1084 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma85 a r:Inference; r:gives { - (2084 6174) :recursionsNeeded 6 . + 2084 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 84}] [ a r:Fact; r:gives {(84 2000) math:sum 2084}] - skolem:lemma1086 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1085 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma86 a r:Inference; r:gives { - (2085 6174) :recursionsNeeded 5 . + 2085 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 85}] [ a r:Fact; r:gives {(85 2000) math:sum 2085}] - skolem:lemma1087 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1086 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma87 a r:Inference; r:gives { - (2086 6174) :recursionsNeeded 2 . + 2086 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 86}] [ a r:Fact; r:gives {(86 2000) math:sum 2086}] - skolem:lemma1088 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1087 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma88 a r:Inference; r:gives { - (2087 6174) :recursionsNeeded 7 . + 2087 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 87}] [ a r:Fact; r:gives {(87 2000) math:sum 2087}] - skolem:lemma1089 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1088 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma89 a r:Inference; r:gives { - (2088 6174) :recursionsNeeded 2 . + 2088 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 88}] [ a r:Fact; r:gives {(88 2000) math:sum 2088}] - skolem:lemma1090 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1089 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma90 a r:Inference; r:gives { - (2089 6174) :recursionsNeeded 7 . + 2089 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 89}] [ a r:Fact; r:gives {(89 2000) math:sum 2089}] - skolem:lemma1091 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1090 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma91 a r:Inference; r:gives { - (2090 6174) :recursionsNeeded 3 . + 2090 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 90}] [ a r:Fact; r:gives {(90 2000) math:sum 2090}] - skolem:lemma1092 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1091 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma92 a r:Inference; r:gives { - (2091 6174) :recursionsNeeded 4 . + 2091 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 91}] [ a r:Fact; r:gives {(91 2000) math:sum 2091}] - skolem:lemma1093 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1092 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma93 a r:Inference; r:gives { - (2092 6174) :recursionsNeeded 4 . + 2092 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 92}] [ a r:Fact; r:gives {(92 2000) math:sum 2092}] - skolem:lemma1094 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1093 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma94 a r:Inference; r:gives { - (2093 6174) :recursionsNeeded 4 . + 2093 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 93}] [ a r:Fact; r:gives {(93 2000) math:sum 2093}] - skolem:lemma1095 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1094 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma95 a r:Inference; r:gives { - (2094 6174) :recursionsNeeded 3 . + 2094 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 94}] [ a r:Fact; r:gives {(94 2000) math:sum 2094}] - skolem:lemma1096 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1095 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma96 a r:Inference; r:gives { - (2095 6174) :recursionsNeeded 3 . + 2095 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 95}] [ a r:Fact; r:gives {(95 2000) math:sum 2095}] - skolem:lemma1097 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1096 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma97 a r:Inference; r:gives { - (2096 6174) :recursionsNeeded 7 . + 2096 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 96}] [ a r:Fact; r:gives {(96 2000) math:sum 2096}] - skolem:lemma1098 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1097 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma98 a r:Inference; r:gives { - (2097 6174) :recursionsNeeded 7 . + 2097 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 97}] [ a r:Fact; r:gives {(97 2000) math:sum 2097}] - skolem:lemma1099 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1098 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma99 a r:Inference; r:gives { - (2098 6174) :recursionsNeeded 7 . + 2098 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 98}] [ a r:Fact; r:gives {(98 2000) math:sum 2098}] - skolem:lemma1100 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1099 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma100 a r:Inference; r:gives { - (2099 6174) :recursionsNeeded 3 . + 2099 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 99}] [ a r:Fact; r:gives {(99 2000) math:sum 2099}] - skolem:lemma1101 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1100 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma101 a r:Inference; r:gives { - (2100 6174) :recursionsNeeded 3 . + 2100 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 100}] [ a r:Fact; r:gives {(100 2000) math:sum 2100}] - skolem:lemma1102 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1101 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma102 a r:Inference; r:gives { - (2101 6174) :recursionsNeeded 4 . + 2101 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 101}] [ a r:Fact; r:gives {(101 2000) math:sum 2101}] - skolem:lemma1103 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1102 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma103 a r:Inference; r:gives { - (2102 6174) :recursionsNeeded 3 . + 2102 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 102}] [ a r:Fact; r:gives {(102 2000) math:sum 2102}] - skolem:lemma1104 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1103 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma104 a r:Inference; r:gives { - (2103 6174) :recursionsNeeded 3 . + 2103 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 103}] [ a r:Fact; r:gives {(103 2000) math:sum 2103}] - skolem:lemma1105 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1104 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma105 a r:Inference; r:gives { - (2104 6174) :recursionsNeeded 7 . + 2104 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 104}] [ a r:Fact; r:gives {(104 2000) math:sum 2104}] - skolem:lemma1106 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1105 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma106 a r:Inference; r:gives { - (2105 6174) :recursionsNeeded 7 . + 2105 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 105}] [ a r:Fact; r:gives {(105 2000) math:sum 2105}] - skolem:lemma1107 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1106 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma107 a r:Inference; r:gives { - (2106 6174) :recursionsNeeded 7 . + 2106 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 106}] [ a r:Fact; r:gives {(106 2000) math:sum 2106}] - skolem:lemma1108 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1107 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma108 a r:Inference; r:gives { - (2107 6174) :recursionsNeeded 3 . + 2107 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 107}] [ a r:Fact; r:gives {(107 2000) math:sum 2107}] - skolem:lemma1109 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1108 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma109 a r:Inference; r:gives { - (2108 6174) :recursionsNeeded 3 . + 2108 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 108}] [ a r:Fact; r:gives {(108 2000) math:sum 2108}] - skolem:lemma1110 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1109 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma110 a r:Inference; r:gives { - (2109 6174) :recursionsNeeded 4 . + 2109 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 109}] [ a r:Fact; r:gives {(109 2000) math:sum 2109}] - skolem:lemma1111 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1110 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma111 a r:Inference; r:gives { - (2110 6174) :recursionsNeeded 4 . + 2110 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 110}] [ a r:Fact; r:gives {(110 2000) math:sum 2110}] - skolem:lemma1112 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1111 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma112 a r:Inference; r:gives { - (2111 6174) :recursionsNeeded 5 . + 2111 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 111}] [ a r:Fact; r:gives {(111 2000) math:sum 2111}] - skolem:lemma1113 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1112 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma113 a r:Inference; r:gives { - (2112 6174) :recursionsNeeded 4 . + 2112 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 112}] [ a r:Fact; r:gives {(112 2000) math:sum 2112}] - skolem:lemma1114 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1113 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma114 a r:Inference; r:gives { - (2113 6174) :recursionsNeeded 3 . + 2113 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 113}] [ a r:Fact; r:gives {(113 2000) math:sum 2113}] - skolem:lemma1115 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1114 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma115 a r:Inference; r:gives { - (2114 6174) :recursionsNeeded 3 . + 2114 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 114}] [ a r:Fact; r:gives {(114 2000) math:sum 2114}] - skolem:lemma1116 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1115 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma116 a r:Inference; r:gives { - (2115 6174) :recursionsNeeded 7 . + 2115 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 115}] [ a r:Fact; r:gives {(115 2000) math:sum 2115}] - skolem:lemma1117 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1116 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma117 a r:Inference; r:gives { - (2116 6174) :recursionsNeeded 7 . + 2116 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 116}] [ a r:Fact; r:gives {(116 2000) math:sum 2116}] - skolem:lemma1118 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1117 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma118 a r:Inference; r:gives { - (2117 6174) :recursionsNeeded 7 . + 2117 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 117}] [ a r:Fact; r:gives {(117 2000) math:sum 2117}] - skolem:lemma1119 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1118 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma119 a r:Inference; r:gives { - (2118 6174) :recursionsNeeded 3 . + 2118 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 118}] [ a r:Fact; r:gives {(118 2000) math:sum 2118}] - skolem:lemma1120 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1119 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma120 a r:Inference; r:gives { - (2119 6174) :recursionsNeeded 3 . + 2119 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 119}] [ a r:Fact; r:gives {(119 2000) math:sum 2119}] - skolem:lemma1121 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1120 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma121 a r:Inference; r:gives { - (2120 6174) :recursionsNeeded 3 . + 2120 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 120}] [ a r:Fact; r:gives {(120 2000) math:sum 2120}] - skolem:lemma1122 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1121 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma122 a r:Inference; r:gives { - (2121 6174) :recursionsNeeded 4 . + 2121 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 121}] [ a r:Fact; r:gives {(121 2000) math:sum 2121}] - skolem:lemma1123 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1122 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma123 a r:Inference; r:gives { - (2122 6174) :recursionsNeeded 5 . + 2122 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 122}] [ a r:Fact; r:gives {(122 2000) math:sum 2122}] - skolem:lemma1124 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1123 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma124 a r:Inference; r:gives { - (2123 6174) :recursionsNeeded 4 . + 2123 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 123}] [ a r:Fact; r:gives {(123 2000) math:sum 2123}] - skolem:lemma1125 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1124 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma125 a r:Inference; r:gives { - (2124 6174) :recursionsNeeded 6 . + 2124 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 124}] [ a r:Fact; r:gives {(124 2000) math:sum 2124}] - skolem:lemma1126 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1125 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma126 a r:Inference; r:gives { - (2125 6174) :recursionsNeeded 4 . + 2125 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 125}] [ a r:Fact; r:gives {(125 2000) math:sum 2125}] - skolem:lemma1127 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1126 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma127 a r:Inference; r:gives { - (2126 6174) :recursionsNeeded 6 . + 2126 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 126}] [ a r:Fact; r:gives {(126 2000) math:sum 2126}] - skolem:lemma1128 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1127 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma128 a r:Inference; r:gives { - (2127 6174) :recursionsNeeded 6 . + 2127 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 127}] [ a r:Fact; r:gives {(127 2000) math:sum 2127}] - skolem:lemma1129 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1128 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma129 a r:Inference; r:gives { - (2128 6174) :recursionsNeeded 4 . + 2128 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 128}] [ a r:Fact; r:gives {(128 2000) math:sum 2128}] - skolem:lemma1130 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1129 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma130 a r:Inference; r:gives { - (2129 6174) :recursionsNeeded 6 . + 2129 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 129}] [ a r:Fact; r:gives {(129 2000) math:sum 2129}] - skolem:lemma1131 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1130 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma131 a r:Inference; r:gives { - (2130 6174) :recursionsNeeded 3 . + 2130 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 130}] [ a r:Fact; r:gives {(130 2000) math:sum 2130}] - skolem:lemma1132 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1131 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma132 a r:Inference; r:gives { - (2131 6174) :recursionsNeeded 3 . + 2131 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 131}] [ a r:Fact; r:gives {(131 2000) math:sum 2131}] - skolem:lemma1133 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1132 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma133 a r:Inference; r:gives { - (2132 6174) :recursionsNeeded 4 . + 2132 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 132}] [ a r:Fact; r:gives {(132 2000) math:sum 2132}] - skolem:lemma1134 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1133 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma134 a r:Inference; r:gives { - (2133 6174) :recursionsNeeded 3 . + 2133 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 133}] [ a r:Fact; r:gives {(133 2000) math:sum 2133}] - skolem:lemma1135 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1134 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma135 a r:Inference; r:gives { - (2134 6174) :recursionsNeeded 3 . + 2134 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 134}] [ a r:Fact; r:gives {(134 2000) math:sum 2134}] - skolem:lemma1136 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1135 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma136 a r:Inference; r:gives { - (2135 6174) :recursionsNeeded 7 . + 2135 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 135}] [ a r:Fact; r:gives {(135 2000) math:sum 2135}] - skolem:lemma1137 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1136 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma137 a r:Inference; r:gives { - (2136 6174) :recursionsNeeded 7 . + 2136 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 136}] [ a r:Fact; r:gives {(136 2000) math:sum 2136}] - skolem:lemma1138 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1137 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma138 a r:Inference; r:gives { - (2137 6174) :recursionsNeeded 7 . + 2137 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 137}] [ a r:Fact; r:gives {(137 2000) math:sum 2137}] - skolem:lemma1139 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1138 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma139 a r:Inference; r:gives { - (2138 6174) :recursionsNeeded 3 . + 2138 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 138}] [ a r:Fact; r:gives {(138 2000) math:sum 2138}] - skolem:lemma1140 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1139 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma140 a r:Inference; r:gives { - (2139 6174) :recursionsNeeded 3 . + 2139 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 139}] [ a r:Fact; r:gives {(139 2000) math:sum 2139}] - skolem:lemma1141 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1140 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma141 a r:Inference; r:gives { - (2140 6174) :recursionsNeeded 7 . + 2140 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 140}] [ a r:Fact; r:gives {(140 2000) math:sum 2140}] - skolem:lemma1142 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1141 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma142 a r:Inference; r:gives { - (2141 6174) :recursionsNeeded 3 . + 2141 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 141}] [ a r:Fact; r:gives {(141 2000) math:sum 2141}] - skolem:lemma1143 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1142 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma143 a r:Inference; r:gives { - (2142 6174) :recursionsNeeded 6 . + 2142 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 142}] [ a r:Fact; r:gives {(142 2000) math:sum 2142}] - skolem:lemma1144 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1143 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma144 a r:Inference; r:gives { - (2143 6174) :recursionsNeeded 3 . + 2143 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 143}] [ a r:Fact; r:gives {(143 2000) math:sum 2143}] - skolem:lemma1145 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1144 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma145 a r:Inference; r:gives { - (2144 6174) :recursionsNeeded 5 . + 2144 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 144}] [ a r:Fact; r:gives {(144 2000) math:sum 2144}] - skolem:lemma1146 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1145 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma146 a r:Inference; r:gives { - (2145 6174) :recursionsNeeded 2 . + 2145 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 145}] [ a r:Fact; r:gives {(145 2000) math:sum 2145}] - skolem:lemma1147 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1146 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma147 a r:Inference; r:gives { - (2146 6174) :recursionsNeeded 7 . + 2146 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 146}] [ a r:Fact; r:gives {(146 2000) math:sum 2146}] - skolem:lemma1148 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1147 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma148 a r:Inference; r:gives { - (2147 6174) :recursionsNeeded 1 . + 2147 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 147}] [ a r:Fact; r:gives {(147 2000) math:sum 2147}] - skolem:lemma1149 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1148 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. skolem:lemma149 a r:Inference; r:gives { - (2148 6174) :recursionsNeeded 5 . + 2148 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 148}] [ a r:Fact; r:gives {(148 2000) math:sum 2148}] - skolem:lemma1150 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1149 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma150 a r:Inference; r:gives { - (2149 6174) :recursionsNeeded 6 . + 2149 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 149}] [ a r:Fact; r:gives {(149 2000) math:sum 2149}] - skolem:lemma1151 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1150 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma151 a r:Inference; r:gives { - (2150 6174) :recursionsNeeded 7 . + 2150 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 150}] [ a r:Fact; r:gives {(150 2000) math:sum 2150}] - skolem:lemma1152 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1151 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma152 a r:Inference; r:gives { - (2151 6174) :recursionsNeeded 7 . + 2151 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 151}] [ a r:Fact; r:gives {(151 2000) math:sum 2151}] - skolem:lemma1153 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1152 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma153 a r:Inference; r:gives { - (2152 6174) :recursionsNeeded 4 . + 2152 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 152}] [ a r:Fact; r:gives {(152 2000) math:sum 2152}] - skolem:lemma1154 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1153 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma154 a r:Inference; r:gives { - (2153 6174) :recursionsNeeded 7 . + 2153 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 153}] [ a r:Fact; r:gives {(153 2000) math:sum 2153}] - skolem:lemma1155 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1154 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma155 a r:Inference; r:gives { - (2154 6174) :recursionsNeeded 2 . + 2154 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 154}] [ a r:Fact; r:gives {(154 2000) math:sum 2154}] - skolem:lemma1156 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1155 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma156 a r:Inference; r:gives { - (2155 6174) :recursionsNeeded 3 . + 2155 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 155}] [ a r:Fact; r:gives {(155 2000) math:sum 2155}] - skolem:lemma1157 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1156 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma157 a r:Inference; r:gives { - (2156 6174) :recursionsNeeded 5 . + 2156 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 156}] [ a r:Fact; r:gives {(156 2000) math:sum 2156}] - skolem:lemma1158 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1157 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma158 a r:Inference; r:gives { - (2157 6174) :recursionsNeeded 3 . + 2157 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 157}] [ a r:Fact; r:gives {(157 2000) math:sum 2157}] - skolem:lemma1159 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1158 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma159 a r:Inference; r:gives { - (2158 6174) :recursionsNeeded 6 . + 2158 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 158}] [ a r:Fact; r:gives {(158 2000) math:sum 2158}] - skolem:lemma1160 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1159 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma160 a r:Inference; r:gives { - (2159 6174) :recursionsNeeded 5 . + 2159 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 159}] [ a r:Fact; r:gives {(159 2000) math:sum 2159}] - skolem:lemma1161 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1160 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma161 a r:Inference; r:gives { - (2160 6174) :recursionsNeeded 7 . + 2160 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 160}] [ a r:Fact; r:gives {(160 2000) math:sum 2160}] - skolem:lemma1162 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1161 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma162 a r:Inference; r:gives { - (2161 6174) :recursionsNeeded 7 . + 2161 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 161}] [ a r:Fact; r:gives {(161 2000) math:sum 2161}] - skolem:lemma1163 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1162 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma163 a r:Inference; r:gives { - (2162 6174) :recursionsNeeded 6 . + 2162 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 162}] [ a r:Fact; r:gives {(162 2000) math:sum 2162}] - skolem:lemma1164 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1163 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma164 a r:Inference; r:gives { - (2163 6174) :recursionsNeeded 7 . + 2163 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 163}] [ a r:Fact; r:gives {(163 2000) math:sum 2163}] - skolem:lemma1165 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1164 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma165 a r:Inference; r:gives { - (2164 6174) :recursionsNeeded 7 . + 2164 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 164}] [ a r:Fact; r:gives {(164 2000) math:sum 2164}] - skolem:lemma1166 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1165 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma166 a r:Inference; r:gives { - (2165 6174) :recursionsNeeded 5 . + 2165 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 165}] [ a r:Fact; r:gives {(165 2000) math:sum 2165}] - skolem:lemma1167 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1166 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma167 a r:Inference; r:gives { - (2166 6174) :recursionsNeeded 5 . + 2166 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 166}] [ a r:Fact; r:gives {(166 2000) math:sum 2166}] - skolem:lemma1168 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1167 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma168 a r:Inference; r:gives { - (2167 6174) :recursionsNeeded 4 . + 2167 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 167}] [ a r:Fact; r:gives {(167 2000) math:sum 2167}] - skolem:lemma1169 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1168 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma169 a r:Inference; r:gives { - (2168 6174) :recursionsNeeded 3 . + 2168 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 168}] [ a r:Fact; r:gives {(168 2000) math:sum 2168}] - skolem:lemma1170 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1169 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma170 a r:Inference; r:gives { - (2169 6174) :recursionsNeeded 2 . + 2169 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 169}] [ a r:Fact; r:gives {(169 2000) math:sum 2169}] - skolem:lemma1171 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1170 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma171 a r:Inference; r:gives { - (2170 6174) :recursionsNeeded 3 . + 2170 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 170}] [ a r:Fact; r:gives {(170 2000) math:sum 2170}] - skolem:lemma1172 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1171 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma172 a r:Inference; r:gives { - (2171 6174) :recursionsNeeded 7 . + 2171 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 171}] [ a r:Fact; r:gives {(171 2000) math:sum 2171}] - skolem:lemma1173 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1172 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma173 a r:Inference; r:gives { - (2172 6174) :recursionsNeeded 6 . + 2172 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 172}] [ a r:Fact; r:gives {(172 2000) math:sum 2172}] - skolem:lemma1174 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1173 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma174 a r:Inference; r:gives { - (2173 6174) :recursionsNeeded 7 . + 2173 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 173}] [ a r:Fact; r:gives {(173 2000) math:sum 2173}] - skolem:lemma1175 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1174 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma175 a r:Inference; r:gives { - (2174 6174) :recursionsNeeded 1 . + 2174 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 174}] [ a r:Fact; r:gives {(174 2000) math:sum 2174}] - skolem:lemma1176 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1175 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. skolem:lemma176 a r:Inference; r:gives { - (2175 6174) :recursionsNeeded 3 . + 2175 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 175}] [ a r:Fact; r:gives {(175 2000) math:sum 2175}] - skolem:lemma1177 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1176 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma177 a r:Inference; r:gives { - (2176 6174) :recursionsNeeded 4 . + 2176 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 176}] [ a r:Fact; r:gives {(176 2000) math:sum 2176}] - skolem:lemma1178 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1177 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma178 a r:Inference; r:gives { - (2177 6174) :recursionsNeeded 5 . + 2177 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 177}] [ a r:Fact; r:gives {(177 2000) math:sum 2177}] - skolem:lemma1179 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1178 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma179 a r:Inference; r:gives { - (2178 6174) :recursionsNeeded 5 . + 2178 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 178}] [ a r:Fact; r:gives {(178 2000) math:sum 2178}] - skolem:lemma1180 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1179 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma180 a r:Inference; r:gives { - (2179 6174) :recursionsNeeded 7 . + 2179 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 179}] [ a r:Fact; r:gives {(179 2000) math:sum 2179}] - skolem:lemma1181 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1180 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma181 a r:Inference; r:gives { - (2180 6174) :recursionsNeeded 3 . + 2180 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 180}] [ a r:Fact; r:gives {(180 2000) math:sum 2180}] - skolem:lemma1182 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1181 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma182 a r:Inference; r:gives { - (2181 6174) :recursionsNeeded 3 . + 2181 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 181}] [ a r:Fact; r:gives {(181 2000) math:sum 2181}] - skolem:lemma1183 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1182 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma183 a r:Inference; r:gives { - (2182 6174) :recursionsNeeded 4 . + 2182 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 182}] [ a r:Fact; r:gives {(182 2000) math:sum 2182}] - skolem:lemma1184 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1183 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma184 a r:Inference; r:gives { - (2183 6174) :recursionsNeeded 3 . + 2183 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 183}] [ a r:Fact; r:gives {(183 2000) math:sum 2183}] - skolem:lemma1185 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1184 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma185 a r:Inference; r:gives { - (2184 6174) :recursionsNeeded 5 . + 2184 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 184}] [ a r:Fact; r:gives {(184 2000) math:sum 2184}] - skolem:lemma1186 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1185 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma186 a r:Inference; r:gives { - (2185 6174) :recursionsNeeded 6 . + 2185 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 185}] [ a r:Fact; r:gives {(185 2000) math:sum 2185}] - skolem:lemma1187 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1186 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma187 a r:Inference; r:gives { - (2186 6174) :recursionsNeeded 3 . + 2186 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 186}] [ a r:Fact; r:gives {(186 2000) math:sum 2186}] - skolem:lemma1188 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1187 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma188 a r:Inference; r:gives { - (2187 6174) :recursionsNeeded 5 . + 2187 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 187}] [ a r:Fact; r:gives {(187 2000) math:sum 2187}] - skolem:lemma1189 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1188 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma189 a r:Inference; r:gives { - (2188 6174) :recursionsNeeded 3 . + 2188 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 188}] [ a r:Fact; r:gives {(188 2000) math:sum 2188}] - skolem:lemma1190 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1189 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma190 a r:Inference; r:gives { - (2189 6174) :recursionsNeeded 2 . + 2189 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 189}] [ a r:Fact; r:gives {(189 2000) math:sum 2189}] - skolem:lemma1191 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1190 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma191 a r:Inference; r:gives { - (2190 6174) :recursionsNeeded 4 . + 2190 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 190}] [ a r:Fact; r:gives {(190 2000) math:sum 2190}] - skolem:lemma1192 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1191 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma192 a r:Inference; r:gives { - (2191 6174) :recursionsNeeded 3 . + 2191 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 191}] [ a r:Fact; r:gives {(191 2000) math:sum 2191}] - skolem:lemma1193 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1192 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma193 a r:Inference; r:gives { - (2192 6174) :recursionsNeeded 6 . + 2192 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 192}] [ a r:Fact; r:gives {(192 2000) math:sum 2192}] - skolem:lemma1194 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1193 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma194 a r:Inference; r:gives { - (2193 6174) :recursionsNeeded 3 . + 2193 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 193}] [ a r:Fact; r:gives {(193 2000) math:sum 2193}] - skolem:lemma1195 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1194 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma195 a r:Inference; r:gives { - (2194 6174) :recursionsNeeded 6 . + 2194 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 194}] [ a r:Fact; r:gives {(194 2000) math:sum 2194}] - skolem:lemma1196 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1195 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma196 a r:Inference; r:gives { - (2195 6174) :recursionsNeeded 5 . + 2195 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 195}] [ a r:Fact; r:gives {(195 2000) math:sum 2195}] - skolem:lemma1197 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1196 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma197 a r:Inference; r:gives { - (2196 6174) :recursionsNeeded 2 . + 2196 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 196}] [ a r:Fact; r:gives {(196 2000) math:sum 2196}] - skolem:lemma1198 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1197 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma198 a r:Inference; r:gives { - (2197 6174) :recursionsNeeded 7 . + 2197 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 197}] [ a r:Fact; r:gives {(197 2000) math:sum 2197}] - skolem:lemma1199 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1198 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. skolem:lemma199 a r:Inference; r:gives { - (2198 6174) :recursionsNeeded 2 . + 2198 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 198}] [ a r:Fact; r:gives {(198 2000) math:sum 2198}] - skolem:lemma1200 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1199 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. skolem:lemma200 a r:Inference; r:gives { - (2199 6174) :recursionsNeeded 5 . + 2199 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 199}] [ a r:Fact; r:gives {(199 2000) math:sum 2199}] - skolem:lemma1201 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1200 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma201 a r:Inference; r:gives { - (2200 6174) :recursionsNeeded 6 . + 2200 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 200}] [ a r:Fact; r:gives {(200 2000) math:sum 2200}] - skolem:lemma1202 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1201 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma202 a r:Inference; r:gives { - (2201 6174) :recursionsNeeded 3 . + 2201 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 201}] [ a r:Fact; r:gives {(201 2000) math:sum 2201}] - skolem:lemma1203 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1202 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma203 a r:Inference; r:gives { - (2202 6174) :recursionsNeeded 4 . + 2202 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 202}] [ a r:Fact; r:gives {(202 2000) math:sum 2202}] - skolem:lemma1204 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1203 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma204 a r:Inference; r:gives { - (2203 6174) :recursionsNeeded 6 . + 2203 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 203}] [ a r:Fact; r:gives {(203 2000) math:sum 2203}] - skolem:lemma1205 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1204 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma205 a r:Inference; r:gives { - (2204 6174) :recursionsNeeded 4 . + 2204 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 204}] [ a r:Fact; r:gives {(204 2000) math:sum 2204}] - skolem:lemma1206 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1205 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma206 a r:Inference; r:gives { - (2205 6174) :recursionsNeeded 6 . + 2205 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 205}] [ a r:Fact; r:gives {(205 2000) math:sum 2205}] - skolem:lemma1207 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1206 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma207 a r:Inference; r:gives { - (2206 6174) :recursionsNeeded 6 . + 2206 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 206}] [ a r:Fact; r:gives {(206 2000) math:sum 2206}] - skolem:lemma1208 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1207 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma208 a r:Inference; r:gives { - (2207 6174) :recursionsNeeded 4 . + 2207 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 207}] [ a r:Fact; r:gives {(207 2000) math:sum 2207}] - skolem:lemma1209 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1208 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma209 a r:Inference; r:gives { - (2208 6174) :recursionsNeeded 6 . + 2208 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 208}] [ a r:Fact; r:gives {(208 2000) math:sum 2208}] - skolem:lemma1210 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1209 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma210 a r:Inference; r:gives { - (2209 6174) :recursionsNeeded 4 . + 2209 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 209}] [ a r:Fact; r:gives {(209 2000) math:sum 2209}] - skolem:lemma1211 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1210 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma211 a r:Inference; r:gives { - (2210 6174) :recursionsNeeded 3 . + 2210 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 210}] [ a r:Fact; r:gives {(210 2000) math:sum 2210}] - skolem:lemma1212 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1211 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. skolem:lemma212 a r:Inference; r:gives { - (2211 6174) :recursionsNeeded 4 . + 2211 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 211}] [ a r:Fact; r:gives {(211 2000) math:sum 2211}] - skolem:lemma1213 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1212 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma213 a r:Inference; r:gives { - (2212 6174) :recursionsNeeded 5 . + 2212 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 212}] [ a r:Fact; r:gives {(212 2000) math:sum 2212}] - skolem:lemma1214 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1213 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma214 a r:Inference; r:gives { - (2213 6174) :recursionsNeeded 4 . + 2213 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 213}] [ a r:Fact; r:gives {(213 2000) math:sum 2213}] - skolem:lemma1215 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1214 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma215 a r:Inference; r:gives { - (2214 6174) :recursionsNeeded 6 . + 2214 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 214}] [ a r:Fact; r:gives {(214 2000) math:sum 2214}] - skolem:lemma1216 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1215 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma216 a r:Inference; r:gives { - (2215 6174) :recursionsNeeded 4 . + 2215 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 215}] [ a r:Fact; r:gives {(215 2000) math:sum 2215}] - skolem:lemma1217 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1216 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma217 a r:Inference; r:gives { - (2216 6174) :recursionsNeeded 6 . + 2216 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 216}] [ a r:Fact; r:gives {(216 2000) math:sum 2216}] - skolem:lemma1218 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1217 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma218 a r:Inference; r:gives { - (2217 6174) :recursionsNeeded 6 . + 2217 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 217}] [ a r:Fact; r:gives {(217 2000) math:sum 2217}] - skolem:lemma1219 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1218 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma219 a r:Inference; r:gives { - (2218 6174) :recursionsNeeded 4 . + 2218 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 218}] [ a r:Fact; r:gives {(218 2000) math:sum 2218}] - skolem:lemma1220 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1219 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma220 a r:Inference; r:gives { - (2219 6174) :recursionsNeeded 6 . + 2219 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 219}] [ a r:Fact; r:gives {(219 2000) math:sum 2219}] - skolem:lemma1221 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1220 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. skolem:lemma221 a r:Inference; r:gives { - (2220 6174) :recursionsNeeded 4 . + 2220 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 220}] [ a r:Fact; r:gives {(220 2000) math:sum 2220}] - skolem:lemma1222 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1221 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. skolem:lemma222 a r:Inference; r:gives { - (2221 6174) :recursionsNeeded 5 . + 2221 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 221}] [ a r:Fact; r:gives {(221 2000) math:sum 2221}] - skolem:lemma1223 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1222 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. skolem:lemma223 a r:Inference; r:gives { - (2222 0) :recursionsNeeded 1 . - }; - r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 222}] - [ a r:Fact; r:gives {(222 2000) math:sum 2222}] - skolem:lemma1224 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2222]; - 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 1]; - r:rule skolem:lemma1002. - -skolem:lemma224 a r:Inference; - r:gives { - (2223 6174) :recursionsNeeded 5 . + 2223 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 223}] [ a r:Fact; r:gives {(223 2000) math:sum 2223}] - skolem:lemma1225 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1223 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma225 a r:Inference; +skolem:lemma224 a r:Inference; r:gives { - (2224 6174) :recursionsNeeded 4 . + 2224 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 224}] [ a r:Fact; r:gives {(224 2000) math:sum 2224}] - skolem:lemma1226 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1224 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma226 a r:Inference; +skolem:lemma225 a r:Inference; r:gives { - (2225 6174) :recursionsNeeded 6 . + 2225 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 225}] [ a r:Fact; r:gives {(225 2000) math:sum 2225}] - skolem:lemma1227 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1225 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma227 a r:Inference; +skolem:lemma226 a r:Inference; r:gives { - (2226 6174) :recursionsNeeded 4 . + 2226 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 226}] [ a r:Fact; r:gives {(226 2000) math:sum 2226}] - skolem:lemma1228 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1226 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma228 a r:Inference; +skolem:lemma227 a r:Inference; r:gives { - (2227 6174) :recursionsNeeded 6 . + 2227 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 227}] [ a r:Fact; r:gives {(227 2000) math:sum 2227}] - skolem:lemma1229 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1227 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma229 a r:Inference; +skolem:lemma228 a r:Inference; r:gives { - (2228 6174) :recursionsNeeded 6 . + 2228 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 228}] [ a r:Fact; r:gives {(228 2000) math:sum 2228}] - skolem:lemma1230 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1228 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma230 a r:Inference; +skolem:lemma229 a r:Inference; r:gives { - (2229 6174) :recursionsNeeded 4 . + 2229 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 229}] [ a r:Fact; r:gives {(229 2000) math:sum 2229}] - skolem:lemma1231 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1229 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma231 a r:Inference; +skolem:lemma230 a r:Inference; r:gives { - (2230 6174) :recursionsNeeded 6 . + 2230 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 230}] [ a r:Fact; r:gives {(230 2000) math:sum 2230}] - skolem:lemma1232 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1230 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma232 a r:Inference; +skolem:lemma231 a r:Inference; r:gives { - (2231 6174) :recursionsNeeded 4 . + 2231 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 231}] [ a r:Fact; r:gives {(231 2000) math:sum 2231}] - skolem:lemma1233 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1231 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma233 a r:Inference; +skolem:lemma232 a r:Inference; r:gives { - (2232 6174) :recursionsNeeded 5 . + 2232 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 232}] [ a r:Fact; r:gives {(232 2000) math:sum 2232}] - skolem:lemma1234 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1232 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma234 a r:Inference; +skolem:lemma233 a r:Inference; r:gives { - (2233 6174) :recursionsNeeded 4 . + 2233 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 233}] [ a r:Fact; r:gives {(233 2000) math:sum 2233}] - skolem:lemma1235 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1233 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma235 a r:Inference; +skolem:lemma234 a r:Inference; r:gives { - (2234 6174) :recursionsNeeded 3 . + 2234 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 234}] [ a r:Fact; r:gives {(234 2000) math:sum 2234}] - skolem:lemma1236 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1234 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma236 a r:Inference; +skolem:lemma235 a r:Inference; r:gives { - (2235 6174) :recursionsNeeded 3 . + 2235 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 235}] [ a r:Fact; r:gives {(235 2000) math:sum 2235}] - skolem:lemma1237 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1235 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma237 a r:Inference; +skolem:lemma236 a r:Inference; r:gives { - (2236 6174) :recursionsNeeded 7 . + 2236 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 236}] [ a r:Fact; r:gives {(236 2000) math:sum 2236}] - skolem:lemma1238 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1236 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma238 a r:Inference; +skolem:lemma237 a r:Inference; r:gives { - (2237 6174) :recursionsNeeded 7 . + 2237 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 237}] [ a r:Fact; r:gives {(237 2000) math:sum 2237}] - skolem:lemma1239 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1237 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma239 a r:Inference; +skolem:lemma238 a r:Inference; r:gives { - (2238 6174) :recursionsNeeded 7 . + 2238 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 238}] [ a r:Fact; r:gives {(238 2000) math:sum 2238}] - skolem:lemma1240 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1238 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma240 a r:Inference; +skolem:lemma239 a r:Inference; r:gives { - (2239 6174) :recursionsNeeded 3 . + 2239 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 239}] [ a r:Fact; r:gives {(239 2000) math:sum 2239}] - skolem:lemma1241 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1239 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma241 a r:Inference; +skolem:lemma240 a r:Inference; r:gives { - (2240 6174) :recursionsNeeded 4 . + 2240 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 240}] [ a r:Fact; r:gives {(240 2000) math:sum 2240}] - skolem:lemma1242 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1240 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma242 a r:Inference; +skolem:lemma241 a r:Inference; r:gives { - (2241 6174) :recursionsNeeded 6 . + 2241 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 241}] [ a r:Fact; r:gives {(241 2000) math:sum 2241}] - skolem:lemma1243 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1241 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma243 a r:Inference; +skolem:lemma242 a r:Inference; r:gives { - (2242 6174) :recursionsNeeded 4 . + 2242 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 242}] [ a r:Fact; r:gives {(242 2000) math:sum 2242}] - skolem:lemma1244 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1242 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma244 a r:Inference; +skolem:lemma243 a r:Inference; r:gives { - (2243 6174) :recursionsNeeded 3 . + 2243 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 243}] [ a r:Fact; r:gives {(243 2000) math:sum 2243}] - skolem:lemma1245 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1243 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma245 a r:Inference; +skolem:lemma244 a r:Inference; r:gives { - (2244 6174) :recursionsNeeded 6 . + 2244 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 244}] [ a r:Fact; r:gives {(244 2000) math:sum 2244}] - skolem:lemma1246 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1244 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma246 a r:Inference; +skolem:lemma245 a r:Inference; r:gives { - (2245 6174) :recursionsNeeded 5 . + 2245 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 245}] [ a r:Fact; r:gives {(245 2000) math:sum 2245}] - skolem:lemma1247 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1245 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma247 a r:Inference; +skolem:lemma246 a r:Inference; r:gives { - (2246 6174) :recursionsNeeded 2 . + 2246 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 246}] [ a r:Fact; r:gives {(246 2000) math:sum 2246}] - skolem:lemma1248 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1246 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma248 a r:Inference; +skolem:lemma247 a r:Inference; r:gives { - (2247 6174) :recursionsNeeded 7 . + 2247 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 247}] [ a r:Fact; r:gives {(247 2000) math:sum 2247}] - skolem:lemma1249 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1247 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma249 a r:Inference; +skolem:lemma248 a r:Inference; r:gives { - (2248 6174) :recursionsNeeded 1 . + 2248 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 248}] [ a r:Fact; r:gives {(248 2000) math:sum 2248}] - skolem:lemma1250 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1248 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma250 a r:Inference; +skolem:lemma249 a r:Inference; r:gives { - (2249 6174) :recursionsNeeded 5 . + 2249 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 249}] [ a r:Fact; r:gives {(249 2000) math:sum 2249}] - skolem:lemma1251 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1249 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma251 a r:Inference; +skolem:lemma250 a r:Inference; r:gives { - (2250 6174) :recursionsNeeded 6 . + 2250 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 250}] [ a r:Fact; r:gives {(250 2000) math:sum 2250}] - skolem:lemma1252 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1250 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma252 a r:Inference; +skolem:lemma251 a r:Inference; r:gives { - (2251 6174) :recursionsNeeded 4 . + 2251 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 251}] [ a r:Fact; r:gives {(251 2000) math:sum 2251}] - skolem:lemma1253 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1251 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma253 a r:Inference; +skolem:lemma252 a r:Inference; r:gives { - (2252 6174) :recursionsNeeded 6 . + 2252 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 252}] [ a r:Fact; r:gives {(252 2000) math:sum 2252}] - skolem:lemma1254 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1252 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma254 a r:Inference; +skolem:lemma253 a r:Inference; r:gives { - (2253 6174) :recursionsNeeded 3 . + 2253 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 253}] [ a r:Fact; r:gives {(253 2000) math:sum 2253}] - skolem:lemma1255 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1253 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma255 a r:Inference; +skolem:lemma254 a r:Inference; r:gives { - (2254 6174) :recursionsNeeded 5 . + 2254 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 254}] [ a r:Fact; r:gives {(254 2000) math:sum 2254}] - skolem:lemma1256 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1254 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma256 a r:Inference; +skolem:lemma255 a r:Inference; r:gives { - (2255 6174) :recursionsNeeded 6 . + 2255 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 255}] [ a r:Fact; r:gives {(255 2000) math:sum 2255}] - skolem:lemma1257 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1255 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma257 a r:Inference; +skolem:lemma256 a r:Inference; r:gives { - (2256 6174) :recursionsNeeded 3 . + 2256 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 256}] [ a r:Fact; r:gives {(256 2000) math:sum 2256}] - skolem:lemma1258 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1256 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma258 a r:Inference; +skolem:lemma257 a r:Inference; r:gives { - (2257 6174) :recursionsNeeded 5 . + 2257 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 257}] [ a r:Fact; r:gives {(257 2000) math:sum 2257}] - skolem:lemma1259 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1257 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma259 a r:Inference; +skolem:lemma258 a r:Inference; r:gives { - (2258 6174) :recursionsNeeded 3 . + 2258 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 258}] [ a r:Fact; r:gives {(258 2000) math:sum 2258}] - skolem:lemma1260 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1258 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma260 a r:Inference; +skolem:lemma259 a r:Inference; r:gives { - (2259 6174) :recursionsNeeded 6 . + 2259 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 259}] [ a r:Fact; r:gives {(259 2000) math:sum 2259}] - skolem:lemma1261 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1259 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma261 a r:Inference; +skolem:lemma260 a r:Inference; r:gives { - (2260 6174) :recursionsNeeded 6 . + 2260 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 260}] [ a r:Fact; r:gives {(260 2000) math:sum 2260}] - skolem:lemma1262 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1260 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma262 a r:Inference; +skolem:lemma261 a r:Inference; r:gives { - (2261 6174) :recursionsNeeded 6 . + 2261 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 261}] [ a r:Fact; r:gives {(261 2000) math:sum 2261}] - skolem:lemma1263 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1261 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma263 a r:Inference; +skolem:lemma262 a r:Inference; r:gives { - (2262 6174) :recursionsNeeded 4 . + 2262 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 262}] [ a r:Fact; r:gives {(262 2000) math:sum 2262}] - skolem:lemma1264 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1262 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma264 a r:Inference; +skolem:lemma263 a r:Inference; r:gives { - (2263 6174) :recursionsNeeded 7 . + 2263 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 263}] [ a r:Fact; r:gives {(263 2000) math:sum 2263}] - skolem:lemma1265 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1263 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma265 a r:Inference; +skolem:lemma264 a r:Inference; r:gives { - (2264 6174) :recursionsNeeded 2 . + 2264 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 264}] [ a r:Fact; r:gives {(264 2000) math:sum 2264}] - skolem:lemma1266 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1264 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma266 a r:Inference; +skolem:lemma265 a r:Inference; r:gives { - (2265 6174) :recursionsNeeded 3 . + 2265 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 265}] [ a r:Fact; r:gives {(265 2000) math:sum 2265}] - skolem:lemma1267 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1265 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma267 a r:Inference; +skolem:lemma266 a r:Inference; r:gives { - (2266 6174) :recursionsNeeded 4 . + 2266 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 266}] [ a r:Fact; r:gives {(266 2000) math:sum 2266}] - skolem:lemma1268 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1266 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma268 a r:Inference; +skolem:lemma267 a r:Inference; r:gives { - (2267 6174) :recursionsNeeded 5 . + 2267 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 267}] [ a r:Fact; r:gives {(267 2000) math:sum 2267}] - skolem:lemma1269 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1267 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma269 a r:Inference; +skolem:lemma268 a r:Inference; r:gives { - (2268 6174) :recursionsNeeded 4 . + 2268 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 268}] [ a r:Fact; r:gives {(268 2000) math:sum 2268}] - skolem:lemma1270 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1268 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma270 a r:Inference; +skolem:lemma269 a r:Inference; r:gives { - (2269 6174) :recursionsNeeded 3 . + 2269 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 269}] [ a r:Fact; r:gives {(269 2000) math:sum 2269}] - skolem:lemma1271 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1269 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma271 a r:Inference; +skolem:lemma270 a r:Inference; r:gives { - (2270 6174) :recursionsNeeded 4 . + 2270 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 270}] [ a r:Fact; r:gives {(270 2000) math:sum 2270}] - skolem:lemma1272 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1270 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma272 a r:Inference; +skolem:lemma271 a r:Inference; r:gives { - (2271 6174) :recursionsNeeded 6 . + 2271 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 271}] [ a r:Fact; r:gives {(271 2000) math:sum 2271}] - skolem:lemma1273 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1271 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma273 a r:Inference; +skolem:lemma272 a r:Inference; r:gives { - (2272 6174) :recursionsNeeded 6 . + 2272 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 272}] [ a r:Fact; r:gives {(272 2000) math:sum 2272}] - skolem:lemma1274 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1272 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma274 a r:Inference; +skolem:lemma273 a r:Inference; r:gives { - (2273 6174) :recursionsNeeded 7 . + 2273 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 273}] [ a r:Fact; r:gives {(273 2000) math:sum 2273}] - skolem:lemma1275 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1273 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma275 a r:Inference; +skolem:lemma274 a r:Inference; r:gives { - (2274 6174) :recursionsNeeded 7 . + 2274 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 274}] [ a r:Fact; r:gives {(274 2000) math:sum 2274}] - skolem:lemma1276 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1274 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma276 a r:Inference; +skolem:lemma275 a r:Inference; r:gives { - (2275 6174) :recursionsNeeded 5 . + 2275 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 275}] [ a r:Fact; r:gives {(275 2000) math:sum 2275}] - skolem:lemma1277 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1275 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma277 a r:Inference; +skolem:lemma276 a r:Inference; r:gives { - (2276 6174) :recursionsNeeded 5 . + 2276 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 276}] [ a r:Fact; r:gives {(276 2000) math:sum 2276}] - skolem:lemma1278 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1276 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma278 a r:Inference; +skolem:lemma277 a r:Inference; r:gives { - (2277 6174) :recursionsNeeded 5 . + 2277 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 277}] [ a r:Fact; r:gives {(277 2000) math:sum 2277}] - skolem:lemma1279 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1277 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma279 a r:Inference; +skolem:lemma278 a r:Inference; r:gives { - (2278 6174) :recursionsNeeded 5 . + 2278 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 278}] [ a r:Fact; r:gives {(278 2000) math:sum 2278}] - skolem:lemma1280 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1278 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma280 a r:Inference; +skolem:lemma279 a r:Inference; r:gives { - (2279 6174) :recursionsNeeded 5 . + 2279 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 279}] [ a r:Fact; r:gives {(279 2000) math:sum 2279}] - skolem:lemma1281 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1279 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma281 a r:Inference; +skolem:lemma280 a r:Inference; r:gives { - (2280 6174) :recursionsNeeded 6 . + 2280 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 280}] [ a r:Fact; r:gives {(280 2000) math:sum 2280}] - skolem:lemma1282 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1280 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma282 a r:Inference; +skolem:lemma281 a r:Inference; r:gives { - (2281 6174) :recursionsNeeded 4 . + 2281 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 281}] [ a r:Fact; r:gives {(281 2000) math:sum 2281}] - skolem:lemma1283 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1281 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma283 a r:Inference; +skolem:lemma282 a r:Inference; r:gives { - (2282 6174) :recursionsNeeded 6 . + 2282 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 282}] [ a r:Fact; r:gives {(282 2000) math:sum 2282}] - skolem:lemma1284 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1282 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma284 a r:Inference; +skolem:lemma283 a r:Inference; r:gives { - (2283 6174) :recursionsNeeded 7 . + 2283 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 283}] [ a r:Fact; r:gives {(283 2000) math:sum 2283}] - skolem:lemma1285 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1283 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma285 a r:Inference; +skolem:lemma284 a r:Inference; r:gives { - (2284 6174) :recursionsNeeded 1 . + 2284 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 284}] [ a r:Fact; r:gives {(284 2000) math:sum 2284}] - skolem:lemma1286 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1284 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma286 a r:Inference; +skolem:lemma285 a r:Inference; r:gives { - (2285 6174) :recursionsNeeded 3 . + 2285 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 285}] [ a r:Fact; r:gives {(285 2000) math:sum 2285}] - skolem:lemma1287 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1285 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma287 a r:Inference; +skolem:lemma286 a r:Inference; r:gives { - (2286 6174) :recursionsNeeded 4 . + 2286 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 286}] [ a r:Fact; r:gives {(286 2000) math:sum 2286}] - skolem:lemma1288 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1286 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma288 a r:Inference; +skolem:lemma287 a r:Inference; r:gives { - (2287 6174) :recursionsNeeded 5 . + 2287 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 287}] [ a r:Fact; r:gives {(287 2000) math:sum 2287}] - skolem:lemma1289 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1287 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma289 a r:Inference; +skolem:lemma288 a r:Inference; r:gives { - (2288 6174) :recursionsNeeded 4 . + 2288 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 288}] [ a r:Fact; r:gives {(288 2000) math:sum 2288}] - skolem:lemma1290 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1288 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma290 a r:Inference; +skolem:lemma289 a r:Inference; r:gives { - (2289 6174) :recursionsNeeded 3 . + 2289 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 289}] [ a r:Fact; r:gives {(289 2000) math:sum 2289}] - skolem:lemma1291 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1289 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma291 a r:Inference; +skolem:lemma290 a r:Inference; r:gives { - (2290 6174) :recursionsNeeded 4 . + 2290 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 290}] [ a r:Fact; r:gives {(290 2000) math:sum 2290}] - skolem:lemma1292 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1290 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma292 a r:Inference; +skolem:lemma291 a r:Inference; r:gives { - (2291 6174) :recursionsNeeded 6 . + 2291 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 291}] [ a r:Fact; r:gives {(291 2000) math:sum 2291}] - skolem:lemma1293 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1291 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma293 a r:Inference; +skolem:lemma292 a r:Inference; r:gives { - (2292 6174) :recursionsNeeded 4 . + 2292 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 292}] [ a r:Fact; r:gives {(292 2000) math:sum 2292}] - skolem:lemma1294 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1292 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma294 a r:Inference; +skolem:lemma293 a r:Inference; r:gives { - (2293 6174) :recursionsNeeded 3 . + 2293 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 293}] [ a r:Fact; r:gives {(293 2000) math:sum 2293}] - skolem:lemma1295 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1293 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma295 a r:Inference; +skolem:lemma294 a r:Inference; r:gives { - (2294 6174) :recursionsNeeded 5 . + 2294 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 294}] [ a r:Fact; r:gives {(294 2000) math:sum 2294}] - skolem:lemma1296 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1294 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma296 a r:Inference; +skolem:lemma295 a r:Inference; r:gives { - (2295 6174) :recursionsNeeded 6 . + 2295 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 295}] [ a r:Fact; r:gives {(295 2000) math:sum 2295}] - skolem:lemma1297 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1295 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma297 a r:Inference; +skolem:lemma296 a r:Inference; r:gives { - (2296 6174) :recursionsNeeded 3 . + 2296 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 296}] [ a r:Fact; r:gives {(296 2000) math:sum 2296}] - skolem:lemma1298 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1296 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma298 a r:Inference; +skolem:lemma297 a r:Inference; r:gives { - (2297 6174) :recursionsNeeded 5 . + 2297 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 297}] [ a r:Fact; r:gives {(297 2000) math:sum 2297}] - skolem:lemma1299 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1297 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma299 a r:Inference; +skolem:lemma298 a r:Inference; r:gives { - (2298 6174) :recursionsNeeded 3 . + 2298 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 298}] [ a r:Fact; r:gives {(298 2000) math:sum 2298}] - skolem:lemma1300 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1298 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma300 a r:Inference; +skolem:lemma299 a r:Inference; r:gives { - (2299 6174) :recursionsNeeded 6 . + 2299 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 299}] [ a r:Fact; r:gives {(299 2000) math:sum 2299}] - skolem:lemma1301 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1299 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma301 a r:Inference; +skolem:lemma300 a r:Inference; r:gives { - (2300 6174) :recursionsNeeded 5 . + 2300 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 300}] [ a r:Fact; r:gives {(300 2000) math:sum 2300}] - skolem:lemma1302 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1300 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma302 a r:Inference; +skolem:lemma301 a r:Inference; r:gives { - (2301 6174) :recursionsNeeded 3 . + 2301 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 301}] [ a r:Fact; r:gives {(301 2000) math:sum 2301}] - skolem:lemma1303 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1301 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma303 a r:Inference; +skolem:lemma302 a r:Inference; r:gives { - (2302 6174) :recursionsNeeded 6 . + 2302 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 302}] [ a r:Fact; r:gives {(302 2000) math:sum 2302}] - skolem:lemma1304 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1302 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma304 a r:Inference; +skolem:lemma303 a r:Inference; r:gives { - (2303 6174) :recursionsNeeded 3 . + 2303 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 303}] [ a r:Fact; r:gives {(303 2000) math:sum 2303}] - skolem:lemma1305 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1303 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma305 a r:Inference; +skolem:lemma304 a r:Inference; r:gives { - (2304 6174) :recursionsNeeded 7 . + 2304 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 304}] [ a r:Fact; r:gives {(304 2000) math:sum 2304}] - skolem:lemma1306 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1304 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma306 a r:Inference; +skolem:lemma305 a r:Inference; r:gives { - (2305 6174) :recursionsNeeded 7 . + 2305 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 305}] [ a r:Fact; r:gives {(305 2000) math:sum 2305}] - skolem:lemma1307 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1305 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma307 a r:Inference; +skolem:lemma306 a r:Inference; r:gives { - (2306 6174) :recursionsNeeded 7 . + 2306 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 306}] [ a r:Fact; r:gives {(306 2000) math:sum 2306}] - skolem:lemma1308 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1306 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma308 a r:Inference; +skolem:lemma307 a r:Inference; r:gives { - (2307 6174) :recursionsNeeded 3 . + 2307 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 307}] [ a r:Fact; r:gives {(307 2000) math:sum 2307}] - skolem:lemma1309 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1307 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma309 a r:Inference; +skolem:lemma308 a r:Inference; r:gives { - (2308 6174) :recursionsNeeded 3 . + 2308 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 308}] [ a r:Fact; r:gives {(308 2000) math:sum 2308}] - skolem:lemma1310 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1308 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma310 a r:Inference; +skolem:lemma309 a r:Inference; r:gives { - (2309 6174) :recursionsNeeded 4 . + 2309 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 309}] [ a r:Fact; r:gives {(309 2000) math:sum 2309}] - skolem:lemma1311 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1309 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma311 a r:Inference; +skolem:lemma310 a r:Inference; r:gives { - (2310 6174) :recursionsNeeded 3 . + 2310 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 310}] [ a r:Fact; r:gives {(310 2000) math:sum 2310}] - skolem:lemma1312 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1310 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma312 a r:Inference; +skolem:lemma311 a r:Inference; r:gives { - (2311 6174) :recursionsNeeded 3 . + 2311 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 311}] [ a r:Fact; r:gives {(311 2000) math:sum 2311}] - skolem:lemma1313 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1311 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma313 a r:Inference; +skolem:lemma312 a r:Inference; r:gives { - (2312 6174) :recursionsNeeded 4 . + 2312 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 312}] [ a r:Fact; r:gives {(312 2000) math:sum 2312}] - skolem:lemma1314 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1312 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma314 a r:Inference; +skolem:lemma313 a r:Inference; r:gives { - (2313 6174) :recursionsNeeded 3 . + 2313 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 313}] [ a r:Fact; r:gives {(313 2000) math:sum 2313}] - skolem:lemma1315 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1313 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma315 a r:Inference; +skolem:lemma314 a r:Inference; r:gives { - (2314 6174) :recursionsNeeded 3 . + 2314 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 314}] [ a r:Fact; r:gives {(314 2000) math:sum 2314}] - skolem:lemma1316 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1314 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma316 a r:Inference; +skolem:lemma315 a r:Inference; r:gives { - (2315 6174) :recursionsNeeded 7 . + 2315 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 315}] [ a r:Fact; r:gives {(315 2000) math:sum 2315}] - skolem:lemma1317 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1315 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma317 a r:Inference; +skolem:lemma316 a r:Inference; r:gives { - (2316 6174) :recursionsNeeded 7 . + 2316 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 316}] [ a r:Fact; r:gives {(316 2000) math:sum 2316}] - skolem:lemma1318 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1316 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma318 a r:Inference; +skolem:lemma317 a r:Inference; r:gives { - (2317 6174) :recursionsNeeded 7 . + 2317 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 317}] [ a r:Fact; r:gives {(317 2000) math:sum 2317}] - skolem:lemma1319 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1317 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma319 a r:Inference; +skolem:lemma318 a r:Inference; r:gives { - (2318 6174) :recursionsNeeded 3 . + 2318 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 318}] [ a r:Fact; r:gives {(318 2000) math:sum 2318}] - skolem:lemma1320 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1318 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma320 a r:Inference; +skolem:lemma319 a r:Inference; r:gives { - (2319 6174) :recursionsNeeded 3 . + 2319 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 319}] [ a r:Fact; r:gives {(319 2000) math:sum 2319}] - skolem:lemma1321 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1319 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma321 a r:Inference; +skolem:lemma320 a r:Inference; r:gives { - (2320 6174) :recursionsNeeded 6 . + 2320 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 320}] [ a r:Fact; r:gives {(320 2000) math:sum 2320}] - skolem:lemma1322 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1320 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma322 a r:Inference; +skolem:lemma321 a r:Inference; r:gives { - (2321 6174) :recursionsNeeded 4 . + 2321 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 321}] [ a r:Fact; r:gives {(321 2000) math:sum 2321}] - skolem:lemma1323 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1321 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma323 a r:Inference; +skolem:lemma322 a r:Inference; r:gives { - (2322 6174) :recursionsNeeded 5 . + 2322 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 322}] [ a r:Fact; r:gives {(322 2000) math:sum 2322}] - skolem:lemma1324 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1322 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma324 a r:Inference; +skolem:lemma323 a r:Inference; r:gives { - (2323 6174) :recursionsNeeded 4 . + 2323 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 323}] [ a r:Fact; r:gives {(323 2000) math:sum 2323}] - skolem:lemma1325 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1323 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma325 a r:Inference; +skolem:lemma324 a r:Inference; r:gives { - (2324 6174) :recursionsNeeded 3 . + 2324 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 324}] [ a r:Fact; r:gives {(324 2000) math:sum 2324}] - skolem:lemma1326 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1324 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma326 a r:Inference; +skolem:lemma325 a r:Inference; r:gives { - (2325 6174) :recursionsNeeded 3 . + 2325 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 325}] [ a r:Fact; r:gives {(325 2000) math:sum 2325}] - skolem:lemma1327 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1325 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma327 a r:Inference; +skolem:lemma326 a r:Inference; r:gives { - (2326 6174) :recursionsNeeded 7 . + 2326 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 326}] [ a r:Fact; r:gives {(326 2000) math:sum 2326}] - skolem:lemma1328 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1326 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma328 a r:Inference; +skolem:lemma327 a r:Inference; r:gives { - (2327 6174) :recursionsNeeded 7 . + 2327 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 327}] [ a r:Fact; r:gives {(327 2000) math:sum 2327}] - skolem:lemma1329 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1327 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma329 a r:Inference; +skolem:lemma328 a r:Inference; r:gives { - (2328 6174) :recursionsNeeded 7 . + 2328 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 328}] [ a r:Fact; r:gives {(328 2000) math:sum 2328}] - skolem:lemma1330 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1328 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma330 a r:Inference; +skolem:lemma329 a r:Inference; r:gives { - (2329 6174) :recursionsNeeded 3 . + 2329 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 329}] [ a r:Fact; r:gives {(329 2000) math:sum 2329}] - skolem:lemma1331 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1329 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma331 a r:Inference; +skolem:lemma330 a r:Inference; r:gives { - (2330 6174) :recursionsNeeded 3 . + 2330 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 330}] [ a r:Fact; r:gives {(330 2000) math:sum 2330}] - skolem:lemma1332 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1330 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma332 a r:Inference; +skolem:lemma331 a r:Inference; r:gives { - (2331 6174) :recursionsNeeded 3 . + 2331 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 331}] [ a r:Fact; r:gives {(331 2000) math:sum 2331}] - skolem:lemma1333 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1331 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma333 a r:Inference; +skolem:lemma332 a r:Inference; r:gives { - (2332 6174) :recursionsNeeded 4 . + 2332 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 332}] [ a r:Fact; r:gives {(332 2000) math:sum 2332}] - skolem:lemma1334 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1332 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma334 a r:Inference; +skolem:lemma333 a r:Inference; r:gives { - (2333 6174) :recursionsNeeded 5 . + 2333 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 333}] [ a r:Fact; r:gives {(333 2000) math:sum 2333}] - skolem:lemma1335 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1333 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma335 a r:Inference; +skolem:lemma334 a r:Inference; r:gives { - (2334 6174) :recursionsNeeded 4 . + 2334 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 334}] [ a r:Fact; r:gives {(334 2000) math:sum 2334}] - skolem:lemma1336 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1334 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma336 a r:Inference; +skolem:lemma335 a r:Inference; r:gives { - (2335 6174) :recursionsNeeded 6 . + 2335 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 335}] [ a r:Fact; r:gives {(335 2000) math:sum 2335}] - skolem:lemma1337 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1335 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma337 a r:Inference; +skolem:lemma336 a r:Inference; r:gives { - (2336 6174) :recursionsNeeded 4 . + 2336 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 336}] [ a r:Fact; r:gives {(336 2000) math:sum 2336}] - skolem:lemma1338 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1336 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma338 a r:Inference; +skolem:lemma337 a r:Inference; r:gives { - (2337 6174) :recursionsNeeded 6 . + 2337 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 337}] [ a r:Fact; r:gives {(337 2000) math:sum 2337}] - skolem:lemma1339 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1337 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma339 a r:Inference; +skolem:lemma338 a r:Inference; r:gives { - (2338 6174) :recursionsNeeded 6 . + 2338 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 338}] [ a r:Fact; r:gives {(338 2000) math:sum 2338}] - skolem:lemma1340 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1338 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma340 a r:Inference; +skolem:lemma339 a r:Inference; r:gives { - (2339 6174) :recursionsNeeded 4 . + 2339 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 339}] [ a r:Fact; r:gives {(339 2000) math:sum 2339}] - skolem:lemma1341 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1339 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma341 a r:Inference; +skolem:lemma340 a r:Inference; r:gives { - (2340 6174) :recursionsNeeded 7 . + 2340 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 340}] [ a r:Fact; r:gives {(340 2000) math:sum 2340}] - skolem:lemma1342 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1340 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma342 a r:Inference; +skolem:lemma341 a r:Inference; r:gives { - (2341 6174) :recursionsNeeded 3 . + 2341 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 341}] [ a r:Fact; r:gives {(341 2000) math:sum 2341}] - skolem:lemma1343 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1341 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma343 a r:Inference; +skolem:lemma342 a r:Inference; r:gives { - (2342 6174) :recursionsNeeded 3 . + 2342 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 342}] [ a r:Fact; r:gives {(342 2000) math:sum 2342}] - skolem:lemma1344 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1342 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma344 a r:Inference; +skolem:lemma343 a r:Inference; r:gives { - (2343 6174) :recursionsNeeded 4 . + 2343 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 343}] [ a r:Fact; r:gives {(343 2000) math:sum 2343}] - skolem:lemma1345 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1343 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma345 a r:Inference; +skolem:lemma344 a r:Inference; r:gives { - (2344 6174) :recursionsNeeded 3 . + 2344 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 344}] [ a r:Fact; r:gives {(344 2000) math:sum 2344}] - skolem:lemma1346 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1344 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma346 a r:Inference; +skolem:lemma345 a r:Inference; r:gives { - (2345 6174) :recursionsNeeded 3 . + 2345 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 345}] [ a r:Fact; r:gives {(345 2000) math:sum 2345}] - skolem:lemma1347 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1345 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma347 a r:Inference; +skolem:lemma346 a r:Inference; r:gives { - (2346 6174) :recursionsNeeded 7 . + 2346 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 346}] [ a r:Fact; r:gives {(346 2000) math:sum 2346}] - skolem:lemma1348 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1346 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma348 a r:Inference; +skolem:lemma347 a r:Inference; r:gives { - (2347 6174) :recursionsNeeded 7 . + 2347 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 347}] [ a r:Fact; r:gives {(347 2000) math:sum 2347}] - skolem:lemma1349 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1347 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma349 a r:Inference; +skolem:lemma348 a r:Inference; r:gives { - (2348 6174) :recursionsNeeded 7 . + 2348 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 348}] [ a r:Fact; r:gives {(348 2000) math:sum 2348}] - skolem:lemma1350 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1348 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma350 a r:Inference; +skolem:lemma349 a r:Inference; r:gives { - (2349 6174) :recursionsNeeded 3 . + 2349 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 349}] [ a r:Fact; r:gives {(349 2000) math:sum 2349}] - skolem:lemma1351 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1349 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma351 a r:Inference; +skolem:lemma350 a r:Inference; r:gives { - (2350 6174) :recursionsNeeded 7 . + 2350 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 350}] [ a r:Fact; r:gives {(350 2000) math:sum 2350}] - skolem:lemma1352 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1350 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma352 a r:Inference; +skolem:lemma351 a r:Inference; r:gives { - (2351 6174) :recursionsNeeded 7 . + 2351 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 351}] [ a r:Fact; r:gives {(351 2000) math:sum 2351}] - skolem:lemma1353 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1351 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma353 a r:Inference; +skolem:lemma352 a r:Inference; r:gives { - (2352 6174) :recursionsNeeded 3 . + 2352 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 352}] [ a r:Fact; r:gives {(352 2000) math:sum 2352}] - skolem:lemma1354 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1352 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma354 a r:Inference; +skolem:lemma353 a r:Inference; r:gives { - (2353 6174) :recursionsNeeded 6 . + 2353 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 353}] [ a r:Fact; r:gives {(353 2000) math:sum 2353}] - skolem:lemma1355 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1353 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma355 a r:Inference; +skolem:lemma354 a r:Inference; r:gives { - (2354 6174) :recursionsNeeded 3 . + 2354 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 354}] [ a r:Fact; r:gives {(354 2000) math:sum 2354}] - skolem:lemma1356 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1354 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma356 a r:Inference; +skolem:lemma355 a r:Inference; r:gives { - (2355 6174) :recursionsNeeded 5 . + 2355 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 355}] [ a r:Fact; r:gives {(355 2000) math:sum 2355}] - skolem:lemma1357 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1355 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma357 a r:Inference; +skolem:lemma356 a r:Inference; r:gives { - (2356 6174) :recursionsNeeded 2 . + 2356 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 356}] [ a r:Fact; r:gives {(356 2000) math:sum 2356}] - skolem:lemma1358 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1356 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma358 a r:Inference; +skolem:lemma357 a r:Inference; r:gives { - (2357 6174) :recursionsNeeded 7 . + 2357 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 357}] [ a r:Fact; r:gives {(357 2000) math:sum 2357}] - skolem:lemma1359 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1357 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma359 a r:Inference; +skolem:lemma358 a r:Inference; r:gives { - (2358 6174) :recursionsNeeded 1 . + 2358 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 358}] [ a r:Fact; r:gives {(358 2000) math:sum 2358}] - skolem:lemma1360 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1358 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma360 a r:Inference; +skolem:lemma359 a r:Inference; r:gives { - (2359 6174) :recursionsNeeded 5 . + 2359 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 359}] [ a r:Fact; r:gives {(359 2000) math:sum 2359}] - skolem:lemma1361 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1359 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma361 a r:Inference; +skolem:lemma360 a r:Inference; r:gives { - (2360 6174) :recursionsNeeded 7 . + 2360 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 360}] [ a r:Fact; r:gives {(360 2000) math:sum 2360}] - skolem:lemma1362 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1360 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma362 a r:Inference; +skolem:lemma361 a r:Inference; r:gives { - (2361 6174) :recursionsNeeded 7 . + 2361 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 361}] [ a r:Fact; r:gives {(361 2000) math:sum 2361}] - skolem:lemma1363 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1361 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma363 a r:Inference; +skolem:lemma362 a r:Inference; r:gives { - (2362 6174) :recursionsNeeded 7 . + 2362 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 362}] [ a r:Fact; r:gives {(362 2000) math:sum 2362}] - skolem:lemma1364 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1362 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma364 a r:Inference; +skolem:lemma363 a r:Inference; r:gives { - (2363 6174) :recursionsNeeded 4 . + 2363 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 363}] [ a r:Fact; r:gives {(363 2000) math:sum 2363}] - skolem:lemma1365 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1363 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma365 a r:Inference; +skolem:lemma364 a r:Inference; r:gives { - (2364 6174) :recursionsNeeded 7 . + 2364 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 364}] [ a r:Fact; r:gives {(364 2000) math:sum 2364}] - skolem:lemma1366 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1364 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma366 a r:Inference; +skolem:lemma365 a r:Inference; r:gives { - (2365 6174) :recursionsNeeded 2 . + 2365 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 365}] [ a r:Fact; r:gives {(365 2000) math:sum 2365}] - skolem:lemma1367 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1365 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma367 a r:Inference; +skolem:lemma366 a r:Inference; r:gives { - (2366 6174) :recursionsNeeded 3 . + 2366 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 366}] [ a r:Fact; r:gives {(366 2000) math:sum 2366}] - skolem:lemma1368 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1366 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma368 a r:Inference; +skolem:lemma367 a r:Inference; r:gives { - (2367 6174) :recursionsNeeded 5 . + 2367 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 367}] [ a r:Fact; r:gives {(367 2000) math:sum 2367}] - skolem:lemma1369 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1367 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma369 a r:Inference; +skolem:lemma368 a r:Inference; r:gives { - (2368 6174) :recursionsNeeded 3 . + 2368 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 368}] [ a r:Fact; r:gives {(368 2000) math:sum 2368}] - skolem:lemma1370 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1368 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma370 a r:Inference; +skolem:lemma369 a r:Inference; r:gives { - (2369 6174) :recursionsNeeded 6 . + 2369 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 369}] [ a r:Fact; r:gives {(369 2000) math:sum 2369}] - skolem:lemma1371 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1369 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma371 a r:Inference; +skolem:lemma370 a r:Inference; r:gives { - (2370 6174) :recursionsNeeded 3 . + 2370 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 370}] [ a r:Fact; r:gives {(370 2000) math:sum 2370}] - skolem:lemma1372 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1370 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma372 a r:Inference; +skolem:lemma371 a r:Inference; r:gives { - (2371 6174) :recursionsNeeded 7 . + 2371 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 371}] [ a r:Fact; r:gives {(371 2000) math:sum 2371}] - skolem:lemma1373 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1371 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma373 a r:Inference; +skolem:lemma372 a r:Inference; r:gives { - (2372 6174) :recursionsNeeded 7 . + 2372 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 372}] [ a r:Fact; r:gives {(372 2000) math:sum 2372}] - skolem:lemma1374 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1372 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma374 a r:Inference; +skolem:lemma373 a r:Inference; r:gives { - (2373 6174) :recursionsNeeded 6 . + 2373 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 373}] [ a r:Fact; r:gives {(373 2000) math:sum 2373}] - skolem:lemma1375 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1373 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma375 a r:Inference; +skolem:lemma374 a r:Inference; r:gives { - (2374 6174) :recursionsNeeded 7 . + 2374 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 374}] [ a r:Fact; r:gives {(374 2000) math:sum 2374}] - skolem:lemma1376 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1374 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma376 a r:Inference; +skolem:lemma375 a r:Inference; r:gives { - (2375 6174) :recursionsNeeded 7 . + 2375 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 375}] [ a r:Fact; r:gives {(375 2000) math:sum 2375}] - skolem:lemma1377 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1375 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma377 a r:Inference; +skolem:lemma376 a r:Inference; r:gives { - (2376 6174) :recursionsNeeded 5 . + 2376 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 376}] [ a r:Fact; r:gives {(376 2000) math:sum 2376}] - skolem:lemma1378 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1376 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma378 a r:Inference; +skolem:lemma377 a r:Inference; r:gives { - (2377 6174) :recursionsNeeded 5 . + 2377 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 377}] [ a r:Fact; r:gives {(377 2000) math:sum 2377}] - skolem:lemma1379 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1377 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma379 a r:Inference; +skolem:lemma378 a r:Inference; r:gives { - (2378 6174) :recursionsNeeded 4 . + 2378 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 378}] [ a r:Fact; r:gives {(378 2000) math:sum 2378}] - skolem:lemma1380 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1378 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma380 a r:Inference; +skolem:lemma379 a r:Inference; r:gives { - (2379 6174) :recursionsNeeded 3 . + 2379 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 379}] [ a r:Fact; r:gives {(379 2000) math:sum 2379}] - skolem:lemma1381 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1379 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma381 a r:Inference; +skolem:lemma380 a r:Inference; r:gives { - (2380 6174) :recursionsNeeded 3 . + 2380 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 380}] [ a r:Fact; r:gives {(380 2000) math:sum 2380}] - skolem:lemma1382 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1380 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma382 a r:Inference; +skolem:lemma381 a r:Inference; r:gives { - (2381 6174) :recursionsNeeded 3 . + 2381 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 381}] [ a r:Fact; r:gives {(381 2000) math:sum 2381}] - skolem:lemma1383 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1381 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma383 a r:Inference; +skolem:lemma382 a r:Inference; r:gives { - (2382 6174) :recursionsNeeded 7 . + 2382 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 382}] [ a r:Fact; r:gives {(382 2000) math:sum 2382}] - skolem:lemma1384 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1382 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma384 a r:Inference; +skolem:lemma383 a r:Inference; r:gives { - (2383 6174) :recursionsNeeded 6 . + 2383 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 383}] [ a r:Fact; r:gives {(383 2000) math:sum 2383}] - skolem:lemma1385 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1383 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma385 a r:Inference; +skolem:lemma384 a r:Inference; r:gives { - (2384 6174) :recursionsNeeded 7 . + 2384 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 384}] [ a r:Fact; r:gives {(384 2000) math:sum 2384}] - skolem:lemma1386 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1384 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma386 a r:Inference; +skolem:lemma385 a r:Inference; r:gives { - (2385 6174) :recursionsNeeded 1 . + 2385 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 385}] [ a r:Fact; r:gives {(385 2000) math:sum 2385}] - skolem:lemma1387 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1385 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma387 a r:Inference; +skolem:lemma386 a r:Inference; r:gives { - (2386 6174) :recursionsNeeded 3 . + 2386 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 386}] [ a r:Fact; r:gives {(386 2000) math:sum 2386}] - skolem:lemma1388 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1386 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma388 a r:Inference; +skolem:lemma387 a r:Inference; r:gives { - (2387 6174) :recursionsNeeded 4 . + 2387 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 387}] [ a r:Fact; r:gives {(387 2000) math:sum 2387}] - skolem:lemma1389 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1387 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma389 a r:Inference; +skolem:lemma388 a r:Inference; r:gives { - (2388 6174) :recursionsNeeded 5 . + 2388 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 388}] [ a r:Fact; r:gives {(388 2000) math:sum 2388}] - skolem:lemma1390 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1388 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma390 a r:Inference; +skolem:lemma389 a r:Inference; r:gives { - (2389 6174) :recursionsNeeded 5 . + 2389 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 389}] [ a r:Fact; r:gives {(389 2000) math:sum 2389}] - skolem:lemma1391 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1389 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma391 a r:Inference; +skolem:lemma390 a r:Inference; r:gives { - (2390 6174) :recursionsNeeded 4 . + 2390 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 390}] [ a r:Fact; r:gives {(390 2000) math:sum 2390}] - skolem:lemma1392 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1390 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma392 a r:Inference; +skolem:lemma391 a r:Inference; r:gives { - (2391 6174) :recursionsNeeded 3 . + 2391 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 391}] [ a r:Fact; r:gives {(391 2000) math:sum 2391}] - skolem:lemma1393 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1391 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma393 a r:Inference; +skolem:lemma392 a r:Inference; r:gives { - (2392 6174) :recursionsNeeded 3 . + 2392 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 392}] [ a r:Fact; r:gives {(392 2000) math:sum 2392}] - skolem:lemma1394 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1392 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma394 a r:Inference; +skolem:lemma393 a r:Inference; r:gives { - (2393 6174) :recursionsNeeded 4 . + 2393 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 393}] [ a r:Fact; r:gives {(393 2000) math:sum 2393}] - skolem:lemma1395 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1393 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma395 a r:Inference; +skolem:lemma394 a r:Inference; r:gives { - (2394 6174) :recursionsNeeded 3 . + 2394 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 394}] [ a r:Fact; r:gives {(394 2000) math:sum 2394}] - skolem:lemma1396 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1394 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma396 a r:Inference; +skolem:lemma395 a r:Inference; r:gives { - (2395 6174) :recursionsNeeded 5 . + 2395 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 395}] [ a r:Fact; r:gives {(395 2000) math:sum 2395}] - skolem:lemma1397 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1395 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma397 a r:Inference; +skolem:lemma396 a r:Inference; r:gives { - (2396 6174) :recursionsNeeded 6 . + 2396 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 396}] [ a r:Fact; r:gives {(396 2000) math:sum 2396}] - skolem:lemma1398 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1396 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma398 a r:Inference; +skolem:lemma397 a r:Inference; r:gives { - (2397 6174) :recursionsNeeded 3 . + 2397 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 397}] [ a r:Fact; r:gives {(397 2000) math:sum 2397}] - skolem:lemma1399 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1397 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma399 a r:Inference; +skolem:lemma398 a r:Inference; r:gives { - (2398 6174) :recursionsNeeded 5 . + 2398 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 398}] [ a r:Fact; r:gives {(398 2000) math:sum 2398}] - skolem:lemma1400 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1398 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma400 a r:Inference; +skolem:lemma399 a r:Inference; r:gives { - (2399 6174) :recursionsNeeded 3 . + 2399 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 399}] [ a r:Fact; r:gives {(399 2000) math:sum 2399}] - skolem:lemma1401 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1399 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma401 a r:Inference; +skolem:lemma400 a r:Inference; r:gives { - (2400 6174) :recursionsNeeded 2 . + 2400 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 400}] [ a r:Fact; r:gives {(400 2000) math:sum 2400}] - skolem:lemma1402 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1400 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma402 a r:Inference; +skolem:lemma401 a r:Inference; r:gives { - (2401 6174) :recursionsNeeded 7 . + 2401 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 401}] [ a r:Fact; r:gives {(401 2000) math:sum 2401}] - skolem:lemma1403 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1401 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma403 a r:Inference; +skolem:lemma402 a r:Inference; r:gives { - (2402 6174) :recursionsNeeded 4 . + 2402 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 402}] [ a r:Fact; r:gives {(402 2000) math:sum 2402}] - skolem:lemma1404 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1402 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma404 a r:Inference; +skolem:lemma403 a r:Inference; r:gives { - (2403 6174) :recursionsNeeded 7 . + 2403 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 403}] [ a r:Fact; r:gives {(403 2000) math:sum 2403}] - skolem:lemma1405 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1403 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma405 a r:Inference; +skolem:lemma404 a r:Inference; r:gives { - (2404 6174) :recursionsNeeded 2 . + 2404 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 404}] [ a r:Fact; r:gives {(404 2000) math:sum 2404}] - skolem:lemma1406 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1404 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma406 a r:Inference; +skolem:lemma405 a r:Inference; r:gives { - (2405 6174) :recursionsNeeded 7 . + 2405 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 405}] [ a r:Fact; r:gives {(405 2000) math:sum 2405}] - skolem:lemma1407 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1405 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma407 a r:Inference; +skolem:lemma406 a r:Inference; r:gives { - (2406 6174) :recursionsNeeded 1 . + 2406 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 406}] [ a r:Fact; r:gives {(406 2000) math:sum 2406}] - skolem:lemma1408 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1406 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma408 a r:Inference; +skolem:lemma407 a r:Inference; r:gives { - (2407 6174) :recursionsNeeded 5 . + 2407 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 407}] [ a r:Fact; r:gives {(407 2000) math:sum 2407}] - skolem:lemma1409 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1407 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma409 a r:Inference; +skolem:lemma408 a r:Inference; r:gives { - (2408 6174) :recursionsNeeded 6 . + 2408 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 408}] [ a r:Fact; r:gives {(408 2000) math:sum 2408}] - skolem:lemma1410 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1408 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma410 a r:Inference; +skolem:lemma409 a r:Inference; r:gives { - (2409 6174) :recursionsNeeded 3 . + 2409 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 409}] [ a r:Fact; r:gives {(409 2000) math:sum 2409}] - skolem:lemma1411 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1409 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma411 a r:Inference; +skolem:lemma410 a r:Inference; r:gives { - (2410 6174) :recursionsNeeded 7 . + 2410 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 410}] [ a r:Fact; r:gives {(410 2000) math:sum 2410}] - skolem:lemma1412 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1410 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma412 a r:Inference; +skolem:lemma411 a r:Inference; r:gives { - (2411 6174) :recursionsNeeded 3 . + 2411 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 411}] [ a r:Fact; r:gives {(411 2000) math:sum 2411}] - skolem:lemma1413 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1411 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma413 a r:Inference; +skolem:lemma412 a r:Inference; r:gives { - (2412 6174) :recursionsNeeded 6 . + 2412 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 412}] [ a r:Fact; r:gives {(412 2000) math:sum 2412}] - skolem:lemma1414 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1412 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma414 a r:Inference; +skolem:lemma413 a r:Inference; r:gives { - (2413 6174) :recursionsNeeded 3 . + 2413 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 413}] [ a r:Fact; r:gives {(413 2000) math:sum 2413}] - skolem:lemma1415 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1413 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma415 a r:Inference; +skolem:lemma414 a r:Inference; r:gives { - (2414 6174) :recursionsNeeded 5 . + 2414 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 414}] [ a r:Fact; r:gives {(414 2000) math:sum 2414}] - skolem:lemma1416 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1414 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma416 a r:Inference; +skolem:lemma415 a r:Inference; r:gives { - (2415 6174) :recursionsNeeded 2 . + 2415 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 415}] [ a r:Fact; r:gives {(415 2000) math:sum 2415}] - skolem:lemma1417 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1415 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma417 a r:Inference; +skolem:lemma416 a r:Inference; r:gives { - (2416 6174) :recursionsNeeded 7 . + 2416 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 416}] [ a r:Fact; r:gives {(416 2000) math:sum 2416}] - skolem:lemma1418 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1416 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma418 a r:Inference; +skolem:lemma417 a r:Inference; r:gives { - (2417 6174) :recursionsNeeded 1 . + 2417 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 417}] [ a r:Fact; r:gives {(417 2000) math:sum 2417}] - skolem:lemma1419 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1417 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma419 a r:Inference; +skolem:lemma418 a r:Inference; r:gives { - (2418 6174) :recursionsNeeded 5 . + 2418 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 418}] [ a r:Fact; r:gives {(418 2000) math:sum 2418}] - skolem:lemma1420 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1418 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma420 a r:Inference; +skolem:lemma419 a r:Inference; r:gives { - (2419 6174) :recursionsNeeded 6 . + 2419 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 419}] [ a r:Fact; r:gives {(419 2000) math:sum 2419}] - skolem:lemma1421 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1419 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma421 a r:Inference; +skolem:lemma420 a r:Inference; r:gives { - (2420 6174) :recursionsNeeded 4 . + 2420 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 420}] [ a r:Fact; r:gives {(420 2000) math:sum 2420}] - skolem:lemma1422 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1420 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma422 a r:Inference; +skolem:lemma421 a r:Inference; r:gives { - (2421 6174) :recursionsNeeded 6 . + 2421 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 421}] [ a r:Fact; r:gives {(421 2000) math:sum 2421}] - skolem:lemma1423 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1421 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma423 a r:Inference; +skolem:lemma422 a r:Inference; r:gives { - (2422 6174) :recursionsNeeded 4 . + 2422 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 422}] [ a r:Fact; r:gives {(422 2000) math:sum 2422}] - skolem:lemma1424 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1422 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma424 a r:Inference; +skolem:lemma423 a r:Inference; r:gives { - (2423 6174) :recursionsNeeded 3 . + 2423 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 423}] [ a r:Fact; r:gives {(423 2000) math:sum 2423}] - skolem:lemma1425 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1423 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma425 a r:Inference; +skolem:lemma424 a r:Inference; r:gives { - (2424 6174) :recursionsNeeded 6 . + 2424 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 424}] [ a r:Fact; r:gives {(424 2000) math:sum 2424}] - skolem:lemma1426 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1424 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma426 a r:Inference; +skolem:lemma425 a r:Inference; r:gives { - (2425 6174) :recursionsNeeded 5 . + 2425 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 425}] [ a r:Fact; r:gives {(425 2000) math:sum 2425}] - skolem:lemma1427 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1425 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma427 a r:Inference; +skolem:lemma426 a r:Inference; r:gives { - (2426 6174) :recursionsNeeded 2 . + 2426 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 426}] [ a r:Fact; r:gives {(426 2000) math:sum 2426}] - skolem:lemma1428 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1426 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma428 a r:Inference; +skolem:lemma427 a r:Inference; r:gives { - (2427 6174) :recursionsNeeded 7 . + 2427 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 427}] [ a r:Fact; r:gives {(427 2000) math:sum 2427}] - skolem:lemma1429 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1427 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma429 a r:Inference; +skolem:lemma428 a r:Inference; r:gives { - (2428 6174) :recursionsNeeded 1 . + 2428 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 428}] [ a r:Fact; r:gives {(428 2000) math:sum 2428}] - skolem:lemma1430 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1428 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma430 a r:Inference; +skolem:lemma429 a r:Inference; r:gives { - (2429 6174) :recursionsNeeded 5 . + 2429 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 429}] [ a r:Fact; r:gives {(429 2000) math:sum 2429}] - skolem:lemma1431 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1429 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma431 a r:Inference; +skolem:lemma430 a r:Inference; r:gives { - (2430 6174) :recursionsNeeded 7 . + 2430 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 430}] [ a r:Fact; r:gives {(430 2000) math:sum 2430}] - skolem:lemma1432 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1430 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma432 a r:Inference; +skolem:lemma431 a r:Inference; r:gives { - (2431 6174) :recursionsNeeded 3 . + 2431 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 431}] [ a r:Fact; r:gives {(431 2000) math:sum 2431}] - skolem:lemma1433 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1431 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma433 a r:Inference; +skolem:lemma432 a r:Inference; r:gives { - (2432 6174) :recursionsNeeded 3 . + 2432 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 432}] [ a r:Fact; r:gives {(432 2000) math:sum 2432}] - skolem:lemma1434 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1432 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma434 a r:Inference; +skolem:lemma433 a r:Inference; r:gives { - (2433 6174) :recursionsNeeded 4 . + 2433 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 433}] [ a r:Fact; r:gives {(433 2000) math:sum 2433}] - skolem:lemma1435 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1433 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma435 a r:Inference; +skolem:lemma434 a r:Inference; r:gives { - (2434 6174) :recursionsNeeded 3 . + 2434 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 434}] [ a r:Fact; r:gives {(434 2000) math:sum 2434}] - skolem:lemma1436 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1434 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma436 a r:Inference; +skolem:lemma435 a r:Inference; r:gives { - (2435 6174) :recursionsNeeded 3 . + 2435 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 435}] [ a r:Fact; r:gives {(435 2000) math:sum 2435}] - skolem:lemma1437 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1435 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma437 a r:Inference; +skolem:lemma436 a r:Inference; r:gives { - (2436 6174) :recursionsNeeded 7 . + 2436 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 436}] [ a r:Fact; r:gives {(436 2000) math:sum 2436}] - skolem:lemma1438 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1436 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma438 a r:Inference; +skolem:lemma437 a r:Inference; r:gives { - (2437 6174) :recursionsNeeded 7 . + 2437 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 437}] [ a r:Fact; r:gives {(437 2000) math:sum 2437}] - skolem:lemma1439 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1437 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma439 a r:Inference; +skolem:lemma438 a r:Inference; r:gives { - (2438 6174) :recursionsNeeded 7 . + 2438 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 438}] [ a r:Fact; r:gives {(438 2000) math:sum 2438}] - skolem:lemma1440 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1438 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma440 a r:Inference; +skolem:lemma439 a r:Inference; r:gives { - (2439 6174) :recursionsNeeded 3 . + 2439 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 439}] [ a r:Fact; r:gives {(439 2000) math:sum 2439}] - skolem:lemma1441 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1439 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma441 a r:Inference; +skolem:lemma440 a r:Inference; r:gives { - (2440 6174) :recursionsNeeded 2 . + 2440 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 440}] [ a r:Fact; r:gives {(440 2000) math:sum 2440}] - skolem:lemma1442 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1440 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma442 a r:Inference; +skolem:lemma441 a r:Inference; r:gives { - (2441 6174) :recursionsNeeded 5 . + 2441 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 441}] [ a r:Fact; r:gives {(441 2000) math:sum 2441}] - skolem:lemma1443 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1441 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma443 a r:Inference; +skolem:lemma442 a r:Inference; r:gives { - (2442 6174) :recursionsNeeded 6 . + 2442 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 442}] [ a r:Fact; r:gives {(442 2000) math:sum 2442}] - skolem:lemma1444 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1442 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma444 a r:Inference; +skolem:lemma443 a r:Inference; r:gives { - (2443 6174) :recursionsNeeded 3 . + 2443 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 443}] [ a r:Fact; r:gives {(443 2000) math:sum 2443}] - skolem:lemma1445 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1443 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma445 a r:Inference; +skolem:lemma444 a r:Inference; r:gives { - (2444 6174) :recursionsNeeded 4 . + 2444 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 444}] [ a r:Fact; r:gives {(444 2000) math:sum 2444}] - skolem:lemma1446 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1444 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma446 a r:Inference; +skolem:lemma445 a r:Inference; r:gives { - (2445 6174) :recursionsNeeded 6 . + 2445 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 445}] [ a r:Fact; r:gives {(445 2000) math:sum 2445}] - skolem:lemma1447 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1445 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma447 a r:Inference; +skolem:lemma446 a r:Inference; r:gives { - (2446 6174) :recursionsNeeded 4 . + 2446 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 446}] [ a r:Fact; r:gives {(446 2000) math:sum 2446}] - skolem:lemma1448 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1446 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma448 a r:Inference; +skolem:lemma447 a r:Inference; r:gives { - (2447 6174) :recursionsNeeded 6 . + 2447 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 447}] [ a r:Fact; r:gives {(447 2000) math:sum 2447}] - skolem:lemma1449 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1447 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma449 a r:Inference; +skolem:lemma448 a r:Inference; r:gives { - (2448 6174) :recursionsNeeded 6 . + 2448 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 448}] [ a r:Fact; r:gives {(448 2000) math:sum 2448}] - skolem:lemma1450 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1448 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma450 a r:Inference; +skolem:lemma449 a r:Inference; r:gives { - (2449 6174) :recursionsNeeded 4 . + 2449 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 449}] [ a r:Fact; r:gives {(449 2000) math:sum 2449}] - skolem:lemma1451 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1449 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma451 a r:Inference; +skolem:lemma450 a r:Inference; r:gives { - (2450 6174) :recursionsNeeded 7 . + 2450 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 450}] [ a r:Fact; r:gives {(450 2000) math:sum 2450}] - skolem:lemma1452 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1450 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma452 a r:Inference; +skolem:lemma451 a r:Inference; r:gives { - (2451 6174) :recursionsNeeded 2 . + 2451 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 451}] [ a r:Fact; r:gives {(451 2000) math:sum 2451}] - skolem:lemma1453 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1451 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma453 a r:Inference; +skolem:lemma452 a r:Inference; r:gives { - (2452 6174) :recursionsNeeded 5 . + 2452 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 452}] [ a r:Fact; r:gives {(452 2000) math:sum 2452}] - skolem:lemma1454 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1452 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma454 a r:Inference; +skolem:lemma453 a r:Inference; r:gives { - (2453 6174) :recursionsNeeded 3 . + 2453 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 453}] [ a r:Fact; r:gives {(453 2000) math:sum 2453}] - skolem:lemma1455 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1453 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma455 a r:Inference; +skolem:lemma454 a r:Inference; r:gives { - (2454 6174) :recursionsNeeded 6 . + 2454 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 454}] [ a r:Fact; r:gives {(454 2000) math:sum 2454}] - skolem:lemma1456 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1454 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma456 a r:Inference; +skolem:lemma455 a r:Inference; r:gives { - (2455 6174) :recursionsNeeded 3 . + 2455 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 455}] [ a r:Fact; r:gives {(455 2000) math:sum 2455}] - skolem:lemma1457 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1455 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma457 a r:Inference; +skolem:lemma456 a r:Inference; r:gives { - (2456 6174) :recursionsNeeded 7 . + 2456 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 456}] [ a r:Fact; r:gives {(456 2000) math:sum 2456}] - skolem:lemma1458 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1456 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma458 a r:Inference; +skolem:lemma457 a r:Inference; r:gives { - (2457 6174) :recursionsNeeded 7 . + 2457 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 457}] [ a r:Fact; r:gives {(457 2000) math:sum 2457}] - skolem:lemma1459 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1457 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma459 a r:Inference; +skolem:lemma458 a r:Inference; r:gives { - (2458 6174) :recursionsNeeded 7 . + 2458 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 458}] [ a r:Fact; r:gives {(458 2000) math:sum 2458}] - skolem:lemma1460 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1458 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma460 a r:Inference; +skolem:lemma459 a r:Inference; r:gives { - (2459 6174) :recursionsNeeded 3 . + 2459 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 459}] [ a r:Fact; r:gives {(459 2000) math:sum 2459}] - skolem:lemma1461 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1459 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma461 a r:Inference; +skolem:lemma460 a r:Inference; r:gives { - (2460 6174) :recursionsNeeded 1 . + 2460 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 460}] [ a r:Fact; r:gives {(460 2000) math:sum 2460}] - skolem:lemma1462 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1460 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma462 a r:Inference; +skolem:lemma461 a r:Inference; r:gives { - (2461 6174) :recursionsNeeded 7 . + 2461 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 461}] [ a r:Fact; r:gives {(461 2000) math:sum 2461}] - skolem:lemma1463 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1461 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma463 a r:Inference; +skolem:lemma462 a r:Inference; r:gives { - (2462 6174) :recursionsNeeded 2 . + 2462 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 462}] [ a r:Fact; r:gives {(462 2000) math:sum 2462}] - skolem:lemma1464 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1462 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma464 a r:Inference; +skolem:lemma463 a r:Inference; r:gives { - (2463 6174) :recursionsNeeded 7 . + 2463 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 463}] [ a r:Fact; r:gives {(463 2000) math:sum 2463}] - skolem:lemma1465 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1463 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma465 a r:Inference; +skolem:lemma464 a r:Inference; r:gives { - (2464 6174) :recursionsNeeded 4 . + 2464 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 464}] [ a r:Fact; r:gives {(464 2000) math:sum 2464}] - skolem:lemma1466 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1464 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma466 a r:Inference; +skolem:lemma465 a r:Inference; r:gives { - (2465 6174) :recursionsNeeded 7 . + 2465 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 465}] [ a r:Fact; r:gives {(465 2000) math:sum 2465}] - skolem:lemma1467 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1465 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma467 a r:Inference; +skolem:lemma466 a r:Inference; r:gives { - (2466 6174) :recursionsNeeded 2 . + 2466 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 466}] [ a r:Fact; r:gives {(466 2000) math:sum 2466}] - skolem:lemma1468 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1466 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma468 a r:Inference; +skolem:lemma467 a r:Inference; r:gives { - (2467 6174) :recursionsNeeded 7 . + 2467 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 467}] [ a r:Fact; r:gives {(467 2000) math:sum 2467}] - skolem:lemma1469 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1467 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma469 a r:Inference; +skolem:lemma468 a r:Inference; r:gives { - (2468 6174) :recursionsNeeded 1 . + 2468 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 468}] [ a r:Fact; r:gives {(468 2000) math:sum 2468}] - skolem:lemma1470 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1468 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma470 a r:Inference; +skolem:lemma469 a r:Inference; r:gives { - (2469 6174) :recursionsNeeded 5 . + 2469 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 469}] [ a r:Fact; r:gives {(469 2000) math:sum 2469}] - skolem:lemma1471 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1469 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma471 a r:Inference; +skolem:lemma470 a r:Inference; r:gives { - (2470 6174) :recursionsNeeded 5 . + 2470 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 470}] [ a r:Fact; r:gives {(470 2000) math:sum 2470}] - skolem:lemma1472 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1470 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma472 a r:Inference; +skolem:lemma471 a r:Inference; r:gives { - (2471 6174) :recursionsNeeded 1 . + 2471 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 471}] [ a r:Fact; r:gives {(471 2000) math:sum 2471}] - skolem:lemma1473 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1471 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma473 a r:Inference; +skolem:lemma472 a r:Inference; r:gives { - (2472 6174) :recursionsNeeded 7 . + 2472 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 472}] [ a r:Fact; r:gives {(472 2000) math:sum 2472}] - skolem:lemma1474 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1472 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma474 a r:Inference; +skolem:lemma473 a r:Inference; r:gives { - (2473 6174) :recursionsNeeded 7 . + 2473 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 473}] [ a r:Fact; r:gives {(473 2000) math:sum 2473}] - skolem:lemma1475 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1473 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma475 a r:Inference; +skolem:lemma474 a r:Inference; r:gives { - (2474 6174) :recursionsNeeded 6 . + 2474 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 474}] [ a r:Fact; r:gives {(474 2000) math:sum 2474}] - skolem:lemma1476 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1474 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma476 a r:Inference; +skolem:lemma475 a r:Inference; r:gives { - (2475 6174) :recursionsNeeded 7 . + 2475 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 475}] [ a r:Fact; r:gives {(475 2000) math:sum 2475}] - skolem:lemma1477 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1475 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma477 a r:Inference; +skolem:lemma476 a r:Inference; r:gives { - (2476 6174) :recursionsNeeded 7 . + 2476 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 476}] [ a r:Fact; r:gives {(476 2000) math:sum 2476}] - skolem:lemma1478 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1476 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma478 a r:Inference; +skolem:lemma477 a r:Inference; r:gives { - (2477 6174) :recursionsNeeded 5 . + 2477 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 477}] [ a r:Fact; r:gives {(477 2000) math:sum 2477}] - skolem:lemma1479 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1477 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma479 a r:Inference; +skolem:lemma478 a r:Inference; r:gives { - (2478 6174) :recursionsNeeded 3 . + 2478 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 478}] [ a r:Fact; r:gives {(478 2000) math:sum 2478}] - skolem:lemma1480 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1478 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma480 a r:Inference; +skolem:lemma479 a r:Inference; r:gives { - (2479 6174) :recursionsNeeded 6 . + 2479 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 479}] [ a r:Fact; r:gives {(479 2000) math:sum 2479}] - skolem:lemma1481 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1479 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma481 a r:Inference; +skolem:lemma480 a r:Inference; r:gives { - (2480 6174) :recursionsNeeded 6 . + 2480 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 480}] [ a r:Fact; r:gives {(480 2000) math:sum 2480}] - skolem:lemma1482 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1480 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma482 a r:Inference; +skolem:lemma481 a r:Inference; r:gives { - (2481 6174) :recursionsNeeded 5 . + 2481 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 481}] [ a r:Fact; r:gives {(481 2000) math:sum 2481}] - skolem:lemma1483 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1481 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma483 a r:Inference; +skolem:lemma482 a r:Inference; r:gives { - (2482 6174) :recursionsNeeded 1 . + 2482 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 482}] [ a r:Fact; r:gives {(482 2000) math:sum 2482}] - skolem:lemma1484 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1482 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma484 a r:Inference; +skolem:lemma483 a r:Inference; r:gives { - (2483 6174) :recursionsNeeded 7 . + 2483 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 483}] [ a r:Fact; r:gives {(483 2000) math:sum 2483}] - skolem:lemma1485 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1483 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma485 a r:Inference; +skolem:lemma484 a r:Inference; r:gives { - (2484 6174) :recursionsNeeded 6 . + 2484 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 484}] [ a r:Fact; r:gives {(484 2000) math:sum 2484}] - skolem:lemma1486 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1484 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma486 a r:Inference; +skolem:lemma485 a r:Inference; r:gives { - (2485 6174) :recursionsNeeded 7 . + 2485 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 485}] [ a r:Fact; r:gives {(485 2000) math:sum 2485}] - skolem:lemma1487 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1485 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma487 a r:Inference; +skolem:lemma486 a r:Inference; r:gives { - (2486 6174) :recursionsNeeded 1 . + 2486 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 486}] [ a r:Fact; r:gives {(486 2000) math:sum 2486}] - skolem:lemma1488 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1486 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma488 a r:Inference; +skolem:lemma487 a r:Inference; r:gives { - (2487 6174) :recursionsNeeded 3 . + 2487 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 487}] [ a r:Fact; r:gives {(487 2000) math:sum 2487}] - skolem:lemma1489 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1487 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma489 a r:Inference; +skolem:lemma488 a r:Inference; r:gives { - (2488 6174) :recursionsNeeded 4 . + 2488 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 488}] [ a r:Fact; r:gives {(488 2000) math:sum 2488}] - skolem:lemma1490 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1488 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma490 a r:Inference; +skolem:lemma489 a r:Inference; r:gives { - (2489 6174) :recursionsNeeded 3 . + 2489 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 489}] [ a r:Fact; r:gives {(489 2000) math:sum 2489}] - skolem:lemma1491 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1489 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma491 a r:Inference; +skolem:lemma490 a r:Inference; r:gives { - (2490 6174) :recursionsNeeded 3 . + 2490 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 490}] [ a r:Fact; r:gives {(490 2000) math:sum 2490}] - skolem:lemma1492 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1490 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma492 a r:Inference; +skolem:lemma491 a r:Inference; r:gives { - (2491 6174) :recursionsNeeded 6 . + 2491 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 491}] [ a r:Fact; r:gives {(491 2000) math:sum 2491}] - skolem:lemma1493 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1491 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma493 a r:Inference; +skolem:lemma492 a r:Inference; r:gives { - (2492 6174) :recursionsNeeded 5 . + 2492 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 492}] [ a r:Fact; r:gives {(492 2000) math:sum 2492}] - skolem:lemma1494 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1492 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma494 a r:Inference; +skolem:lemma493 a r:Inference; r:gives { - (2493 6174) :recursionsNeeded 3 . + 2493 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 493}] [ a r:Fact; r:gives {(493 2000) math:sum 2493}] - skolem:lemma1495 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1493 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma495 a r:Inference; +skolem:lemma494 a r:Inference; r:gives { - (2494 6174) :recursionsNeeded 4 . + 2494 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 494}] [ a r:Fact; r:gives {(494 2000) math:sum 2494}] - skolem:lemma1496 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1494 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma496 a r:Inference; +skolem:lemma495 a r:Inference; r:gives { - (2495 6174) :recursionsNeeded 3 . + 2495 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 495}] [ a r:Fact; r:gives {(495 2000) math:sum 2495}] - skolem:lemma1497 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1495 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma497 a r:Inference; +skolem:lemma496 a r:Inference; r:gives { - (2496 6174) :recursionsNeeded 5 . + 2496 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 496}] [ a r:Fact; r:gives {(496 2000) math:sum 2496}] - skolem:lemma1498 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1496 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma498 a r:Inference; +skolem:lemma497 a r:Inference; r:gives { - (2497 6174) :recursionsNeeded 6 . + 2497 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 497}] [ a r:Fact; r:gives {(497 2000) math:sum 2497}] - skolem:lemma1499 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1497 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma499 a r:Inference; +skolem:lemma498 a r:Inference; r:gives { - (2498 6174) :recursionsNeeded 3 . + 2498 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 498}] [ a r:Fact; r:gives {(498 2000) math:sum 2498}] - skolem:lemma1500 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1498 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma500 a r:Inference; +skolem:lemma499 a r:Inference; r:gives { - (2499 6174) :recursionsNeeded 5 . + 2499 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 499}] [ a r:Fact; r:gives {(499 2000) math:sum 2499}] - skolem:lemma1501 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1499 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma501 a r:Inference; +skolem:lemma500 a r:Inference; r:gives { - (2500 6174) :recursionsNeeded 7 . + 2500 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 500}] [ a r:Fact; r:gives {(500 2000) math:sum 2500}] - skolem:lemma1502 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1500 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma502 a r:Inference; +skolem:lemma501 a r:Inference; r:gives { - (2501 6174) :recursionsNeeded 7 . + 2501 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 501}] [ a r:Fact; r:gives {(501 2000) math:sum 2501}] - skolem:lemma1503 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1501 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma503 a r:Inference; +skolem:lemma502 a r:Inference; r:gives { - (2502 6174) :recursionsNeeded 6 . + 2502 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 502}] [ a r:Fact; r:gives {(502 2000) math:sum 2502}] - skolem:lemma1504 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1502 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma504 a r:Inference; +skolem:lemma503 a r:Inference; r:gives { - (2503 6174) :recursionsNeeded 7 . + 2503 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 503}] [ a r:Fact; r:gives {(503 2000) math:sum 2503}] - skolem:lemma1505 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1503 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma505 a r:Inference; +skolem:lemma504 a r:Inference; r:gives { - (2504 6174) :recursionsNeeded 7 . + 2504 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 504}] [ a r:Fact; r:gives {(504 2000) math:sum 2504}] - skolem:lemma1506 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1504 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma506 a r:Inference; +skolem:lemma505 a r:Inference; r:gives { - (2505 6174) :recursionsNeeded 5 . + 2505 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 505}] [ a r:Fact; r:gives {(505 2000) math:sum 2505}] - skolem:lemma1507 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1505 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma507 a r:Inference; +skolem:lemma506 a r:Inference; r:gives { - (2506 6174) :recursionsNeeded 3 . + 2506 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 506}] [ a r:Fact; r:gives {(506 2000) math:sum 2506}] - skolem:lemma1508 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1506 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma508 a r:Inference; +skolem:lemma507 a r:Inference; r:gives { - (2507 6174) :recursionsNeeded 6 . + 2507 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 507}] [ a r:Fact; r:gives {(507 2000) math:sum 2507}] - skolem:lemma1509 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1507 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma509 a r:Inference; +skolem:lemma508 a r:Inference; r:gives { - (2508 6174) :recursionsNeeded 5 . + 2508 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 508}] [ a r:Fact; r:gives {(508 2000) math:sum 2508}] - skolem:lemma1510 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1508 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma510 a r:Inference; +skolem:lemma509 a r:Inference; r:gives { - (2509 6174) :recursionsNeeded 3 . + 2509 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 509}] [ a r:Fact; r:gives {(509 2000) math:sum 2509}] - skolem:lemma1511 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1509 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma511 a r:Inference; +skolem:lemma510 a r:Inference; r:gives { - (2510 6174) :recursionsNeeded 7 . + 2510 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 510}] [ a r:Fact; r:gives {(510 2000) math:sum 2510}] - skolem:lemma1512 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1510 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma512 a r:Inference; +skolem:lemma511 a r:Inference; r:gives { - (2511 6174) :recursionsNeeded 7 . + 2511 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 511}] [ a r:Fact; r:gives {(511 2000) math:sum 2511}] - skolem:lemma1513 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1511 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma513 a r:Inference; +skolem:lemma512 a r:Inference; r:gives { - (2512 6174) :recursionsNeeded 4 . + 2512 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 512}] [ a r:Fact; r:gives {(512 2000) math:sum 2512}] - skolem:lemma1514 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1512 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma514 a r:Inference; +skolem:lemma513 a r:Inference; r:gives { - (2513 6174) :recursionsNeeded 7 . + 2513 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 513}] [ a r:Fact; r:gives {(513 2000) math:sum 2513}] - skolem:lemma1515 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1513 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma515 a r:Inference; +skolem:lemma514 a r:Inference; r:gives { - (2514 6174) :recursionsNeeded 2 . + 2514 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 514}] [ a r:Fact; r:gives {(514 2000) math:sum 2514}] - skolem:lemma1516 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1514 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma516 a r:Inference; +skolem:lemma515 a r:Inference; r:gives { - (2515 6174) :recursionsNeeded 3 . + 2515 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 515}] [ a r:Fact; r:gives {(515 2000) math:sum 2515}] - skolem:lemma1517 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1515 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma517 a r:Inference; +skolem:lemma516 a r:Inference; r:gives { - (2516 6174) :recursionsNeeded 5 . + 2516 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 516}] [ a r:Fact; r:gives {(516 2000) math:sum 2516}] - skolem:lemma1518 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1516 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma518 a r:Inference; +skolem:lemma517 a r:Inference; r:gives { - (2517 6174) :recursionsNeeded 3 . + 2517 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 517}] [ a r:Fact; r:gives {(517 2000) math:sum 2517}] - skolem:lemma1519 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1517 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma519 a r:Inference; +skolem:lemma518 a r:Inference; r:gives { - (2518 6174) :recursionsNeeded 6 . + 2518 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 518}] [ a r:Fact; r:gives {(518 2000) math:sum 2518}] - skolem:lemma1520 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1518 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma520 a r:Inference; +skolem:lemma519 a r:Inference; r:gives { - (2519 6174) :recursionsNeeded 5 . + 2519 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 519}] [ a r:Fact; r:gives {(519 2000) math:sum 2519}] - skolem:lemma1521 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1519 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma521 a r:Inference; +skolem:lemma520 a r:Inference; r:gives { - (2520 6174) :recursionsNeeded 6 . + 2520 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 520}] [ a r:Fact; r:gives {(520 2000) math:sum 2520}] - skolem:lemma1522 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1520 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma522 a r:Inference; +skolem:lemma521 a r:Inference; r:gives { - (2521 6174) :recursionsNeeded 4 . + 2521 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 521}] [ a r:Fact; r:gives {(521 2000) math:sum 2521}] - skolem:lemma1523 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1521 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma523 a r:Inference; +skolem:lemma522 a r:Inference; r:gives { - (2522 6174) :recursionsNeeded 6 . + 2522 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 522}] [ a r:Fact; r:gives {(522 2000) math:sum 2522}] - skolem:lemma1524 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1522 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma524 a r:Inference; +skolem:lemma523 a r:Inference; r:gives { - (2523 6174) :recursionsNeeded 3 . + 2523 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 523}] [ a r:Fact; r:gives {(523 2000) math:sum 2523}] - skolem:lemma1525 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1523 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma525 a r:Inference; +skolem:lemma524 a r:Inference; r:gives { - (2524 6174) :recursionsNeeded 5 . + 2524 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 524}] [ a r:Fact; r:gives {(524 2000) math:sum 2524}] - skolem:lemma1526 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1524 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma526 a r:Inference; +skolem:lemma525 a r:Inference; r:gives { - (2525 6174) :recursionsNeeded 6 . + 2525 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 525}] [ a r:Fact; r:gives {(525 2000) math:sum 2525}] - skolem:lemma1527 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1525 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma527 a r:Inference; +skolem:lemma526 a r:Inference; r:gives { - (2526 6174) :recursionsNeeded 3 . + 2526 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 526}] [ a r:Fact; r:gives {(526 2000) math:sum 2526}] - skolem:lemma1528 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1526 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma528 a r:Inference; +skolem:lemma527 a r:Inference; r:gives { - (2527 6174) :recursionsNeeded 5 . + 2527 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 527}] [ a r:Fact; r:gives {(527 2000) math:sum 2527}] - skolem:lemma1529 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1527 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma529 a r:Inference; +skolem:lemma528 a r:Inference; r:gives { - (2528 6174) :recursionsNeeded 3 . + 2528 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 528}] [ a r:Fact; r:gives {(528 2000) math:sum 2528}] - skolem:lemma1530 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1528 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma530 a r:Inference; +skolem:lemma529 a r:Inference; r:gives { - (2529 6174) :recursionsNeeded 6 . + 2529 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 529}] [ a r:Fact; r:gives {(529 2000) math:sum 2529}] - skolem:lemma1531 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1529 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma531 a r:Inference; +skolem:lemma530 a r:Inference; r:gives { - (2530 6174) :recursionsNeeded 7 . + 2530 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 530}] [ a r:Fact; r:gives {(530 2000) math:sum 2530}] - skolem:lemma1532 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1530 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma532 a r:Inference; +skolem:lemma531 a r:Inference; r:gives { - (2531 6174) :recursionsNeeded 7 . + 2531 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 531}] [ a r:Fact; r:gives {(531 2000) math:sum 2531}] - skolem:lemma1533 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1531 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma533 a r:Inference; +skolem:lemma532 a r:Inference; r:gives { - (2532 6174) :recursionsNeeded 3 . + 2532 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 532}] [ a r:Fact; r:gives {(532 2000) math:sum 2532}] - skolem:lemma1534 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1532 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma534 a r:Inference; +skolem:lemma533 a r:Inference; r:gives { - (2533 6174) :recursionsNeeded 6 . + 2533 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 533}] [ a r:Fact; r:gives {(533 2000) math:sum 2533}] - skolem:lemma1535 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1533 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma535 a r:Inference; +skolem:lemma534 a r:Inference; r:gives { - (2534 6174) :recursionsNeeded 3 . + 2534 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 534}] [ a r:Fact; r:gives {(534 2000) math:sum 2534}] - skolem:lemma1536 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1534 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma536 a r:Inference; +skolem:lemma535 a r:Inference; r:gives { - (2535 6174) :recursionsNeeded 5 . + 2535 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 535}] [ a r:Fact; r:gives {(535 2000) math:sum 2535}] - skolem:lemma1537 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1535 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma537 a r:Inference; +skolem:lemma536 a r:Inference; r:gives { - (2536 6174) :recursionsNeeded 2 . + 2536 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 536}] [ a r:Fact; r:gives {(536 2000) math:sum 2536}] - skolem:lemma1538 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1536 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma538 a r:Inference; +skolem:lemma537 a r:Inference; r:gives { - (2537 6174) :recursionsNeeded 7 . + 2537 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 537}] [ a r:Fact; r:gives {(537 2000) math:sum 2537}] - skolem:lemma1539 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1537 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma539 a r:Inference; +skolem:lemma538 a r:Inference; r:gives { - (2538 6174) :recursionsNeeded 1 . + 2538 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 538}] [ a r:Fact; r:gives {(538 2000) math:sum 2538}] - skolem:lemma1540 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1538 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma540 a r:Inference; +skolem:lemma539 a r:Inference; r:gives { - (2539 6174) :recursionsNeeded 5 . + 2539 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 539}] [ a r:Fact; r:gives {(539 2000) math:sum 2539}] - skolem:lemma1541 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1539 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma541 a r:Inference; +skolem:lemma540 a r:Inference; r:gives { - (2540 6174) :recursionsNeeded 7 . + 2540 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 540}] [ a r:Fact; r:gives {(540 2000) math:sum 2540}] - skolem:lemma1542 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1540 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma542 a r:Inference; +skolem:lemma541 a r:Inference; r:gives { - (2541 6174) :recursionsNeeded 2 . + 2541 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 541}] [ a r:Fact; r:gives {(541 2000) math:sum 2541}] - skolem:lemma1543 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1541 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma543 a r:Inference; +skolem:lemma542 a r:Inference; r:gives { - (2542 6174) :recursionsNeeded 5 . + 2542 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 542}] [ a r:Fact; r:gives {(542 2000) math:sum 2542}] - skolem:lemma1544 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1542 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma544 a r:Inference; +skolem:lemma543 a r:Inference; r:gives { - (2543 6174) :recursionsNeeded 3 . + 2543 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 543}] [ a r:Fact; r:gives {(543 2000) math:sum 2543}] - skolem:lemma1545 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1543 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma545 a r:Inference; +skolem:lemma544 a r:Inference; r:gives { - (2544 6174) :recursionsNeeded 6 . + 2544 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 544}] [ a r:Fact; r:gives {(544 2000) math:sum 2544}] - skolem:lemma1546 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1544 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma546 a r:Inference; +skolem:lemma545 a r:Inference; r:gives { - (2545 6174) :recursionsNeeded 3 . + 2545 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 545}] [ a r:Fact; r:gives {(545 2000) math:sum 2545}] - skolem:lemma1547 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1545 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma547 a r:Inference; +skolem:lemma546 a r:Inference; r:gives { - (2546 6174) :recursionsNeeded 7 . + 2546 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 546}] [ a r:Fact; r:gives {(546 2000) math:sum 2546}] - skolem:lemma1548 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1546 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma548 a r:Inference; +skolem:lemma547 a r:Inference; r:gives { - (2547 6174) :recursionsNeeded 7 . + 2547 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 547}] [ a r:Fact; r:gives {(547 2000) math:sum 2547}] - skolem:lemma1549 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1547 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma549 a r:Inference; +skolem:lemma548 a r:Inference; r:gives { - (2548 6174) :recursionsNeeded 7 . + 2548 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 548}] [ a r:Fact; r:gives {(548 2000) math:sum 2548}] - skolem:lemma1550 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1548 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma550 a r:Inference; +skolem:lemma549 a r:Inference; r:gives { - (2549 6174) :recursionsNeeded 3 . + 2549 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 549}] [ a r:Fact; r:gives {(549 2000) math:sum 2549}] - skolem:lemma1551 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1549 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma551 a r:Inference; +skolem:lemma550 a r:Inference; r:gives { - (2550 6174) :recursionsNeeded 5 . + 2550 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 550}] [ a r:Fact; r:gives {(550 2000) math:sum 2550}] - skolem:lemma1552 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1550 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma552 a r:Inference; +skolem:lemma551 a r:Inference; r:gives { - (2551 6174) :recursionsNeeded 3 . + 2551 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 551}] [ a r:Fact; r:gives {(551 2000) math:sum 2551}] - skolem:lemma1553 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1551 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma553 a r:Inference; +skolem:lemma552 a r:Inference; r:gives { - (2552 6174) :recursionsNeeded 6 . + 2552 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 552}] [ a r:Fact; r:gives {(552 2000) math:sum 2552}] - skolem:lemma1554 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1552 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma554 a r:Inference; +skolem:lemma553 a r:Inference; r:gives { - (2553 6174) :recursionsNeeded 5 . + 2553 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 553}] [ a r:Fact; r:gives {(553 2000) math:sum 2553}] - skolem:lemma1555 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1553 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma555 a r:Inference; +skolem:lemma554 a r:Inference; r:gives { - (2554 6174) :recursionsNeeded 3 . + 2554 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 554}] [ a r:Fact; r:gives {(554 2000) math:sum 2554}] - skolem:lemma1556 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1554 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma556 a r:Inference; +skolem:lemma555 a r:Inference; r:gives { - (2555 6174) :recursionsNeeded 6 . + 2555 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 555}] [ a r:Fact; r:gives {(555 2000) math:sum 2555}] - skolem:lemma1557 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1555 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma557 a r:Inference; +skolem:lemma556 a r:Inference; r:gives { - (2556 6174) :recursionsNeeded 4 . + 2556 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 556}] [ a r:Fact; r:gives {(556 2000) math:sum 2556}] - skolem:lemma1558 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1556 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma558 a r:Inference; +skolem:lemma557 a r:Inference; r:gives { - (2557 6174) :recursionsNeeded 6 . + 2557 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 557}] [ a r:Fact; r:gives {(557 2000) math:sum 2557}] - skolem:lemma1559 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1557 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma559 a r:Inference; +skolem:lemma558 a r:Inference; r:gives { - (2558 6174) :recursionsNeeded 6 . + 2558 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 558}] [ a r:Fact; r:gives {(558 2000) math:sum 2558}] - skolem:lemma1560 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1558 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma560 a r:Inference; +skolem:lemma559 a r:Inference; r:gives { - (2559 6174) :recursionsNeeded 4 . + 2559 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 559}] [ a r:Fact; r:gives {(559 2000) math:sum 2559}] - skolem:lemma1561 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1559 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma561 a r:Inference; +skolem:lemma560 a r:Inference; r:gives { - (2560 6174) :recursionsNeeded 3 . + 2560 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 560}] [ a r:Fact; r:gives {(560 2000) math:sum 2560}] - skolem:lemma1562 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1560 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma562 a r:Inference; +skolem:lemma561 a r:Inference; r:gives { - (2561 6174) :recursionsNeeded 5 . + 2561 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 561}] [ a r:Fact; r:gives {(561 2000) math:sum 2561}] - skolem:lemma1563 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1561 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma563 a r:Inference; +skolem:lemma562 a r:Inference; r:gives { - (2562 6174) :recursionsNeeded 3 . + 2562 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 562}] [ a r:Fact; r:gives {(562 2000) math:sum 2562}] - skolem:lemma1564 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1562 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma564 a r:Inference; +skolem:lemma563 a r:Inference; r:gives { - (2563 6174) :recursionsNeeded 2 . + 2563 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 563}] [ a r:Fact; r:gives {(563 2000) math:sum 2563}] - skolem:lemma1565 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1563 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma565 a r:Inference; +skolem:lemma564 a r:Inference; r:gives { - (2564 6174) :recursionsNeeded 7 . + 2564 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 564}] [ a r:Fact; r:gives {(564 2000) math:sum 2564}] - skolem:lemma1566 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1564 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma566 a r:Inference; +skolem:lemma565 a r:Inference; r:gives { - (2565 6174) :recursionsNeeded 4 . + 2565 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 565}] [ a r:Fact; r:gives {(565 2000) math:sum 2565}] - skolem:lemma1567 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1565 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma567 a r:Inference; +skolem:lemma566 a r:Inference; r:gives { - (2566 6174) :recursionsNeeded 7 . + 2566 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 566}] [ a r:Fact; r:gives {(566 2000) math:sum 2566}] - skolem:lemma1568 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1566 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma568 a r:Inference; +skolem:lemma567 a r:Inference; r:gives { - (2567 6174) :recursionsNeeded 7 . + 2567 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 567}] [ a r:Fact; r:gives {(567 2000) math:sum 2567}] - skolem:lemma1569 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1567 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma569 a r:Inference; +skolem:lemma568 a r:Inference; r:gives { - (2568 6174) :recursionsNeeded 7 . + 2568 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 568}] [ a r:Fact; r:gives {(568 2000) math:sum 2568}] - skolem:lemma1570 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1568 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma570 a r:Inference; +skolem:lemma569 a r:Inference; r:gives { - (2569 6174) :recursionsNeeded 3 . + 2569 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 569}] [ a r:Fact; r:gives {(569 2000) math:sum 2569}] - skolem:lemma1571 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1569 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma571 a r:Inference; +skolem:lemma570 a r:Inference; r:gives { - (2570 6174) :recursionsNeeded 6 . + 2570 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 570}] [ a r:Fact; r:gives {(570 2000) math:sum 2570}] - skolem:lemma1572 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1570 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma572 a r:Inference; +skolem:lemma571 a r:Inference; r:gives { - (2571 6174) :recursionsNeeded 3 . + 2571 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 571}] [ a r:Fact; r:gives {(571 2000) math:sum 2571}] - skolem:lemma1573 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1571 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma573 a r:Inference; +skolem:lemma572 a r:Inference; r:gives { - (2572 6174) :recursionsNeeded 5 . + 2572 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 572}] [ a r:Fact; r:gives {(572 2000) math:sum 2572}] - skolem:lemma1574 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1572 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma574 a r:Inference; +skolem:lemma573 a r:Inference; r:gives { - (2573 6174) :recursionsNeeded 7 . + 2573 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 573}] [ a r:Fact; r:gives {(573 2000) math:sum 2573}] - skolem:lemma1575 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1573 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma575 a r:Inference; +skolem:lemma574 a r:Inference; r:gives { - (2574 6174) :recursionsNeeded 7 . + 2574 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 574}] [ a r:Fact; r:gives {(574 2000) math:sum 2574}] - skolem:lemma1576 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1574 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma576 a r:Inference; +skolem:lemma575 a r:Inference; r:gives { - (2575 6174) :recursionsNeeded 6 . + 2575 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 575}] [ a r:Fact; r:gives {(575 2000) math:sum 2575}] - skolem:lemma1577 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1575 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma577 a r:Inference; +skolem:lemma576 a r:Inference; r:gives { - (2576 6174) :recursionsNeeded 7 . + 2576 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 576}] [ a r:Fact; r:gives {(576 2000) math:sum 2576}] - skolem:lemma1578 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1576 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma578 a r:Inference; +skolem:lemma577 a r:Inference; r:gives { - (2577 6174) :recursionsNeeded 7 . + 2577 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 577}] [ a r:Fact; r:gives {(577 2000) math:sum 2577}] - skolem:lemma1579 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1577 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma579 a r:Inference; +skolem:lemma578 a r:Inference; r:gives { - (2578 6174) :recursionsNeeded 1 . + 2578 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 578}] [ a r:Fact; r:gives {(578 2000) math:sum 2578}] - skolem:lemma1580 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1578 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma580 a r:Inference; +skolem:lemma579 a r:Inference; r:gives { - (2579 6174) :recursionsNeeded 5 . + 2579 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 579}] [ a r:Fact; r:gives {(579 2000) math:sum 2579}] - skolem:lemma1581 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1579 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma581 a r:Inference; +skolem:lemma580 a r:Inference; r:gives { - (2580 6174) :recursionsNeeded 5 . + 2580 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 580}] [ a r:Fact; r:gives {(580 2000) math:sum 2580}] - skolem:lemma1582 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1580 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma582 a r:Inference; +skolem:lemma581 a r:Inference; r:gives { - (2581 6174) :recursionsNeeded 6 . + 2581 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 581}] [ a r:Fact; r:gives {(581 2000) math:sum 2581}] - skolem:lemma1583 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1581 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma583 a r:Inference; +skolem:lemma582 a r:Inference; r:gives { - (2582 6174) :recursionsNeeded 3 . + 2582 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 582}] [ a r:Fact; r:gives {(582 2000) math:sum 2582}] - skolem:lemma1584 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1582 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma584 a r:Inference; +skolem:lemma583 a r:Inference; r:gives { - (2583 6174) :recursionsNeeded 1 . + 2583 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 583}] [ a r:Fact; r:gives {(583 2000) math:sum 2583}] - skolem:lemma1585 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1583 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma585 a r:Inference; +skolem:lemma584 a r:Inference; r:gives { - (2584 6174) :recursionsNeeded 7 . + 2584 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 584}] [ a r:Fact; r:gives {(584 2000) math:sum 2584}] - skolem:lemma1586 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1584 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma586 a r:Inference; +skolem:lemma585 a r:Inference; r:gives { - (2585 6174) :recursionsNeeded 6 . + 2585 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 585}] [ a r:Fact; r:gives {(585 2000) math:sum 2585}] - skolem:lemma1587 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1585 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma587 a r:Inference; +skolem:lemma586 a r:Inference; r:gives { - (2586 6174) :recursionsNeeded 7 . + 2586 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 586}] [ a r:Fact; r:gives {(586 2000) math:sum 2586}] - skolem:lemma1588 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1586 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma588 a r:Inference; +skolem:lemma587 a r:Inference; r:gives { - (2587 6174) :recursionsNeeded 1 . + 2587 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 587}] [ a r:Fact; r:gives {(587 2000) math:sum 2587}] - skolem:lemma1589 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1587 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma589 a r:Inference; +skolem:lemma588 a r:Inference; r:gives { - (2588 6174) :recursionsNeeded 3 . + 2588 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 588}] [ a r:Fact; r:gives {(588 2000) math:sum 2588}] - skolem:lemma1590 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1588 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma590 a r:Inference; +skolem:lemma589 a r:Inference; r:gives { - (2589 6174) :recursionsNeeded 6 . + 2589 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 589}] [ a r:Fact; r:gives {(589 2000) math:sum 2589}] - skolem:lemma1591 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1589 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma591 a r:Inference; +skolem:lemma590 a r:Inference; r:gives { - (2590 6174) :recursionsNeeded 3 . + 2590 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 590}] [ a r:Fact; r:gives {(590 2000) math:sum 2590}] - skolem:lemma1592 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1590 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma592 a r:Inference; +skolem:lemma591 a r:Inference; r:gives { - (2591 6174) :recursionsNeeded 5 . + 2591 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 591}] [ a r:Fact; r:gives {(591 2000) math:sum 2591}] - skolem:lemma1593 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1591 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma593 a r:Inference; +skolem:lemma592 a r:Inference; r:gives { - (2592 6174) :recursionsNeeded 6 . + 2592 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 592}] [ a r:Fact; r:gives {(592 2000) math:sum 2592}] - skolem:lemma1594 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1592 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma594 a r:Inference; +skolem:lemma593 a r:Inference; r:gives { - (2593 6174) :recursionsNeeded 5 . + 2593 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 593}] [ a r:Fact; r:gives {(593 2000) math:sum 2593}] - skolem:lemma1595 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1593 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma595 a r:Inference; +skolem:lemma594 a r:Inference; r:gives { - (2594 6174) :recursionsNeeded 3 . + 2594 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 594}] [ a r:Fact; r:gives {(594 2000) math:sum 2594}] - skolem:lemma1596 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1594 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma596 a r:Inference; +skolem:lemma595 a r:Inference; r:gives { - (2595 6174) :recursionsNeeded 4 . + 2595 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 595}] [ a r:Fact; r:gives {(595 2000) math:sum 2595}] - skolem:lemma1597 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1595 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma597 a r:Inference; +skolem:lemma596 a r:Inference; r:gives { - (2596 6174) :recursionsNeeded 3 . + 2596 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 596}] [ a r:Fact; r:gives {(596 2000) math:sum 2596}] - skolem:lemma1598 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1596 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma598 a r:Inference; +skolem:lemma597 a r:Inference; r:gives { - (2597 6174) :recursionsNeeded 5 . + 2597 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 597}] [ a r:Fact; r:gives {(597 2000) math:sum 2597}] - skolem:lemma1599 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1597 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma599 a r:Inference; +skolem:lemma598 a r:Inference; r:gives { - (2598 6174) :recursionsNeeded 6 . + 2598 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 598}] [ a r:Fact; r:gives {(598 2000) math:sum 2598}] - skolem:lemma1600 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1598 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma600 a r:Inference; +skolem:lemma599 a r:Inference; r:gives { - (2599 6174) :recursionsNeeded 3 . + 2599 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 599}] [ a r:Fact; r:gives {(599 2000) math:sum 2599}] - skolem:lemma1601 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1599 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma601 a r:Inference; +skolem:lemma600 a r:Inference; r:gives { - (2600 6174) :recursionsNeeded 1 . + 2600 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 600}] [ a r:Fact; r:gives {(600 2000) math:sum 2600}] - skolem:lemma1602 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1600 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma602 a r:Inference; +skolem:lemma601 a r:Inference; r:gives { - (2601 6174) :recursionsNeeded 7 . + 2601 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 601}] [ a r:Fact; r:gives {(601 2000) math:sum 2601}] - skolem:lemma1603 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1601 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma603 a r:Inference; +skolem:lemma602 a r:Inference; r:gives { - (2602 6174) :recursionsNeeded 6 . + 2602 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 602}] [ a r:Fact; r:gives {(602 2000) math:sum 2602}] - skolem:lemma1604 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1602 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma604 a r:Inference; +skolem:lemma603 a r:Inference; r:gives { - (2603 6174) :recursionsNeeded 7 . + 2603 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 603}] [ a r:Fact; r:gives {(603 2000) math:sum 2603}] - skolem:lemma1605 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1603 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma605 a r:Inference; +skolem:lemma604 a r:Inference; r:gives { - (2604 6174) :recursionsNeeded 1 . + 2604 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 604}] [ a r:Fact; r:gives {(604 2000) math:sum 2604}] - skolem:lemma1606 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1604 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma606 a r:Inference; +skolem:lemma605 a r:Inference; r:gives { - (2605 6174) :recursionsNeeded 3 . + 2605 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 605}] [ a r:Fact; r:gives {(605 2000) math:sum 2605}] - skolem:lemma1607 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1605 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma607 a r:Inference; +skolem:lemma606 a r:Inference; r:gives { - (2606 6174) :recursionsNeeded 4 . + 2606 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 606}] [ a r:Fact; r:gives {(606 2000) math:sum 2606}] - skolem:lemma1608 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1606 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma608 a r:Inference; +skolem:lemma607 a r:Inference; r:gives { - (2607 6174) :recursionsNeeded 3 . + 2607 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 607}] [ a r:Fact; r:gives {(607 2000) math:sum 2607}] - skolem:lemma1609 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1607 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma609 a r:Inference; +skolem:lemma608 a r:Inference; r:gives { - (2608 6174) :recursionsNeeded 2 . + 2608 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 608}] [ a r:Fact; r:gives {(608 2000) math:sum 2608}] - skolem:lemma1610 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1608 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma610 a r:Inference; +skolem:lemma609 a r:Inference; r:gives { - (2609 6174) :recursionsNeeded 7 . + 2609 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 609}] [ a r:Fact; r:gives {(609 2000) math:sum 2609}] - skolem:lemma1611 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1609 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma611 a r:Inference; +skolem:lemma610 a r:Inference; r:gives { - (2610 6174) :recursionsNeeded 7 . + 2610 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 610}] [ a r:Fact; r:gives {(610 2000) math:sum 2610}] - skolem:lemma1612 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1610 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma612 a r:Inference; +skolem:lemma611 a r:Inference; r:gives { - (2611 6174) :recursionsNeeded 7 . + 2611 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 611}] [ a r:Fact; r:gives {(611 2000) math:sum 2611}] - skolem:lemma1613 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1611 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma613 a r:Inference; +skolem:lemma612 a r:Inference; r:gives { - (2612 6174) :recursionsNeeded 6 . + 2612 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 612}] [ a r:Fact; r:gives {(612 2000) math:sum 2612}] - skolem:lemma1614 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1612 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma614 a r:Inference; +skolem:lemma613 a r:Inference; r:gives { - (2613 6174) :recursionsNeeded 7 . + 2613 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 613}] [ a r:Fact; r:gives {(613 2000) math:sum 2613}] - skolem:lemma1615 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1613 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma615 a r:Inference; +skolem:lemma614 a r:Inference; r:gives { - (2614 6174) :recursionsNeeded 7 . + 2614 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 614}] [ a r:Fact; r:gives {(614 2000) math:sum 2614}] - skolem:lemma1616 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1614 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma616 a r:Inference; +skolem:lemma615 a r:Inference; r:gives { - (2615 6174) :recursionsNeeded 5 . + 2615 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 615}] [ a r:Fact; r:gives {(615 2000) math:sum 2615}] - skolem:lemma1617 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1615 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma617 a r:Inference; +skolem:lemma616 a r:Inference; r:gives { - (2616 6174) :recursionsNeeded 5 . + 2616 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 616}] [ a r:Fact; r:gives {(616 2000) math:sum 2616}] - skolem:lemma1618 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1616 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma618 a r:Inference; +skolem:lemma617 a r:Inference; r:gives { - (2617 6174) :recursionsNeeded 4 . + 2617 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 617}] [ a r:Fact; r:gives {(617 2000) math:sum 2617}] - skolem:lemma1619 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1617 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma619 a r:Inference; +skolem:lemma618 a r:Inference; r:gives { - (2618 6174) :recursionsNeeded 3 . + 2618 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 618}] [ a r:Fact; r:gives {(618 2000) math:sum 2618}] - skolem:lemma1620 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1618 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma620 a r:Inference; +skolem:lemma619 a r:Inference; r:gives { - (2619 6174) :recursionsNeeded 2 . + 2619 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 619}] [ a r:Fact; r:gives {(619 2000) math:sum 2619}] - skolem:lemma1621 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1619 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma621 a r:Inference; +skolem:lemma620 a r:Inference; r:gives { - (2620 6174) :recursionsNeeded 6 . + 2620 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 620}] [ a r:Fact; r:gives {(620 2000) math:sum 2620}] - skolem:lemma1622 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1620 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma622 a r:Inference; +skolem:lemma621 a r:Inference; r:gives { - (2621 6174) :recursionsNeeded 6 . + 2621 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 621}] [ a r:Fact; r:gives {(621 2000) math:sum 2621}] - skolem:lemma1623 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1621 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma623 a r:Inference; +skolem:lemma622 a r:Inference; r:gives { - (2622 6174) :recursionsNeeded 4 . + 2622 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 622}] [ a r:Fact; r:gives {(622 2000) math:sum 2622}] - skolem:lemma1624 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1622 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma624 a r:Inference; +skolem:lemma623 a r:Inference; r:gives { - (2623 6174) :recursionsNeeded 7 . + 2623 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 623}] [ a r:Fact; r:gives {(623 2000) math:sum 2623}] - skolem:lemma1625 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1623 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma625 a r:Inference; +skolem:lemma624 a r:Inference; r:gives { - (2624 6174) :recursionsNeeded 2 . + 2624 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 624}] [ a r:Fact; r:gives {(624 2000) math:sum 2624}] - skolem:lemma1626 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1624 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma626 a r:Inference; +skolem:lemma625 a r:Inference; r:gives { - (2625 6174) :recursionsNeeded 3 . + 2625 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 625}] [ a r:Fact; r:gives {(625 2000) math:sum 2625}] - skolem:lemma1627 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1625 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma627 a r:Inference; +skolem:lemma626 a r:Inference; r:gives { - (2626 6174) :recursionsNeeded 4 . + 2626 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 626}] [ a r:Fact; r:gives {(626 2000) math:sum 2626}] - skolem:lemma1628 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1626 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma628 a r:Inference; +skolem:lemma627 a r:Inference; r:gives { - (2627 6174) :recursionsNeeded 5 . + 2627 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 627}] [ a r:Fact; r:gives {(627 2000) math:sum 2627}] - skolem:lemma1629 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1627 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma629 a r:Inference; +skolem:lemma628 a r:Inference; r:gives { - (2628 6174) :recursionsNeeded 4 . + 2628 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 628}] [ a r:Fact; r:gives {(628 2000) math:sum 2628}] - skolem:lemma1630 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1628 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma630 a r:Inference; +skolem:lemma629 a r:Inference; r:gives { - (2629 6174) :recursionsNeeded 3 . + 2629 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 629}] [ a r:Fact; r:gives {(629 2000) math:sum 2629}] - skolem:lemma1631 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1629 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma631 a r:Inference; +skolem:lemma630 a r:Inference; r:gives { - (2630 6174) :recursionsNeeded 7 . + 2630 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 630}] [ a r:Fact; r:gives {(630 2000) math:sum 2630}] - skolem:lemma1632 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1630 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma632 a r:Inference; +skolem:lemma631 a r:Inference; r:gives { - (2631 6174) :recursionsNeeded 7 . + 2631 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 631}] [ a r:Fact; r:gives {(631 2000) math:sum 2631}] - skolem:lemma1633 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1631 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma633 a r:Inference; +skolem:lemma632 a r:Inference; r:gives { - (2632 6174) :recursionsNeeded 7 . + 2632 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 632}] [ a r:Fact; r:gives {(632 2000) math:sum 2632}] - skolem:lemma1634 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1632 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma634 a r:Inference; +skolem:lemma633 a r:Inference; r:gives { - (2633 6174) :recursionsNeeded 4 . + 2633 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 633}] [ a r:Fact; r:gives {(633 2000) math:sum 2633}] - skolem:lemma1635 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1633 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma635 a r:Inference; +skolem:lemma634 a r:Inference; r:gives { - (2634 6174) :recursionsNeeded 7 . + 2634 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 634}] [ a r:Fact; r:gives {(634 2000) math:sum 2634}] - skolem:lemma1636 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1634 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma636 a r:Inference; +skolem:lemma635 a r:Inference; r:gives { - (2635 6174) :recursionsNeeded 2 . + 2635 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 635}] [ a r:Fact; r:gives {(635 2000) math:sum 2635}] - skolem:lemma1637 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1635 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma637 a r:Inference; +skolem:lemma636 a r:Inference; r:gives { - (2636 6174) :recursionsNeeded 3 . + 2636 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 636}] [ a r:Fact; r:gives {(636 2000) math:sum 2636}] - skolem:lemma1638 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1636 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma638 a r:Inference; +skolem:lemma637 a r:Inference; r:gives { - (2637 6174) :recursionsNeeded 5 . + 2637 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 637}] [ a r:Fact; r:gives {(637 2000) math:sum 2637}] - skolem:lemma1639 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1637 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma639 a r:Inference; +skolem:lemma638 a r:Inference; r:gives { - (2638 6174) :recursionsNeeded 3 . + 2638 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 638}] [ a r:Fact; r:gives {(638 2000) math:sum 2638}] - skolem:lemma1640 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1638 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma640 a r:Inference; +skolem:lemma639 a r:Inference; r:gives { - (2639 6174) :recursionsNeeded 6 . + 2639 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 639}] [ a r:Fact; r:gives {(639 2000) math:sum 2639}] - skolem:lemma1641 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1639 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma641 a r:Inference; +skolem:lemma640 a r:Inference; r:gives { - (2640 6174) :recursionsNeeded 1 . + 2640 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 640}] [ a r:Fact; r:gives {(640 2000) math:sum 2640}] - skolem:lemma1642 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1640 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma642 a r:Inference; +skolem:lemma641 a r:Inference; r:gives { - (2641 6174) :recursionsNeeded 7 . + 2641 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 641}] [ a r:Fact; r:gives {(641 2000) math:sum 2641}] - skolem:lemma1643 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1641 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma643 a r:Inference; +skolem:lemma642 a r:Inference; r:gives { - (2642 6174) :recursionsNeeded 2 . + 2642 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 642}] [ a r:Fact; r:gives {(642 2000) math:sum 2642}] - skolem:lemma1644 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1642 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma644 a r:Inference; +skolem:lemma643 a r:Inference; r:gives { - (2643 6174) :recursionsNeeded 7 . + 2643 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 643}] [ a r:Fact; r:gives {(643 2000) math:sum 2643}] - skolem:lemma1645 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1643 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma645 a r:Inference; +skolem:lemma644 a r:Inference; r:gives { - (2644 6174) :recursionsNeeded 4 . + 2644 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 644}] [ a r:Fact; r:gives {(644 2000) math:sum 2644}] - skolem:lemma1646 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1644 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma646 a r:Inference; +skolem:lemma645 a r:Inference; r:gives { - (2645 6174) :recursionsNeeded 7 . + 2645 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 645}] [ a r:Fact; r:gives {(645 2000) math:sum 2645}] - skolem:lemma1647 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1645 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma647 a r:Inference; +skolem:lemma646 a r:Inference; r:gives { - (2646 6174) :recursionsNeeded 2 . + 2646 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 646}] [ a r:Fact; r:gives {(646 2000) math:sum 2646}] - skolem:lemma1648 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1646 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma648 a r:Inference; +skolem:lemma647 a r:Inference; r:gives { - (2647 6174) :recursionsNeeded 7 . + 2647 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 647}] [ a r:Fact; r:gives {(647 2000) math:sum 2647}] - skolem:lemma1649 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1647 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma649 a r:Inference; +skolem:lemma648 a r:Inference; r:gives { - (2648 6174) :recursionsNeeded 1 . + 2648 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 648}] [ a r:Fact; r:gives {(648 2000) math:sum 2648}] - skolem:lemma1650 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1648 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma650 a r:Inference; +skolem:lemma649 a r:Inference; r:gives { - (2649 6174) :recursionsNeeded 5 . + 2649 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 649}] [ a r:Fact; r:gives {(649 2000) math:sum 2649}] - skolem:lemma1651 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1649 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma651 a r:Inference; +skolem:lemma650 a r:Inference; r:gives { - (2650 6174) :recursionsNeeded 3 . + 2650 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 650}] [ a r:Fact; r:gives {(650 2000) math:sum 2650}] - skolem:lemma1652 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1650 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma652 a r:Inference; +skolem:lemma651 a r:Inference; r:gives { - (2651 6174) :recursionsNeeded 5 . + 2651 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 651}] [ a r:Fact; r:gives {(651 2000) math:sum 2651}] - skolem:lemma1653 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1651 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma653 a r:Inference; +skolem:lemma652 a r:Inference; r:gives { - (2652 6174) :recursionsNeeded 3 . + 2652 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 652}] [ a r:Fact; r:gives {(652 2000) math:sum 2652}] - skolem:lemma1654 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1652 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma654 a r:Inference; +skolem:lemma653 a r:Inference; r:gives { - (2653 6174) :recursionsNeeded 2 . + 2653 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 653}] [ a r:Fact; r:gives {(653 2000) math:sum 2653}] - skolem:lemma1655 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1653 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma655 a r:Inference; +skolem:lemma654 a r:Inference; r:gives { - (2654 6174) :recursionsNeeded 7 . + 2654 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 654}] [ a r:Fact; r:gives {(654 2000) math:sum 2654}] - skolem:lemma1656 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1654 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma656 a r:Inference; +skolem:lemma655 a r:Inference; r:gives { - (2655 6174) :recursionsNeeded 4 . + 2655 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 655}] [ a r:Fact; r:gives {(655 2000) math:sum 2655}] - skolem:lemma1657 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1655 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma657 a r:Inference; +skolem:lemma656 a r:Inference; r:gives { - (2656 6174) :recursionsNeeded 7 . + 2656 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 656}] [ a r:Fact; r:gives {(656 2000) math:sum 2656}] - skolem:lemma1658 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1656 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma658 a r:Inference; +skolem:lemma657 a r:Inference; r:gives { - (2657 6174) :recursionsNeeded 7 . + 2657 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 657}] [ a r:Fact; r:gives {(657 2000) math:sum 2657}] - skolem:lemma1659 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1657 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma659 a r:Inference; +skolem:lemma658 a r:Inference; r:gives { - (2658 6174) :recursionsNeeded 7 . + 2658 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 658}] [ a r:Fact; r:gives {(658 2000) math:sum 2658}] - skolem:lemma1660 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1658 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma660 a r:Inference; +skolem:lemma659 a r:Inference; r:gives { - (2659 6174) :recursionsNeeded 3 . + 2659 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 659}] [ a r:Fact; r:gives {(659 2000) math:sum 2659}] - skolem:lemma1661 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1659 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma661 a r:Inference; +skolem:lemma660 a r:Inference; r:gives { - (2660 6174) :recursionsNeeded 4 . + 2660 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 660}] [ a r:Fact; r:gives {(660 2000) math:sum 2660}] - skolem:lemma1662 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1660 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma662 a r:Inference; +skolem:lemma661 a r:Inference; r:gives { - (2661 6174) :recursionsNeeded 5 . + 2661 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 661}] [ a r:Fact; r:gives {(661 2000) math:sum 2661}] - skolem:lemma1663 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1661 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma663 a r:Inference; +skolem:lemma662 a r:Inference; r:gives { - (2662 6174) :recursionsNeeded 4 . + 2662 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 662}] [ a r:Fact; r:gives {(662 2000) math:sum 2662}] - skolem:lemma1664 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1662 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma664 a r:Inference; +skolem:lemma663 a r:Inference; r:gives { - (2663 6174) :recursionsNeeded 3 . + 2663 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 663}] [ a r:Fact; r:gives {(663 2000) math:sum 2663}] - skolem:lemma1665 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1663 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma665 a r:Inference; +skolem:lemma664 a r:Inference; r:gives { - (2664 6174) :recursionsNeeded 2 . + 2664 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 664}] [ a r:Fact; r:gives {(664 2000) math:sum 2664}] - skolem:lemma1666 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1664 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma666 a r:Inference; +skolem:lemma665 a r:Inference; r:gives { - (2665 6174) :recursionsNeeded 7 . + 2665 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 665}] [ a r:Fact; r:gives {(665 2000) math:sum 2665}] - skolem:lemma1667 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1665 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma667 a r:Inference; +skolem:lemma666 a r:Inference; r:gives { - (2666 6174) :recursionsNeeded 4 . + 2666 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 666}] [ a r:Fact; r:gives {(666 2000) math:sum 2666}] - skolem:lemma1668 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1666 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma668 a r:Inference; +skolem:lemma667 a r:Inference; r:gives { - (2667 6174) :recursionsNeeded 6 . + 2667 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 667}] [ a r:Fact; r:gives {(667 2000) math:sum 2667}] - skolem:lemma1669 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1667 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma669 a r:Inference; +skolem:lemma668 a r:Inference; r:gives { - (2668 6174) :recursionsNeeded 6 . + 2668 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 668}] [ a r:Fact; r:gives {(668 2000) math:sum 2668}] - skolem:lemma1670 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1668 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma670 a r:Inference; +skolem:lemma669 a r:Inference; r:gives { - (2669 6174) :recursionsNeeded 4 . + 2669 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 669}] [ a r:Fact; r:gives {(669 2000) math:sum 2669}] - skolem:lemma1671 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1669 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma671 a r:Inference; +skolem:lemma670 a r:Inference; r:gives { - (2670 6174) :recursionsNeeded 3 . + 2670 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 670}] [ a r:Fact; r:gives {(670 2000) math:sum 2670}] - skolem:lemma1672 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1670 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma672 a r:Inference; +skolem:lemma671 a r:Inference; r:gives { - (2671 6174) :recursionsNeeded 4 . + 2671 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 671}] [ a r:Fact; r:gives {(671 2000) math:sum 2671}] - skolem:lemma1673 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1671 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma673 a r:Inference; +skolem:lemma672 a r:Inference; r:gives { - (2672 6174) :recursionsNeeded 5 . + 2672 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 672}] [ a r:Fact; r:gives {(672 2000) math:sum 2672}] - skolem:lemma1674 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1672 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma674 a r:Inference; +skolem:lemma673 a r:Inference; r:gives { - (2673 6174) :recursionsNeeded 5 . + 2673 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 673}] [ a r:Fact; r:gives {(673 2000) math:sum 2673}] - skolem:lemma1675 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1673 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma675 a r:Inference; +skolem:lemma674 a r:Inference; r:gives { - (2674 6174) :recursionsNeeded 7 . + 2674 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 674}] [ a r:Fact; r:gives {(674 2000) math:sum 2674}] - skolem:lemma1676 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1674 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma676 a r:Inference; +skolem:lemma675 a r:Inference; r:gives { - (2675 6174) :recursionsNeeded 7 . + 2675 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 675}] [ a r:Fact; r:gives {(675 2000) math:sum 2675}] - skolem:lemma1677 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1675 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma677 a r:Inference; +skolem:lemma676 a r:Inference; r:gives { - (2676 6174) :recursionsNeeded 6 . + 2676 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 676}] [ a r:Fact; r:gives {(676 2000) math:sum 2676}] - skolem:lemma1678 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1676 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma678 a r:Inference; +skolem:lemma677 a r:Inference; r:gives { - (2677 6174) :recursionsNeeded 7 . + 2677 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 677}] [ a r:Fact; r:gives {(677 2000) math:sum 2677}] - skolem:lemma1679 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1677 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma679 a r:Inference; +skolem:lemma678 a r:Inference; r:gives { - (2678 6174) :recursionsNeeded 7 . + 2678 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 678}] [ a r:Fact; r:gives {(678 2000) math:sum 2678}] - skolem:lemma1680 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1678 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma680 a r:Inference; +skolem:lemma679 a r:Inference; r:gives { - (2679 6174) :recursionsNeeded 3 . + 2679 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 679}] [ a r:Fact; r:gives {(679 2000) math:sum 2679}] - skolem:lemma1681 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1679 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma681 a r:Inference; +skolem:lemma680 a r:Inference; r:gives { - (2680 6174) :recursionsNeeded 2 . + 2680 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 680}] [ a r:Fact; r:gives {(680 2000) math:sum 2680}] - skolem:lemma1682 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1680 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma682 a r:Inference; +skolem:lemma681 a r:Inference; r:gives { - (2681 6174) :recursionsNeeded 3 . + 2681 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 681}] [ a r:Fact; r:gives {(681 2000) math:sum 2681}] - skolem:lemma1683 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1681 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma683 a r:Inference; +skolem:lemma682 a r:Inference; r:gives { - (2682 6174) :recursionsNeeded 4 . + 2682 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 682}] [ a r:Fact; r:gives {(682 2000) math:sum 2682}] - skolem:lemma1684 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1682 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma684 a r:Inference; +skolem:lemma683 a r:Inference; r:gives { - (2683 6174) :recursionsNeeded 3 . + 2683 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 683}] [ a r:Fact; r:gives {(683 2000) math:sum 2683}] - skolem:lemma1685 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1683 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma685 a r:Inference; +skolem:lemma684 a r:Inference; r:gives { - (2684 6174) :recursionsNeeded 1 . + 2684 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 684}] [ a r:Fact; r:gives {(684 2000) math:sum 2684}] - skolem:lemma1686 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1684 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma686 a r:Inference; +skolem:lemma685 a r:Inference; r:gives { - (2685 6174) :recursionsNeeded 7 . + 2685 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 685}] [ a r:Fact; r:gives {(685 2000) math:sum 2685}] - skolem:lemma1687 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1685 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma687 a r:Inference; +skolem:lemma686 a r:Inference; r:gives { - (2686 6174) :recursionsNeeded 6 . + 2686 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 686}] [ a r:Fact; r:gives {(686 2000) math:sum 2686}] - skolem:lemma1688 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1686 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma688 a r:Inference; +skolem:lemma687 a r:Inference; r:gives { - (2687 6174) :recursionsNeeded 7 . + 2687 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 687}] [ a r:Fact; r:gives {(687 2000) math:sum 2687}] - skolem:lemma1689 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1687 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma689 a r:Inference; +skolem:lemma688 a r:Inference; r:gives { - (2688 6174) :recursionsNeeded 1 . + 2688 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 688}] [ a r:Fact; r:gives {(688 2000) math:sum 2688}] - skolem:lemma1690 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1688 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma690 a r:Inference; +skolem:lemma689 a r:Inference; r:gives { - (2689 6174) :recursionsNeeded 5 . + 2689 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 689}] [ a r:Fact; r:gives {(689 2000) math:sum 2689}] - skolem:lemma1691 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1689 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma691 a r:Inference; +skolem:lemma690 a r:Inference; r:gives { - (2690 6174) :recursionsNeeded 7 . + 2690 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 690}] [ a r:Fact; r:gives {(690 2000) math:sum 2690}] - skolem:lemma1692 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1690 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma692 a r:Inference; +skolem:lemma691 a r:Inference; r:gives { - (2691 6174) :recursionsNeeded 2 . + 2691 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 691}] [ a r:Fact; r:gives {(691 2000) math:sum 2691}] - skolem:lemma1693 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1691 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma693 a r:Inference; +skolem:lemma692 a r:Inference; r:gives { - (2692 6174) :recursionsNeeded 3 . + 2692 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 692}] [ a r:Fact; r:gives {(692 2000) math:sum 2692}] - skolem:lemma1694 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1692 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma694 a r:Inference; +skolem:lemma693 a r:Inference; r:gives { - (2693 6174) :recursionsNeeded 6 . + 2693 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 693}] [ a r:Fact; r:gives {(693 2000) math:sum 2693}] - skolem:lemma1695 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1693 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma695 a r:Inference; +skolem:lemma694 a r:Inference; r:gives { - (2694 6174) :recursionsNeeded 5 . + 2694 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 694}] [ a r:Fact; r:gives {(694 2000) math:sum 2694}] - skolem:lemma1696 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1694 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma696 a r:Inference; +skolem:lemma695 a r:Inference; r:gives { - (2695 6174) :recursionsNeeded 3 . + 2695 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 695}] [ a r:Fact; r:gives {(695 2000) math:sum 2695}] - skolem:lemma1697 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1695 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma697 a r:Inference; +skolem:lemma696 a r:Inference; r:gives { - (2696 6174) :recursionsNeeded 4 . + 2696 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 696}] [ a r:Fact; r:gives {(696 2000) math:sum 2696}] - skolem:lemma1698 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1696 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma698 a r:Inference; +skolem:lemma697 a r:Inference; r:gives { - (2697 6174) :recursionsNeeded 3 . + 2697 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 697}] [ a r:Fact; r:gives {(697 2000) math:sum 2697}] - skolem:lemma1699 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1697 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma699 a r:Inference; +skolem:lemma698 a r:Inference; r:gives { - (2698 6174) :recursionsNeeded 5 . + 2698 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 698}] [ a r:Fact; r:gives {(698 2000) math:sum 2698}] - skolem:lemma1700 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1698 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma700 a r:Inference; +skolem:lemma699 a r:Inference; r:gives { - (2699 6174) :recursionsNeeded 6 . + 2699 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 699}] [ a r:Fact; r:gives {(699 2000) math:sum 2699}] - skolem:lemma1701 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1699 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma701 a r:Inference; +skolem:lemma700 a r:Inference; r:gives { - (2700 6174) :recursionsNeeded 5 . + 2700 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 700}] [ a r:Fact; r:gives {(700 2000) math:sum 2700}] - skolem:lemma1702 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1700 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma702 a r:Inference; +skolem:lemma701 a r:Inference; r:gives { - (2701 6174) :recursionsNeeded 3 . + 2701 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 701}] [ a r:Fact; r:gives {(701 2000) math:sum 2701}] - skolem:lemma1703 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1701 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma703 a r:Inference; +skolem:lemma702 a r:Inference; r:gives { - (2702 6174) :recursionsNeeded 4 . + 2702 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 702}] [ a r:Fact; r:gives {(702 2000) math:sum 2702}] - skolem:lemma1704 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1702 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma704 a r:Inference; +skolem:lemma703 a r:Inference; r:gives { - (2703 6174) :recursionsNeeded 3 . + 2703 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 703}] [ a r:Fact; r:gives {(703 2000) math:sum 2703}] - skolem:lemma1705 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1703 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma705 a r:Inference; +skolem:lemma704 a r:Inference; r:gives { - (2704 6174) :recursionsNeeded 5 . + 2704 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 704}] [ a r:Fact; r:gives {(704 2000) math:sum 2704}] - skolem:lemma1706 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1704 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma706 a r:Inference; +skolem:lemma705 a r:Inference; r:gives { - (2705 6174) :recursionsNeeded 6 . + 2705 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 705}] [ a r:Fact; r:gives {(705 2000) math:sum 2705}] - skolem:lemma1707 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1705 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma707 a r:Inference; +skolem:lemma706 a r:Inference; r:gives { - (2706 6174) :recursionsNeeded 3 . + 2706 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 706}] [ a r:Fact; r:gives {(706 2000) math:sum 2706}] - skolem:lemma1708 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1706 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma708 a r:Inference; +skolem:lemma707 a r:Inference; r:gives { - (2707 6174) :recursionsNeeded 5 . + 2707 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 707}] [ a r:Fact; r:gives {(707 2000) math:sum 2707}] - skolem:lemma1709 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1707 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma709 a r:Inference; +skolem:lemma708 a r:Inference; r:gives { - (2708 6174) :recursionsNeeded 7 . + 2708 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 708}] [ a r:Fact; r:gives {(708 2000) math:sum 2708}] - skolem:lemma1710 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1708 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma710 a r:Inference; +skolem:lemma709 a r:Inference; r:gives { - (2709 6174) :recursionsNeeded 7 . + 2709 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 709}] [ a r:Fact; r:gives {(709 2000) math:sum 2709}] - skolem:lemma1711 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1709 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma711 a r:Inference; +skolem:lemma710 a r:Inference; r:gives { - (2710 6174) :recursionsNeeded 3 . + 2710 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 710}] [ a r:Fact; r:gives {(710 2000) math:sum 2710}] - skolem:lemma1712 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1710 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma712 a r:Inference; +skolem:lemma711 a r:Inference; r:gives { - (2711 6174) :recursionsNeeded 7 . + 2711 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 711}] [ a r:Fact; r:gives {(711 2000) math:sum 2711}] - skolem:lemma1713 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1711 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma713 a r:Inference; +skolem:lemma712 a r:Inference; r:gives { - (2712 6174) :recursionsNeeded 6 . + 2712 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 712}] [ a r:Fact; r:gives {(712 2000) math:sum 2712}] - skolem:lemma1714 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1712 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma714 a r:Inference; +skolem:lemma713 a r:Inference; r:gives { - (2713 6174) :recursionsNeeded 7 . + 2713 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 713}] [ a r:Fact; r:gives {(713 2000) math:sum 2713}] - skolem:lemma1715 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1713 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma715 a r:Inference; +skolem:lemma714 a r:Inference; r:gives { - (2714 6174) :recursionsNeeded 1 . + 2714 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 714}] [ a r:Fact; r:gives {(714 2000) math:sum 2714}] - skolem:lemma1716 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1714 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma716 a r:Inference; +skolem:lemma715 a r:Inference; r:gives { - (2715 6174) :recursionsNeeded 3 . + 2715 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 715}] [ a r:Fact; r:gives {(715 2000) math:sum 2715}] - skolem:lemma1717 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1715 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma717 a r:Inference; +skolem:lemma716 a r:Inference; r:gives { - (2716 6174) :recursionsNeeded 4 . + 2716 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 716}] [ a r:Fact; r:gives {(716 2000) math:sum 2716}] - skolem:lemma1718 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1716 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma718 a r:Inference; +skolem:lemma717 a r:Inference; r:gives { - (2717 6174) :recursionsNeeded 5 . + 2717 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 717}] [ a r:Fact; r:gives {(717 2000) math:sum 2717}] - skolem:lemma1719 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1717 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma719 a r:Inference; +skolem:lemma718 a r:Inference; r:gives { - (2718 6174) :recursionsNeeded 5 . + 2718 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 718}] [ a r:Fact; r:gives {(718 2000) math:sum 2718}] - skolem:lemma1720 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1718 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma720 a r:Inference; +skolem:lemma719 a r:Inference; r:gives { - (2719 6174) :recursionsNeeded 7 . + 2719 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 719}] [ a r:Fact; r:gives {(719 2000) math:sum 2719}] - skolem:lemma1721 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1719 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma721 a r:Inference; +skolem:lemma720 a r:Inference; r:gives { - (2720 6174) :recursionsNeeded 4 . + 2720 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 720}] [ a r:Fact; r:gives {(720 2000) math:sum 2720}] - skolem:lemma1722 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1720 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma722 a r:Inference; +skolem:lemma721 a r:Inference; r:gives { - (2721 6174) :recursionsNeeded 6 . + 2721 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 721}] [ a r:Fact; r:gives {(721 2000) math:sum 2721}] - skolem:lemma1723 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1721 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma723 a r:Inference; +skolem:lemma722 a r:Inference; r:gives { - (2722 6174) :recursionsNeeded 6 . + 2722 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 722}] [ a r:Fact; r:gives {(722 2000) math:sum 2722}] - skolem:lemma1724 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1722 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma724 a r:Inference; +skolem:lemma723 a r:Inference; r:gives { - (2723 6174) :recursionsNeeded 7 . + 2723 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 723}] [ a r:Fact; r:gives {(723 2000) math:sum 2723}] - skolem:lemma1725 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1723 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma725 a r:Inference; +skolem:lemma724 a r:Inference; r:gives { - (2724 6174) :recursionsNeeded 7 . + 2724 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 724}] [ a r:Fact; r:gives {(724 2000) math:sum 2724}] - skolem:lemma1726 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1724 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma726 a r:Inference; +skolem:lemma725 a r:Inference; r:gives { - (2725 6174) :recursionsNeeded 5 . + 2725 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 725}] [ a r:Fact; r:gives {(725 2000) math:sum 2725}] - skolem:lemma1727 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1725 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma727 a r:Inference; +skolem:lemma726 a r:Inference; r:gives { - (2726 6174) :recursionsNeeded 5 . + 2726 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 726}] [ a r:Fact; r:gives {(726 2000) math:sum 2726}] - skolem:lemma1728 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1726 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma728 a r:Inference; +skolem:lemma727 a r:Inference; r:gives { - (2727 6174) :recursionsNeeded 5 . + 2727 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 727}] [ a r:Fact; r:gives {(727 2000) math:sum 2727}] - skolem:lemma1729 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1727 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma729 a r:Inference; +skolem:lemma728 a r:Inference; r:gives { - (2728 6174) :recursionsNeeded 5 . + 2728 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 728}] [ a r:Fact; r:gives {(728 2000) math:sum 2728}] - skolem:lemma1730 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1728 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma730 a r:Inference; +skolem:lemma729 a r:Inference; r:gives { - (2729 6174) :recursionsNeeded 5 . + 2729 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 729}] [ a r:Fact; r:gives {(729 2000) math:sum 2729}] - skolem:lemma1731 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1729 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma731 a r:Inference; +skolem:lemma730 a r:Inference; r:gives { - (2730 6174) :recursionsNeeded 3 . + 2730 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 730}] [ a r:Fact; r:gives {(730 2000) math:sum 2730}] - skolem:lemma1732 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1730 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma732 a r:Inference; +skolem:lemma731 a r:Inference; r:gives { - (2731 6174) :recursionsNeeded 7 . + 2731 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 731}] [ a r:Fact; r:gives {(731 2000) math:sum 2731}] - skolem:lemma1733 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1731 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma733 a r:Inference; +skolem:lemma732 a r:Inference; r:gives { - (2732 6174) :recursionsNeeded 7 . + 2732 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 732}] [ a r:Fact; r:gives {(732 2000) math:sum 2732}] - skolem:lemma1734 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1732 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma734 a r:Inference; +skolem:lemma733 a r:Inference; r:gives { - (2733 6174) :recursionsNeeded 6 . + 2733 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 733}] [ a r:Fact; r:gives {(733 2000) math:sum 2733}] - skolem:lemma1735 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1733 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma735 a r:Inference; +skolem:lemma734 a r:Inference; r:gives { - (2734 6174) :recursionsNeeded 7 . + 2734 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 734}] [ a r:Fact; r:gives {(734 2000) math:sum 2734}] - skolem:lemma1736 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1734 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma736 a r:Inference; +skolem:lemma735 a r:Inference; r:gives { - (2735 6174) :recursionsNeeded 7 . + 2735 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 735}] [ a r:Fact; r:gives {(735 2000) math:sum 2735}] - skolem:lemma1737 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1735 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma737 a r:Inference; +skolem:lemma736 a r:Inference; r:gives { - (2736 6174) :recursionsNeeded 5 . + 2736 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 736}] [ a r:Fact; r:gives {(736 2000) math:sum 2736}] - skolem:lemma1738 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1736 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma738 a r:Inference; +skolem:lemma737 a r:Inference; r:gives { - (2737 6174) :recursionsNeeded 5 . + 2737 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 737}] [ a r:Fact; r:gives {(737 2000) math:sum 2737}] - skolem:lemma1739 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1737 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma739 a r:Inference; +skolem:lemma738 a r:Inference; r:gives { - (2738 6174) :recursionsNeeded 4 . + 2738 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 738}] [ a r:Fact; r:gives {(738 2000) math:sum 2738}] - skolem:lemma1740 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1738 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma740 a r:Inference; +skolem:lemma739 a r:Inference; r:gives { - (2739 6174) :recursionsNeeded 3 . + 2739 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 739}] [ a r:Fact; r:gives {(739 2000) math:sum 2739}] - skolem:lemma1741 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1739 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma741 a r:Inference; +skolem:lemma740 a r:Inference; r:gives { - (2740 6174) :recursionsNeeded 5 . + 2740 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 740}] [ a r:Fact; r:gives {(740 2000) math:sum 2740}] - skolem:lemma1742 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1740 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma742 a r:Inference; +skolem:lemma741 a r:Inference; r:gives { - (2741 6174) :recursionsNeeded 1 . + 2741 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 741}] [ a r:Fact; r:gives {(741 2000) math:sum 2741}] - skolem:lemma1743 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1741 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma743 a r:Inference; +skolem:lemma742 a r:Inference; r:gives { - (2742 6174) :recursionsNeeded 7 . + 2742 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 742}] [ a r:Fact; r:gives {(742 2000) math:sum 2742}] - skolem:lemma1744 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1742 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma744 a r:Inference; +skolem:lemma743 a r:Inference; r:gives { - (2743 6174) :recursionsNeeded 7 . + 2743 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 743}] [ a r:Fact; r:gives {(743 2000) math:sum 2743}] - skolem:lemma1745 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1743 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma745 a r:Inference; +skolem:lemma744 a r:Inference; r:gives { - (2744 6174) :recursionsNeeded 6 . + 2744 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 744}] [ a r:Fact; r:gives {(744 2000) math:sum 2744}] - skolem:lemma1746 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1744 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma746 a r:Inference; +skolem:lemma745 a r:Inference; r:gives { - (2745 6174) :recursionsNeeded 7 . + 2745 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 745}] [ a r:Fact; r:gives {(745 2000) math:sum 2745}] - skolem:lemma1747 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1745 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma747 a r:Inference; +skolem:lemma746 a r:Inference; r:gives { - (2746 6174) :recursionsNeeded 7 . + 2746 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 746}] [ a r:Fact; r:gives {(746 2000) math:sum 2746}] - skolem:lemma1748 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1746 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma748 a r:Inference; +skolem:lemma747 a r:Inference; r:gives { - (2747 6174) :recursionsNeeded 5 . + 2747 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 747}] [ a r:Fact; r:gives {(747 2000) math:sum 2747}] - skolem:lemma1749 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1747 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma749 a r:Inference; +skolem:lemma748 a r:Inference; r:gives { - (2748 6174) :recursionsNeeded 3 . + 2748 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 748}] [ a r:Fact; r:gives {(748 2000) math:sum 2748}] - skolem:lemma1750 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1748 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma750 a r:Inference; +skolem:lemma749 a r:Inference; r:gives { - (2749 6174) :recursionsNeeded 6 . + 2749 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 749}] [ a r:Fact; r:gives {(749 2000) math:sum 2749}] - skolem:lemma1751 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1749 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma751 a r:Inference; +skolem:lemma750 a r:Inference; r:gives { - (2750 6174) :recursionsNeeded 6 . + 2750 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 750}] [ a r:Fact; r:gives {(750 2000) math:sum 2750}] - skolem:lemma1752 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1750 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma752 a r:Inference; +skolem:lemma751 a r:Inference; r:gives { - (2751 6174) :recursionsNeeded 3 . + 2751 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 751}] [ a r:Fact; r:gives {(751 2000) math:sum 2751}] - skolem:lemma1753 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1751 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma753 a r:Inference; +skolem:lemma752 a r:Inference; r:gives { - (2752 6174) :recursionsNeeded 5 . + 2752 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 752}] [ a r:Fact; r:gives {(752 2000) math:sum 2752}] - skolem:lemma1754 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1752 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma754 a r:Inference; +skolem:lemma753 a r:Inference; r:gives { - (2753 6174) :recursionsNeeded 7 . + 2753 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 753}] [ a r:Fact; r:gives {(753 2000) math:sum 2753}] - skolem:lemma1755 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1753 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma755 a r:Inference; +skolem:lemma754 a r:Inference; r:gives { - (2754 6174) :recursionsNeeded 7 . + 2754 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 754}] [ a r:Fact; r:gives {(754 2000) math:sum 2754}] - skolem:lemma1756 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1754 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma756 a r:Inference; +skolem:lemma755 a r:Inference; r:gives { - (2755 6174) :recursionsNeeded 6 . + 2755 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 755}] [ a r:Fact; r:gives {(755 2000) math:sum 2755}] - skolem:lemma1757 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1755 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma757 a r:Inference; +skolem:lemma756 a r:Inference; r:gives { - (2756 6174) :recursionsNeeded 7 . + 2756 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 756}] [ a r:Fact; r:gives {(756 2000) math:sum 2756}] - skolem:lemma1758 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1756 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma758 a r:Inference; +skolem:lemma757 a r:Inference; r:gives { - (2757 6174) :recursionsNeeded 7 . + 2757 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 757}] [ a r:Fact; r:gives {(757 2000) math:sum 2757}] - skolem:lemma1759 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1757 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma759 a r:Inference; +skolem:lemma758 a r:Inference; r:gives { - (2758 6174) :recursionsNeeded 1 . + 2758 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 758}] [ a r:Fact; r:gives {(758 2000) math:sum 2758}] - skolem:lemma1760 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1758 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma760 a r:Inference; +skolem:lemma759 a r:Inference; r:gives { - (2759 6174) :recursionsNeeded 5 . + 2759 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 759}] [ a r:Fact; r:gives {(759 2000) math:sum 2759}] - skolem:lemma1761 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1759 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma761 a r:Inference; +skolem:lemma760 a r:Inference; r:gives { - (2760 6174) :recursionsNeeded 3 . + 2760 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 760}] [ a r:Fact; r:gives {(760 2000) math:sum 2760}] - skolem:lemma1762 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1760 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma762 a r:Inference; +skolem:lemma761 a r:Inference; r:gives { - (2761 6174) :recursionsNeeded 4 . + 2761 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 761}] [ a r:Fact; r:gives {(761 2000) math:sum 2761}] - skolem:lemma1763 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1761 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma763 a r:Inference; +skolem:lemma762 a r:Inference; r:gives { - (2762 6174) :recursionsNeeded 5 . + 2762 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 762}] [ a r:Fact; r:gives {(762 2000) math:sum 2762}] - skolem:lemma1764 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1762 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma764 a r:Inference; +skolem:lemma763 a r:Inference; r:gives { - (2763 6174) :recursionsNeeded 5 . + 2763 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 763}] [ a r:Fact; r:gives {(763 2000) math:sum 2763}] - skolem:lemma1765 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1763 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma765 a r:Inference; +skolem:lemma764 a r:Inference; r:gives { - (2764 6174) :recursionsNeeded 7 . + 2764 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 764}] [ a r:Fact; r:gives {(764 2000) math:sum 2764}] - skolem:lemma1766 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1764 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma766 a r:Inference; +skolem:lemma765 a r:Inference; r:gives { - (2765 6174) :recursionsNeeded 7 . + 2765 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 765}] [ a r:Fact; r:gives {(765 2000) math:sum 2765}] - skolem:lemma1767 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1765 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma767 a r:Inference; +skolem:lemma766 a r:Inference; r:gives { - (2766 6174) :recursionsNeeded 6 . + 2766 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 766}] [ a r:Fact; r:gives {(766 2000) math:sum 2766}] - skolem:lemma1768 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1766 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma768 a r:Inference; +skolem:lemma767 a r:Inference; r:gives { - (2767 6174) :recursionsNeeded 7 . + 2767 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 767}] [ a r:Fact; r:gives {(767 2000) math:sum 2767}] - skolem:lemma1769 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1767 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma769 a r:Inference; +skolem:lemma768 a r:Inference; r:gives { - (2768 6174) :recursionsNeeded 7 . + 2768 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 768}] [ a r:Fact; r:gives {(768 2000) math:sum 2768}] - skolem:lemma1770 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1768 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma770 a r:Inference; +skolem:lemma769 a r:Inference; r:gives { - (2769 6174) :recursionsNeeded 3 . + 2769 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 769}] [ a r:Fact; r:gives {(769 2000) math:sum 2769}] - skolem:lemma1771 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1769 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma771 a r:Inference; +skolem:lemma770 a r:Inference; r:gives { - (2770 6174) :recursionsNeeded 5 . + 2770 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 770}] [ a r:Fact; r:gives {(770 2000) math:sum 2770}] - skolem:lemma1772 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1770 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma772 a r:Inference; +skolem:lemma771 a r:Inference; r:gives { - (2771 6174) :recursionsNeeded 5 . + 2771 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 771}] [ a r:Fact; r:gives {(771 2000) math:sum 2771}] - skolem:lemma1773 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1771 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma773 a r:Inference; +skolem:lemma772 a r:Inference; r:gives { - (2772 6174) :recursionsNeeded 5 . + 2772 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 772}] [ a r:Fact; r:gives {(772 2000) math:sum 2772}] - skolem:lemma1774 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1772 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma774 a r:Inference; +skolem:lemma773 a r:Inference; r:gives { - (2773 6174) :recursionsNeeded 5 . + 2773 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 773}] [ a r:Fact; r:gives {(773 2000) math:sum 2773}] - skolem:lemma1775 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1773 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma775 a r:Inference; +skolem:lemma774 a r:Inference; r:gives { - (2774 6174) :recursionsNeeded 5 . + 2774 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 774}] [ a r:Fact; r:gives {(774 2000) math:sum 2774}] - skolem:lemma1776 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1774 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma776 a r:Inference; +skolem:lemma775 a r:Inference; r:gives { - (2775 6174) :recursionsNeeded 7 . + 2775 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 775}] [ a r:Fact; r:gives {(775 2000) math:sum 2775}] - skolem:lemma1777 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1775 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma777 a r:Inference; +skolem:lemma776 a r:Inference; r:gives { - (2776 6174) :recursionsNeeded 7 . + 2776 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 776}] [ a r:Fact; r:gives {(776 2000) math:sum 2776}] - skolem:lemma1778 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1776 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma778 a r:Inference; +skolem:lemma777 a r:Inference; r:gives { - (2777 6174) :recursionsNeeded 6 . + 2777 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 777}] [ a r:Fact; r:gives {(777 2000) math:sum 2777}] - skolem:lemma1779 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1777 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma779 a r:Inference; +skolem:lemma778 a r:Inference; r:gives { - (2778 6174) :recursionsNeeded 6 . + 2778 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 778}] [ a r:Fact; r:gives {(778 2000) math:sum 2778}] - skolem:lemma1780 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1778 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma780 a r:Inference; +skolem:lemma779 a r:Inference; r:gives { - (2779 6174) :recursionsNeeded 4 . + 2779 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 779}] [ a r:Fact; r:gives {(779 2000) math:sum 2779}] - skolem:lemma1781 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1779 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma781 a r:Inference; +skolem:lemma780 a r:Inference; r:gives { - (2780 6174) :recursionsNeeded 7 . + 2780 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 780}] [ a r:Fact; r:gives {(780 2000) math:sum 2780}] - skolem:lemma1782 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1780 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma782 a r:Inference; +skolem:lemma781 a r:Inference; r:gives { - (2781 6174) :recursionsNeeded 5 . + 2781 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 781}] [ a r:Fact; r:gives {(781 2000) math:sum 2781}] - skolem:lemma1783 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1781 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma783 a r:Inference; +skolem:lemma782 a r:Inference; r:gives { - (2782 6174) :recursionsNeeded 5 . + 2782 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 782}] [ a r:Fact; r:gives {(782 2000) math:sum 2782}] - skolem:lemma1784 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1782 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma784 a r:Inference; +skolem:lemma783 a r:Inference; r:gives { - (2783 6174) :recursionsNeeded 4 . + 2783 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 783}] [ a r:Fact; r:gives {(783 2000) math:sum 2783}] - skolem:lemma1785 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1783 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma785 a r:Inference; +skolem:lemma784 a r:Inference; r:gives { - (2784 6174) :recursionsNeeded 3 . + 2784 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 784}] [ a r:Fact; r:gives {(784 2000) math:sum 2784}] - skolem:lemma1786 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1784 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma786 a r:Inference; +skolem:lemma785 a r:Inference; r:gives { - (2785 6174) :recursionsNeeded 1 . + 2785 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 785}] [ a r:Fact; r:gives {(785 2000) math:sum 2785}] - skolem:lemma1787 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1785 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma787 a r:Inference; +skolem:lemma786 a r:Inference; r:gives { - (2786 6174) :recursionsNeeded 7 . + 2786 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 786}] [ a r:Fact; r:gives {(786 2000) math:sum 2786}] - skolem:lemma1788 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1786 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma788 a r:Inference; +skolem:lemma787 a r:Inference; r:gives { - (2787 6174) :recursionsNeeded 6 . + 2787 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 787}] [ a r:Fact; r:gives {(787 2000) math:sum 2787}] - skolem:lemma1789 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1787 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma789 a r:Inference; +skolem:lemma788 a r:Inference; r:gives { - (2788 6174) :recursionsNeeded 7 . + 2788 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 788}] [ a r:Fact; r:gives {(788 2000) math:sum 2788}] - skolem:lemma1790 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1788 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma790 a r:Inference; +skolem:lemma789 a r:Inference; r:gives { - (2789 6174) :recursionsNeeded 3 . + 2789 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 789}] [ a r:Fact; r:gives {(789 2000) math:sum 2789}] - skolem:lemma1791 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1789 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma791 a r:Inference; +skolem:lemma790 a r:Inference; r:gives { - (2790 6174) :recursionsNeeded 7 . + 2790 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 790}] [ a r:Fact; r:gives {(790 2000) math:sum 2790}] - skolem:lemma1792 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1790 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma792 a r:Inference; +skolem:lemma791 a r:Inference; r:gives { - (2791 6174) :recursionsNeeded 7 . + 2791 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 791}] [ a r:Fact; r:gives {(791 2000) math:sum 2791}] - skolem:lemma1793 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1791 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma793 a r:Inference; +skolem:lemma792 a r:Inference; r:gives { - (2792 6174) :recursionsNeeded 5 . + 2792 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 792}] [ a r:Fact; r:gives {(792 2000) math:sum 2792}] - skolem:lemma1794 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1792 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma794 a r:Inference; +skolem:lemma793 a r:Inference; r:gives { - (2793 6174) :recursionsNeeded 3 . + 2793 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 793}] [ a r:Fact; r:gives {(793 2000) math:sum 2793}] - skolem:lemma1795 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1793 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma795 a r:Inference; +skolem:lemma794 a r:Inference; r:gives { - (2794 6174) :recursionsNeeded 6 . + 2794 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 794}] [ a r:Fact; r:gives {(794 2000) math:sum 2794}] - skolem:lemma1796 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1794 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma796 a r:Inference; +skolem:lemma795 a r:Inference; r:gives { - (2795 6174) :recursionsNeeded 5 . + 2795 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 795}] [ a r:Fact; r:gives {(795 2000) math:sum 2795}] - skolem:lemma1797 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1795 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma797 a r:Inference; +skolem:lemma796 a r:Inference; r:gives { - (2796 6174) :recursionsNeeded 3 . + 2796 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 796}] [ a r:Fact; r:gives {(796 2000) math:sum 2796}] - skolem:lemma1798 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1796 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma798 a r:Inference; +skolem:lemma797 a r:Inference; r:gives { - (2797 6174) :recursionsNeeded 4 . + 2797 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 797}] [ a r:Fact; r:gives {(797 2000) math:sum 2797}] - skolem:lemma1799 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1797 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma799 a r:Inference; +skolem:lemma798 a r:Inference; r:gives { - (2798 6174) :recursionsNeeded 3 . + 2798 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 798}] [ a r:Fact; r:gives {(798 2000) math:sum 2798}] - skolem:lemma1800 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1798 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma800 a r:Inference; +skolem:lemma799 a r:Inference; r:gives { - (2799 6174) :recursionsNeeded 5 . + 2799 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 799}] [ a r:Fact; r:gives {(799 2000) math:sum 2799}] - skolem:lemma1801 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1799 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma801 a r:Inference; +skolem:lemma800 a r:Inference; r:gives { - (2800 6174) :recursionsNeeded 6 . + 2800 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 800}] [ a r:Fact; r:gives {(800 2000) math:sum 2800}] - skolem:lemma1802 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1800 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma802 a r:Inference; +skolem:lemma801 a r:Inference; r:gives { - (2801 6174) :recursionsNeeded 3 . + 2801 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 801}] [ a r:Fact; r:gives {(801 2000) math:sum 2801}] - skolem:lemma1803 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1801 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma803 a r:Inference; +skolem:lemma802 a r:Inference; r:gives { - (2802 6174) :recursionsNeeded 6 . + 2802 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 802}] [ a r:Fact; r:gives {(802 2000) math:sum 2802}] - skolem:lemma1804 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1802 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma804 a r:Inference; +skolem:lemma803 a r:Inference; r:gives { - (2803 6174) :recursionsNeeded 3 . + 2803 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 803}] [ a r:Fact; r:gives {(803 2000) math:sum 2803}] - skolem:lemma1805 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1803 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma805 a r:Inference; +skolem:lemma804 a r:Inference; r:gives { - (2804 6174) :recursionsNeeded 6 . + 2804 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 804}] [ a r:Fact; r:gives {(804 2000) math:sum 2804}] - skolem:lemma1806 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1804 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma806 a r:Inference; +skolem:lemma805 a r:Inference; r:gives { - (2805 6174) :recursionsNeeded 5 . + 2805 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 805}] [ a r:Fact; r:gives {(805 2000) math:sum 2805}] - skolem:lemma1807 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1805 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma807 a r:Inference; +skolem:lemma806 a r:Inference; r:gives { - (2806 6174) :recursionsNeeded 2 . + 2806 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 806}] [ a r:Fact; r:gives {(806 2000) math:sum 2806}] - skolem:lemma1808 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1806 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma808 a r:Inference; +skolem:lemma807 a r:Inference; r:gives { - (2807 6174) :recursionsNeeded 7 . + 2807 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 807}] [ a r:Fact; r:gives {(807 2000) math:sum 2807}] - skolem:lemma1809 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1807 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma809 a r:Inference; +skolem:lemma808 a r:Inference; r:gives { - (2808 6174) :recursionsNeeded 2 . + 2808 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 808}] [ a r:Fact; r:gives {(808 2000) math:sum 2808}] - skolem:lemma1810 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1808 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma810 a r:Inference; +skolem:lemma809 a r:Inference; r:gives { - (2809 6174) :recursionsNeeded 7 . + 2809 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 809}] [ a r:Fact; r:gives {(809 2000) math:sum 2809}] - skolem:lemma1811 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1809 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma811 a r:Inference; +skolem:lemma810 a r:Inference; r:gives { - (2810 6174) :recursionsNeeded 3 . + 2810 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 810}] [ a r:Fact; r:gives {(810 2000) math:sum 2810}] - skolem:lemma1812 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1810 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma812 a r:Inference; +skolem:lemma811 a r:Inference; r:gives { - (2811 6174) :recursionsNeeded 3 . + 2811 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 811}] [ a r:Fact; r:gives {(811 2000) math:sum 2811}] - skolem:lemma1813 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1811 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma813 a r:Inference; +skolem:lemma812 a r:Inference; r:gives { - (2812 6174) :recursionsNeeded 4 . + 2812 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 812}] [ a r:Fact; r:gives {(812 2000) math:sum 2812}] - skolem:lemma1814 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1812 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma814 a r:Inference; +skolem:lemma813 a r:Inference; r:gives { - (2813 6174) :recursionsNeeded 3 . + 2813 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 813}] [ a r:Fact; r:gives {(813 2000) math:sum 2813}] - skolem:lemma1815 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1813 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma815 a r:Inference; +skolem:lemma814 a r:Inference; r:gives { - (2814 6174) :recursionsNeeded 5 . + 2814 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 814}] [ a r:Fact; r:gives {(814 2000) math:sum 2814}] - skolem:lemma1816 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1814 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma816 a r:Inference; +skolem:lemma815 a r:Inference; r:gives { - (2815 6174) :recursionsNeeded 6 . + 2815 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 815}] [ a r:Fact; r:gives {(815 2000) math:sum 2815}] - skolem:lemma1817 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1815 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma817 a r:Inference; +skolem:lemma816 a r:Inference; r:gives { - (2816 6174) :recursionsNeeded 3 . + 2816 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 816}] [ a r:Fact; r:gives {(816 2000) math:sum 2816}] - skolem:lemma1818 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1816 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma818 a r:Inference; +skolem:lemma817 a r:Inference; r:gives { - (2817 6174) :recursionsNeeded 5 . + 2817 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 817}] [ a r:Fact; r:gives {(817 2000) math:sum 2817}] - skolem:lemma1819 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1817 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma819 a r:Inference; +skolem:lemma818 a r:Inference; r:gives { - (2818 6174) :recursionsNeeded 3 . + 2818 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 818}] [ a r:Fact; r:gives {(818 2000) math:sum 2818}] - skolem:lemma1820 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1818 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma820 a r:Inference; +skolem:lemma819 a r:Inference; r:gives { - (2819 6174) :recursionsNeeded 2 . + 2819 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 819}] [ a r:Fact; r:gives {(819 2000) math:sum 2819}] - skolem:lemma1821 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1819 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma821 a r:Inference; +skolem:lemma820 a r:Inference; r:gives { - (2820 6174) :recursionsNeeded 6 . + 2820 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 820}] [ a r:Fact; r:gives {(820 2000) math:sum 2820}] - skolem:lemma1822 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1820 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma822 a r:Inference; +skolem:lemma821 a r:Inference; r:gives { - (2821 6174) :recursionsNeeded 4 . + 2821 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 821}] [ a r:Fact; r:gives {(821 2000) math:sum 2821}] - skolem:lemma1823 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1821 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma823 a r:Inference; +skolem:lemma822 a r:Inference; r:gives { - (2822 6174) :recursionsNeeded 6 . + 2822 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 822}] [ a r:Fact; r:gives {(822 2000) math:sum 2822}] - skolem:lemma1824 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1822 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma824 a r:Inference; +skolem:lemma823 a r:Inference; r:gives { - (2823 6174) :recursionsNeeded 7 . + 2823 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 823}] [ a r:Fact; r:gives {(823 2000) math:sum 2823}] - skolem:lemma1825 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1823 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma825 a r:Inference; +skolem:lemma824 a r:Inference; r:gives { - (2824 6174) :recursionsNeeded 1 . + 2824 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 824}] [ a r:Fact; r:gives {(824 2000) math:sum 2824}] - skolem:lemma1826 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1824 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma826 a r:Inference; +skolem:lemma825 a r:Inference; r:gives { - (2825 6174) :recursionsNeeded 3 . + 2825 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 825}] [ a r:Fact; r:gives {(825 2000) math:sum 2825}] - skolem:lemma1827 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1825 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma827 a r:Inference; +skolem:lemma826 a r:Inference; r:gives { - (2826 6174) :recursionsNeeded 4 . + 2826 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 826}] [ a r:Fact; r:gives {(826 2000) math:sum 2826}] - skolem:lemma1828 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1826 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma828 a r:Inference; +skolem:lemma827 a r:Inference; r:gives { - (2827 6174) :recursionsNeeded 5 . + 2827 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 827}] [ a r:Fact; r:gives {(827 2000) math:sum 2827}] - skolem:lemma1829 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1827 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma829 a r:Inference; +skolem:lemma828 a r:Inference; r:gives { - (2828 6174) :recursionsNeeded 4 . + 2828 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 828}] [ a r:Fact; r:gives {(828 2000) math:sum 2828}] - skolem:lemma1830 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1828 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma830 a r:Inference; +skolem:lemma829 a r:Inference; r:gives { - (2829 6174) :recursionsNeeded 3 . + 2829 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 829}] [ a r:Fact; r:gives {(829 2000) math:sum 2829}] - skolem:lemma1831 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1829 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma831 a r:Inference; +skolem:lemma830 a r:Inference; r:gives { - (2830 6174) :recursionsNeeded 3 . + 2830 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 830}] [ a r:Fact; r:gives {(830 2000) math:sum 2830}] - skolem:lemma1832 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1830 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma832 a r:Inference; +skolem:lemma831 a r:Inference; r:gives { - (2831 6174) :recursionsNeeded 3 . + 2831 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 831}] [ a r:Fact; r:gives {(831 2000) math:sum 2831}] - skolem:lemma1833 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1831 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma833 a r:Inference; +skolem:lemma832 a r:Inference; r:gives { - (2832 6174) :recursionsNeeded 7 . + 2832 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 832}] [ a r:Fact; r:gives {(832 2000) math:sum 2832}] - skolem:lemma1834 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1832 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma834 a r:Inference; +skolem:lemma833 a r:Inference; r:gives { - (2833 6174) :recursionsNeeded 6 . + 2833 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 833}] [ a r:Fact; r:gives {(833 2000) math:sum 2833}] - skolem:lemma1835 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1833 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma835 a r:Inference; +skolem:lemma834 a r:Inference; r:gives { - (2834 6174) :recursionsNeeded 7 . + 2834 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 834}] [ a r:Fact; r:gives {(834 2000) math:sum 2834}] - skolem:lemma1836 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1834 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma836 a r:Inference; +skolem:lemma835 a r:Inference; r:gives { - (2835 6174) :recursionsNeeded 1 . + 2835 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 835}] [ a r:Fact; r:gives {(835 2000) math:sum 2835}] - skolem:lemma1837 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1835 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma837 a r:Inference; +skolem:lemma836 a r:Inference; r:gives { - (2836 6174) :recursionsNeeded 3 . + 2836 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 836}] [ a r:Fact; r:gives {(836 2000) math:sum 2836}] - skolem:lemma1838 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1836 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma838 a r:Inference; +skolem:lemma837 a r:Inference; r:gives { - (2837 6174) :recursionsNeeded 4 . + 2837 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 837}] [ a r:Fact; r:gives {(837 2000) math:sum 2837}] - skolem:lemma1839 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1837 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma839 a r:Inference; +skolem:lemma838 a r:Inference; r:gives { - (2838 6174) :recursionsNeeded 5 . + 2838 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 838}] [ a r:Fact; r:gives {(838 2000) math:sum 2838}] - skolem:lemma1840 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1838 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma840 a r:Inference; +skolem:lemma839 a r:Inference; r:gives { - (2839 6174) :recursionsNeeded 5 . + 2839 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 839}] [ a r:Fact; r:gives {(839 2000) math:sum 2839}] - skolem:lemma1841 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1839 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma841 a r:Inference; +skolem:lemma840 a r:Inference; r:gives { - (2840 6174) :recursionsNeeded 6 . + 2840 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 840}] [ a r:Fact; r:gives {(840 2000) math:sum 2840}] - skolem:lemma1842 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1840 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma842 a r:Inference; +skolem:lemma841 a r:Inference; r:gives { - (2841 6174) :recursionsNeeded 5 . + 2841 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 841}] [ a r:Fact; r:gives {(841 2000) math:sum 2841}] - skolem:lemma1843 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1841 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma843 a r:Inference; +skolem:lemma842 a r:Inference; r:gives { - (2842 6174) :recursionsNeeded 1 . + 2842 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 842}] [ a r:Fact; r:gives {(842 2000) math:sum 2842}] - skolem:lemma1844 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1842 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma844 a r:Inference; +skolem:lemma843 a r:Inference; r:gives { - (2843 6174) :recursionsNeeded 7 . + 2843 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 843}] [ a r:Fact; r:gives {(843 2000) math:sum 2843}] - skolem:lemma1845 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1843 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma845 a r:Inference; +skolem:lemma844 a r:Inference; r:gives { - (2844 6174) :recursionsNeeded 6 . + 2844 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 844}] [ a r:Fact; r:gives {(844 2000) math:sum 2844}] - skolem:lemma1846 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1844 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma846 a r:Inference; +skolem:lemma845 a r:Inference; r:gives { - (2845 6174) :recursionsNeeded 7 . + 2845 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 845}] [ a r:Fact; r:gives {(845 2000) math:sum 2845}] - skolem:lemma1847 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1845 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma847 a r:Inference; +skolem:lemma846 a r:Inference; r:gives { - (2846 6174) :recursionsNeeded 1 . + 2846 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 846}] [ a r:Fact; r:gives {(846 2000) math:sum 2846}] - skolem:lemma1848 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1846 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma848 a r:Inference; +skolem:lemma847 a r:Inference; r:gives { - (2847 6174) :recursionsNeeded 3 . + 2847 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 847}] [ a r:Fact; r:gives {(847 2000) math:sum 2847}] - skolem:lemma1849 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1847 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma849 a r:Inference; +skolem:lemma848 a r:Inference; r:gives { - (2848 6174) :recursionsNeeded 4 . + 2848 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 848}] [ a r:Fact; r:gives {(848 2000) math:sum 2848}] - skolem:lemma1850 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1848 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma850 a r:Inference; +skolem:lemma849 a r:Inference; r:gives { - (2849 6174) :recursionsNeeded 3 . + 2849 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 849}] [ a r:Fact; r:gives {(849 2000) math:sum 2849}] - skolem:lemma1851 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1849 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma851 a r:Inference; +skolem:lemma850 a r:Inference; r:gives { - (2850 6174) :recursionsNeeded 5 . + 2850 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 850}] [ a r:Fact; r:gives {(850 2000) math:sum 2850}] - skolem:lemma1852 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1850 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma852 a r:Inference; +skolem:lemma851 a r:Inference; r:gives { - (2851 6174) :recursionsNeeded 6 . + 2851 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 851}] [ a r:Fact; r:gives {(851 2000) math:sum 2851}] - skolem:lemma1853 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1851 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma853 a r:Inference; +skolem:lemma852 a r:Inference; r:gives { - (2852 6174) :recursionsNeeded 3 . + 2852 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 852}] [ a r:Fact; r:gives {(852 2000) math:sum 2852}] - skolem:lemma1854 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1852 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma854 a r:Inference; +skolem:lemma853 a r:Inference; r:gives { - (2853 6174) :recursionsNeeded 1 . + 2853 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 853}] [ a r:Fact; r:gives {(853 2000) math:sum 2853}] - skolem:lemma1855 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1853 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma855 a r:Inference; +skolem:lemma854 a r:Inference; r:gives { - (2854 6174) :recursionsNeeded 7 . + 2854 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 854}] [ a r:Fact; r:gives {(854 2000) math:sum 2854}] - skolem:lemma1856 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1854 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma856 a r:Inference; +skolem:lemma855 a r:Inference; r:gives { - (2855 6174) :recursionsNeeded 6 . + 2855 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 855}] [ a r:Fact; r:gives {(855 2000) math:sum 2855}] - skolem:lemma1857 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1855 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma857 a r:Inference; +skolem:lemma856 a r:Inference; r:gives { - (2856 6174) :recursionsNeeded 7 . + 2856 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 856}] [ a r:Fact; r:gives {(856 2000) math:sum 2856}] - skolem:lemma1858 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1856 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma858 a r:Inference; +skolem:lemma857 a r:Inference; r:gives { - (2857 6174) :recursionsNeeded 1 . + 2857 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 857}] [ a r:Fact; r:gives {(857 2000) math:sum 2857}] - skolem:lemma1859 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1857 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma859 a r:Inference; +skolem:lemma858 a r:Inference; r:gives { - (2858 6174) :recursionsNeeded 3 . + 2858 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 858}] [ a r:Fact; r:gives {(858 2000) math:sum 2858}] - skolem:lemma1860 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1858 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma860 a r:Inference; +skolem:lemma859 a r:Inference; r:gives { - (2859 6174) :recursionsNeeded 6 . + 2859 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 859}] [ a r:Fact; r:gives {(859 2000) math:sum 2859}] - skolem:lemma1861 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1859 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma861 a r:Inference; +skolem:lemma860 a r:Inference; r:gives { - (2860 6174) :recursionsNeeded 2 . + 2860 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 860}] [ a r:Fact; r:gives {(860 2000) math:sum 2860}] - skolem:lemma1862 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1860 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma862 a r:Inference; +skolem:lemma861 a r:Inference; r:gives { - (2861 6174) :recursionsNeeded 3 . + 2861 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 861}] [ a r:Fact; r:gives {(861 2000) math:sum 2861}] - skolem:lemma1863 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1861 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma863 a r:Inference; +skolem:lemma862 a r:Inference; r:gives { - (2862 6174) :recursionsNeeded 4 . + 2862 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 862}] [ a r:Fact; r:gives {(862 2000) math:sum 2862}] - skolem:lemma1864 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1862 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma864 a r:Inference; +skolem:lemma863 a r:Inference; r:gives { - (2863 6174) :recursionsNeeded 3 . + 2863 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 863}] [ a r:Fact; r:gives {(863 2000) math:sum 2863}] - skolem:lemma1865 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1863 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma865 a r:Inference; +skolem:lemma864 a r:Inference; r:gives { - (2864 6174) :recursionsNeeded 1 . + 2864 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 864}] [ a r:Fact; r:gives {(864 2000) math:sum 2864}] - skolem:lemma1866 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1864 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma866 a r:Inference; +skolem:lemma865 a r:Inference; r:gives { - (2865 6174) :recursionsNeeded 7 . + 2865 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 865}] [ a r:Fact; r:gives {(865 2000) math:sum 2865}] - skolem:lemma1867 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1865 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma867 a r:Inference; +skolem:lemma866 a r:Inference; r:gives { - (2866 6174) :recursionsNeeded 6 . + 2866 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 866}] [ a r:Fact; r:gives {(866 2000) math:sum 2866}] - skolem:lemma1868 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1866 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma868 a r:Inference; +skolem:lemma867 a r:Inference; r:gives { - (2867 6174) :recursionsNeeded 7 . + 2867 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 867}] [ a r:Fact; r:gives {(867 2000) math:sum 2867}] - skolem:lemma1869 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1867 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma869 a r:Inference; +skolem:lemma868 a r:Inference; r:gives { - (2868 6174) :recursionsNeeded 1 . + 2868 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 868}] [ a r:Fact; r:gives {(868 2000) math:sum 2868}] - skolem:lemma1870 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1868 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma870 a r:Inference; +skolem:lemma869 a r:Inference; r:gives { - (2869 6174) :recursionsNeeded 5 . + 2869 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 869}] [ a r:Fact; r:gives {(869 2000) math:sum 2869}] - skolem:lemma1871 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1869 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma871 a r:Inference; +skolem:lemma870 a r:Inference; r:gives { - (2870 6174) :recursionsNeeded 7 . + 2870 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 870}] [ a r:Fact; r:gives {(870 2000) math:sum 2870}] - skolem:lemma1872 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1870 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma872 a r:Inference; +skolem:lemma871 a r:Inference; r:gives { - (2871 6174) :recursionsNeeded 5 . + 2871 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 871}] [ a r:Fact; r:gives {(871 2000) math:sum 2871}] - skolem:lemma1873 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1871 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma873 a r:Inference; +skolem:lemma872 a r:Inference; r:gives { - (2872 6174) :recursionsNeeded 5 . + 2872 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 872}] [ a r:Fact; r:gives {(872 2000) math:sum 2872}] - skolem:lemma1874 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1872 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma874 a r:Inference; +skolem:lemma873 a r:Inference; r:gives { - (2873 6174) :recursionsNeeded 4 . + 2873 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 873}] [ a r:Fact; r:gives {(873 2000) math:sum 2873}] - skolem:lemma1875 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1873 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma875 a r:Inference; +skolem:lemma874 a r:Inference; r:gives { - (2874 6174) :recursionsNeeded 3 . + 2874 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 874}] [ a r:Fact; r:gives {(874 2000) math:sum 2874}] - skolem:lemma1876 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1874 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma876 a r:Inference; +skolem:lemma875 a r:Inference; r:gives { - (2875 6174) :recursionsNeeded 1 . + 2875 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 875}] [ a r:Fact; r:gives {(875 2000) math:sum 2875}] - skolem:lemma1877 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1875 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma877 a r:Inference; +skolem:lemma876 a r:Inference; r:gives { - (2876 6174) :recursionsNeeded 7 . + 2876 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 876}] [ a r:Fact; r:gives {(876 2000) math:sum 2876}] - skolem:lemma1878 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1876 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma878 a r:Inference; +skolem:lemma877 a r:Inference; r:gives { - (2877 6174) :recursionsNeeded 6 . + 2877 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 877}] [ a r:Fact; r:gives {(877 2000) math:sum 2877}] - skolem:lemma1879 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1877 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma879 a r:Inference; +skolem:lemma878 a r:Inference; r:gives { - (2878 6174) :recursionsNeeded 7 . + 2878 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 878}] [ a r:Fact; r:gives {(878 2000) math:sum 2878}] - skolem:lemma1880 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1878 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma880 a r:Inference; +skolem:lemma879 a r:Inference; r:gives { - (2879 6174) :recursionsNeeded 3 . + 2879 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 879}] [ a r:Fact; r:gives {(879 2000) math:sum 2879}] - skolem:lemma1881 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1879 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma881 a r:Inference; +skolem:lemma880 a r:Inference; r:gives { - (2880 6174) :recursionsNeeded 2 . + 2880 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 880}] [ a r:Fact; r:gives {(880 2000) math:sum 2880}] - skolem:lemma1882 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1880 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma882 a r:Inference; +skolem:lemma881 a r:Inference; r:gives { - (2881 6174) :recursionsNeeded 3 . + 2881 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 881}] [ a r:Fact; r:gives {(881 2000) math:sum 2881}] - skolem:lemma1883 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1881 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma883 a r:Inference; +skolem:lemma882 a r:Inference; r:gives { - (2882 6174) :recursionsNeeded 4 . + 2882 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 882}] [ a r:Fact; r:gives {(882 2000) math:sum 2882}] - skolem:lemma1884 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1882 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma884 a r:Inference; +skolem:lemma883 a r:Inference; r:gives { - (2883 6174) :recursionsNeeded 5 . + 2883 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 883}] [ a r:Fact; r:gives {(883 2000) math:sum 2883}] - skolem:lemma1885 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1883 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma885 a r:Inference; +skolem:lemma884 a r:Inference; r:gives { - (2884 6174) :recursionsNeeded 4 . + 2884 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 884}] [ a r:Fact; r:gives {(884 2000) math:sum 2884}] - skolem:lemma1886 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1884 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma886 a r:Inference; +skolem:lemma885 a r:Inference; r:gives { - (2885 6174) :recursionsNeeded 3 . + 2885 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 885}] [ a r:Fact; r:gives {(885 2000) math:sum 2885}] - skolem:lemma1887 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1885 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma887 a r:Inference; +skolem:lemma886 a r:Inference; r:gives { - (2886 6174) :recursionsNeeded 1 . + 2886 :recursionCount 1 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 886}] [ a r:Fact; r:gives {(886 2000) math:sum 2886}] - skolem:lemma1888 - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1886 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma1001. -skolem:lemma888 a r:Inference; +skolem:lemma887 a r:Inference; r:gives { - (2887 6174) :recursionsNeeded 7 . + 2887 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 887}] [ a r:Fact; r:gives {(887 2000) math:sum 2887}] - skolem:lemma1889 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1887 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma889 a r:Inference; +skolem:lemma888 a r:Inference; r:gives { - (2888 6174) :recursionsNeeded 6 . + 2888 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 888}] [ a r:Fact; r:gives {(888 2000) math:sum 2888}] - skolem:lemma1890 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1888 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma890 a r:Inference; +skolem:lemma889 a r:Inference; r:gives { - (2889 6174) :recursionsNeeded 4 . + 2889 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 889}] [ a r:Fact; r:gives {(889 2000) math:sum 2889}] - skolem:lemma1891 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1889 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma891 a r:Inference; +skolem:lemma890 a r:Inference; r:gives { - (2890 6174) :recursionsNeeded 7 . + 2890 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 890}] [ a r:Fact; r:gives {(890 2000) math:sum 2890}] - skolem:lemma1892 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1890 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma892 a r:Inference; +skolem:lemma891 a r:Inference; r:gives { - (2891 6174) :recursionsNeeded 2 . + 2891 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 891}] [ a r:Fact; r:gives {(891 2000) math:sum 2891}] - skolem:lemma1893 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1891 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma893 a r:Inference; +skolem:lemma892 a r:Inference; r:gives { - (2892 6174) :recursionsNeeded 3 . + 2892 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 892}] [ a r:Fact; r:gives {(892 2000) math:sum 2892}] - skolem:lemma1894 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1892 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma894 a r:Inference; +skolem:lemma893 a r:Inference; r:gives { - (2893 6174) :recursionsNeeded 5 . + 2893 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 893}] [ a r:Fact; r:gives {(893 2000) math:sum 2893}] - skolem:lemma1895 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1893 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma895 a r:Inference; +skolem:lemma894 a r:Inference; r:gives { - (2894 6174) :recursionsNeeded 3 . + 2894 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 894}] [ a r:Fact; r:gives {(894 2000) math:sum 2894}] - skolem:lemma1896 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1894 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma896 a r:Inference; +skolem:lemma895 a r:Inference; r:gives { - (2895 6174) :recursionsNeeded 6 . + 2895 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 895}] [ a r:Fact; r:gives {(895 2000) math:sum 2895}] - skolem:lemma1897 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1895 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma897 a r:Inference; +skolem:lemma896 a r:Inference; r:gives { - (2896 6174) :recursionsNeeded 5 . + 2896 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 896}] [ a r:Fact; r:gives {(896 2000) math:sum 2896}] - skolem:lemma1898 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1896 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma898 a r:Inference; +skolem:lemma897 a r:Inference; r:gives { - (2897 6174) :recursionsNeeded 3 . + 2897 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 897}] [ a r:Fact; r:gives {(897 2000) math:sum 2897}] - skolem:lemma1899 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1897 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma899 a r:Inference; +skolem:lemma898 a r:Inference; r:gives { - (2898 6174) :recursionsNeeded 4 . + 2898 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 898}] [ a r:Fact; r:gives {(898 2000) math:sum 2898}] - skolem:lemma1900 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1898 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma900 a r:Inference; +skolem:lemma899 a r:Inference; r:gives { - (2899 6174) :recursionsNeeded 3 . + 2899 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 899}] [ a r:Fact; r:gives {(899 2000) math:sum 2899}] - skolem:lemma1901 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1899 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma901 a r:Inference; +skolem:lemma900 a r:Inference; r:gives { - (2900 6174) :recursionsNeeded 3 . + 2900 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 900}] [ a r:Fact; r:gives {(900 2000) math:sum 2900}] - skolem:lemma1902 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1900 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma902 a r:Inference; +skolem:lemma901 a r:Inference; r:gives { - (2901 6174) :recursionsNeeded 4 . + 2901 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 901}] [ a r:Fact; r:gives {(901 2000) math:sum 2901}] - skolem:lemma1903 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1901 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma903 a r:Inference; +skolem:lemma902 a r:Inference; r:gives { - (2902 6174) :recursionsNeeded 4 . + 2902 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 902}] [ a r:Fact; r:gives {(902 2000) math:sum 2902}] - skolem:lemma1904 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1902 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma904 a r:Inference; +skolem:lemma903 a r:Inference; r:gives { - (2903 6174) :recursionsNeeded 4 . + 2903 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 903}] [ a r:Fact; r:gives {(903 2000) math:sum 2903}] - skolem:lemma1905 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1903 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma905 a r:Inference; +skolem:lemma904 a r:Inference; r:gives { - (2904 6174) :recursionsNeeded 3 . + 2904 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 904}] [ a r:Fact; r:gives {(904 2000) math:sum 2904}] - skolem:lemma1906 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1904 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma906 a r:Inference; +skolem:lemma905 a r:Inference; r:gives { - (2905 6174) :recursionsNeeded 3 . + 2905 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 905}] [ a r:Fact; r:gives {(905 2000) math:sum 2905}] - skolem:lemma1907 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1905 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma907 a r:Inference; +skolem:lemma906 a r:Inference; r:gives { - (2906 6174) :recursionsNeeded 7 . + 2906 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 906}] [ a r:Fact; r:gives {(906 2000) math:sum 2906}] - skolem:lemma1908 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1906 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma908 a r:Inference; +skolem:lemma907 a r:Inference; r:gives { - (2907 6174) :recursionsNeeded 7 . + 2907 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 907}] [ a r:Fact; r:gives {(907 2000) math:sum 2907}] - skolem:lemma1909 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1907 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma909 a r:Inference; +skolem:lemma908 a r:Inference; r:gives { - (2908 6174) :recursionsNeeded 7 . + 2908 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 908}] [ a r:Fact; r:gives {(908 2000) math:sum 2908}] - skolem:lemma1910 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1908 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma910 a r:Inference; +skolem:lemma909 a r:Inference; r:gives { - (2909 6174) :recursionsNeeded 3 . + 2909 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 909}] [ a r:Fact; r:gives {(909 2000) math:sum 2909}] - skolem:lemma1911 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1909 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma911 a r:Inference; +skolem:lemma910 a r:Inference; r:gives { - (2910 6174) :recursionsNeeded 4 . + 2910 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 910}] [ a r:Fact; r:gives {(910 2000) math:sum 2910}] - skolem:lemma1912 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1910 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma912 a r:Inference; +skolem:lemma911 a r:Inference; r:gives { - (2911 6174) :recursionsNeeded 3 . + 2911 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 911}] [ a r:Fact; r:gives {(911 2000) math:sum 2911}] - skolem:lemma1913 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1911 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma913 a r:Inference; +skolem:lemma912 a r:Inference; r:gives { - (2912 6174) :recursionsNeeded 6 . + 2912 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 912}] [ a r:Fact; r:gives {(912 2000) math:sum 2912}] - skolem:lemma1914 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1912 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma914 a r:Inference; +skolem:lemma913 a r:Inference; r:gives { - (2913 6174) :recursionsNeeded 3 . + 2913 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 913}] [ a r:Fact; r:gives {(913 2000) math:sum 2913}] - skolem:lemma1915 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1913 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma915 a r:Inference; +skolem:lemma914 a r:Inference; r:gives { - (2914 6174) :recursionsNeeded 6 . + 2914 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 914}] [ a r:Fact; r:gives {(914 2000) math:sum 2914}] - skolem:lemma1916 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1914 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma916 a r:Inference; +skolem:lemma915 a r:Inference; r:gives { - (2915 6174) :recursionsNeeded 5 . + 2915 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 915}] [ a r:Fact; r:gives {(915 2000) math:sum 2915}] - skolem:lemma1917 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1915 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma917 a r:Inference; +skolem:lemma916 a r:Inference; r:gives { - (2916 6174) :recursionsNeeded 2 . + 2916 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 916}] [ a r:Fact; r:gives {(916 2000) math:sum 2916}] - skolem:lemma1918 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1916 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma918 a r:Inference; +skolem:lemma917 a r:Inference; r:gives { - (2917 6174) :recursionsNeeded 7 . + 2917 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 917}] [ a r:Fact; r:gives {(917 2000) math:sum 2917}] - skolem:lemma1919 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1917 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma919 a r:Inference; +skolem:lemma918 a r:Inference; r:gives { - (2918 6174) :recursionsNeeded 2 . + 2918 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 918}] [ a r:Fact; r:gives {(918 2000) math:sum 2918}] - skolem:lemma1920 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1918 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma920 a r:Inference; +skolem:lemma919 a r:Inference; r:gives { - (2919 6174) :recursionsNeeded 5 . + 2919 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 919}] [ a r:Fact; r:gives {(919 2000) math:sum 2919}] - skolem:lemma1921 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1919 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma921 a r:Inference; +skolem:lemma920 a r:Inference; r:gives { - (2920 6174) :recursionsNeeded 4 . + 2920 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 920}] [ a r:Fact; r:gives {(920 2000) math:sum 2920}] - skolem:lemma1922 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1920 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma922 a r:Inference; +skolem:lemma921 a r:Inference; r:gives { - (2921 6174) :recursionsNeeded 6 . + 2921 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 921}] [ a r:Fact; r:gives {(921 2000) math:sum 2921}] - skolem:lemma1923 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1921 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma923 a r:Inference; +skolem:lemma922 a r:Inference; r:gives { - (2922 6174) :recursionsNeeded 4 . + 2922 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 922}] [ a r:Fact; r:gives {(922 2000) math:sum 2922}] - skolem:lemma1924 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1922 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma924 a r:Inference; +skolem:lemma923 a r:Inference; r:gives { - (2923 6174) :recursionsNeeded 3 . + 2923 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 923}] [ a r:Fact; r:gives {(923 2000) math:sum 2923}] - skolem:lemma1925 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1923 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma925 a r:Inference; +skolem:lemma924 a r:Inference; r:gives { - (2924 6174) :recursionsNeeded 5 . + 2924 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 924}] [ a r:Fact; r:gives {(924 2000) math:sum 2924}] - skolem:lemma1926 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1924 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma926 a r:Inference; +skolem:lemma925 a r:Inference; r:gives { - (2925 6174) :recursionsNeeded 6 . + 2925 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 925}] [ a r:Fact; r:gives {(925 2000) math:sum 2925}] - skolem:lemma1927 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1925 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma927 a r:Inference; +skolem:lemma926 a r:Inference; r:gives { - (2926 6174) :recursionsNeeded 3 . + 2926 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 926}] [ a r:Fact; r:gives {(926 2000) math:sum 2926}] - skolem:lemma1928 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1926 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma928 a r:Inference; +skolem:lemma927 a r:Inference; r:gives { - (2927 6174) :recursionsNeeded 5 . + 2927 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 927}] [ a r:Fact; r:gives {(927 2000) math:sum 2927}] - skolem:lemma1929 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1927 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma929 a r:Inference; +skolem:lemma928 a r:Inference; r:gives { - (2928 6174) :recursionsNeeded 3 . + 2928 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 928}] [ a r:Fact; r:gives {(928 2000) math:sum 2928}] - skolem:lemma1930 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1928 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma930 a r:Inference; +skolem:lemma929 a r:Inference; r:gives { - (2929 6174) :recursionsNeeded 6 . + 2929 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 929}] [ a r:Fact; r:gives {(929 2000) math:sum 2929}] - skolem:lemma1931 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1929 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma931 a r:Inference; +skolem:lemma930 a r:Inference; r:gives { - (2930 6174) :recursionsNeeded 4 . + 2930 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 930}] [ a r:Fact; r:gives {(930 2000) math:sum 2930}] - skolem:lemma1932 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1930 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma932 a r:Inference; +skolem:lemma931 a r:Inference; r:gives { - (2931 6174) :recursionsNeeded 3 . + 2931 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 931}] [ a r:Fact; r:gives {(931 2000) math:sum 2931}] - skolem:lemma1933 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1931 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma933 a r:Inference; +skolem:lemma932 a r:Inference; r:gives { - (2932 6174) :recursionsNeeded 3 . + 2932 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 932}] [ a r:Fact; r:gives {(932 2000) math:sum 2932}] - skolem:lemma1934 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1932 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma934 a r:Inference; +skolem:lemma933 a r:Inference; r:gives { - (2933 6174) :recursionsNeeded 4 . + 2933 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 933}] [ a r:Fact; r:gives {(933 2000) math:sum 2933}] - skolem:lemma1935 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1933 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma935 a r:Inference; +skolem:lemma934 a r:Inference; r:gives { - (2934 6174) :recursionsNeeded 3 . + 2934 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 934}] [ a r:Fact; r:gives {(934 2000) math:sum 2934}] - skolem:lemma1936 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1934 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma936 a r:Inference; +skolem:lemma935 a r:Inference; r:gives { - (2935 6174) :recursionsNeeded 5 . + 2935 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 935}] [ a r:Fact; r:gives {(935 2000) math:sum 2935}] - skolem:lemma1937 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1935 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma937 a r:Inference; +skolem:lemma936 a r:Inference; r:gives { - (2936 6174) :recursionsNeeded 6 . + 2936 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 936}] [ a r:Fact; r:gives {(936 2000) math:sum 2936}] - skolem:lemma1938 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1936 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma938 a r:Inference; +skolem:lemma937 a r:Inference; r:gives { - (2937 6174) :recursionsNeeded 3 . + 2937 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 937}] [ a r:Fact; r:gives {(937 2000) math:sum 2937}] - skolem:lemma1939 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1937 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma939 a r:Inference; +skolem:lemma938 a r:Inference; r:gives { - (2938 6174) :recursionsNeeded 5 . + 2938 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 938}] [ a r:Fact; r:gives {(938 2000) math:sum 2938}] - skolem:lemma1940 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1938 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma940 a r:Inference; +skolem:lemma939 a r:Inference; r:gives { - (2939 6174) :recursionsNeeded 3 . + 2939 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 939}] [ a r:Fact; r:gives {(939 2000) math:sum 2939}] - skolem:lemma1941 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1939 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma941 a r:Inference; +skolem:lemma940 a r:Inference; r:gives { - (2940 6174) :recursionsNeeded 3 . + 2940 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 940}] [ a r:Fact; r:gives {(940 2000) math:sum 2940}] - skolem:lemma1942 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1940 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma942 a r:Inference; +skolem:lemma941 a r:Inference; r:gives { - (2941 6174) :recursionsNeeded 6 . + 2941 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 941}] [ a r:Fact; r:gives {(941 2000) math:sum 2941}] - skolem:lemma1943 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1941 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma943 a r:Inference; +skolem:lemma942 a r:Inference; r:gives { - (2942 6174) :recursionsNeeded 5 . + 2942 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 942}] [ a r:Fact; r:gives {(942 2000) math:sum 2942}] - skolem:lemma1944 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1942 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma944 a r:Inference; +skolem:lemma943 a r:Inference; r:gives { - (2943 6174) :recursionsNeeded 3 . + 2943 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 943}] [ a r:Fact; r:gives {(943 2000) math:sum 2943}] - skolem:lemma1945 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1943 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma945 a r:Inference; +skolem:lemma944 a r:Inference; r:gives { - (2944 6174) :recursionsNeeded 4 . + 2944 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 944}] [ a r:Fact; r:gives {(944 2000) math:sum 2944}] - skolem:lemma1946 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1944 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma946 a r:Inference; +skolem:lemma945 a r:Inference; r:gives { - (2945 6174) :recursionsNeeded 3 . + 2945 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 945}] [ a r:Fact; r:gives {(945 2000) math:sum 2945}] - skolem:lemma1947 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1945 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma947 a r:Inference; +skolem:lemma946 a r:Inference; r:gives { - (2946 6174) :recursionsNeeded 5 . + 2946 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 946}] [ a r:Fact; r:gives {(946 2000) math:sum 2946}] - skolem:lemma1948 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1946 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma948 a r:Inference; +skolem:lemma947 a r:Inference; r:gives { - (2947 6174) :recursionsNeeded 6 . + 2947 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 947}] [ a r:Fact; r:gives {(947 2000) math:sum 2947}] - skolem:lemma1949 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1947 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma949 a r:Inference; +skolem:lemma948 a r:Inference; r:gives { - (2948 6174) :recursionsNeeded 3 . + 2948 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 948}] [ a r:Fact; r:gives {(948 2000) math:sum 2948}] - skolem:lemma1950 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1948 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma950 a r:Inference; +skolem:lemma949 a r:Inference; r:gives { - (2949 6174) :recursionsNeeded 5 . + 2949 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 949}] [ a r:Fact; r:gives {(949 2000) math:sum 2949}] - skolem:lemma1951 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1949 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma951 a r:Inference; +skolem:lemma950 a r:Inference; r:gives { - (2950 6174) :recursionsNeeded 3 . + 2950 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 950}] [ a r:Fact; r:gives {(950 2000) math:sum 2950}] - skolem:lemma1952 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1950 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma952 a r:Inference; +skolem:lemma951 a r:Inference; r:gives { - (2951 6174) :recursionsNeeded 5 . + 2951 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 951}] [ a r:Fact; r:gives {(951 2000) math:sum 2951}] - skolem:lemma1953 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1951 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma953 a r:Inference; +skolem:lemma952 a r:Inference; r:gives { - (2952 6174) :recursionsNeeded 6 . + 2952 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 952}] [ a r:Fact; r:gives {(952 2000) math:sum 2952}] - skolem:lemma1954 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1952 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma954 a r:Inference; +skolem:lemma953 a r:Inference; r:gives { - (2953 6174) :recursionsNeeded 5 . + 2953 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 953}] [ a r:Fact; r:gives {(953 2000) math:sum 2953}] - skolem:lemma1955 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1953 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma955 a r:Inference; +skolem:lemma954 a r:Inference; r:gives { - (2954 6174) :recursionsNeeded 3 . + 2954 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 954}] [ a r:Fact; r:gives {(954 2000) math:sum 2954}] - skolem:lemma1956 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1954 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma956 a r:Inference; +skolem:lemma955 a r:Inference; r:gives { - (2955 6174) :recursionsNeeded 4 . + 2955 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 955}] [ a r:Fact; r:gives {(955 2000) math:sum 2955}] - skolem:lemma1957 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1955 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma957 a r:Inference; +skolem:lemma956 a r:Inference; r:gives { - (2956 6174) :recursionsNeeded 3 . + 2956 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 956}] [ a r:Fact; r:gives {(956 2000) math:sum 2956}] - skolem:lemma1958 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1956 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma958 a r:Inference; +skolem:lemma957 a r:Inference; r:gives { - (2957 6174) :recursionsNeeded 5 . + 2957 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 957}] [ a r:Fact; r:gives {(957 2000) math:sum 2957}] - skolem:lemma1959 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1957 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma959 a r:Inference; +skolem:lemma958 a r:Inference; r:gives { - (2958 6174) :recursionsNeeded 6 . + 2958 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 958}] [ a r:Fact; r:gives {(958 2000) math:sum 2958}] - skolem:lemma1960 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1958 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma960 a r:Inference; +skolem:lemma959 a r:Inference; r:gives { - (2959 6174) :recursionsNeeded 3 . + 2959 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 959}] [ a r:Fact; r:gives {(959 2000) math:sum 2959}] - skolem:lemma1961 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1959 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma961 a r:Inference; +skolem:lemma960 a r:Inference; r:gives { - (2960 6174) :recursionsNeeded 7 . + 2960 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 960}] [ a r:Fact; r:gives {(960 2000) math:sum 2960}] - skolem:lemma1962 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1960 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma962 a r:Inference; +skolem:lemma961 a r:Inference; r:gives { - (2961 6174) :recursionsNeeded 2 . + 2961 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 961}] [ a r:Fact; r:gives {(961 2000) math:sum 2961}] - skolem:lemma1963 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1961 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma963 a r:Inference; +skolem:lemma962 a r:Inference; r:gives { - (2962 6174) :recursionsNeeded 3 . + 2962 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 962}] [ a r:Fact; r:gives {(962 2000) math:sum 2962}] - skolem:lemma1964 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1962 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma964 a r:Inference; +skolem:lemma963 a r:Inference; r:gives { - (2963 6174) :recursionsNeeded 6 . + 2963 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 963}] [ a r:Fact; r:gives {(963 2000) math:sum 2963}] - skolem:lemma1965 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1963 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma965 a r:Inference; +skolem:lemma964 a r:Inference; r:gives { - (2964 6174) :recursionsNeeded 5 . + 2964 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 964}] [ a r:Fact; r:gives {(964 2000) math:sum 2964}] - skolem:lemma1966 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1964 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma966 a r:Inference; +skolem:lemma965 a r:Inference; r:gives { - (2965 6174) :recursionsNeeded 3 . + 2965 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 965}] [ a r:Fact; r:gives {(965 2000) math:sum 2965}] - skolem:lemma1967 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1965 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma967 a r:Inference; +skolem:lemma966 a r:Inference; r:gives { - (2966 6174) :recursionsNeeded 4 . + 2966 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 966}] [ a r:Fact; r:gives {(966 2000) math:sum 2966}] - skolem:lemma1968 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1966 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma968 a r:Inference; +skolem:lemma967 a r:Inference; r:gives { - (2967 6174) :recursionsNeeded 3 . + 2967 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 967}] [ a r:Fact; r:gives {(967 2000) math:sum 2967}] - skolem:lemma1969 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1967 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma969 a r:Inference; +skolem:lemma968 a r:Inference; r:gives { - (2968 6174) :recursionsNeeded 5 . + 2968 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 968}] [ a r:Fact; r:gives {(968 2000) math:sum 2968}] - skolem:lemma1970 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1968 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma970 a r:Inference; +skolem:lemma969 a r:Inference; r:gives { - (2969 6174) :recursionsNeeded 6 . + 2969 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 969}] [ a r:Fact; r:gives {(969 2000) math:sum 2969}] - skolem:lemma1971 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1969 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma971 a r:Inference; +skolem:lemma970 a r:Inference; r:gives { - (2970 6174) :recursionsNeeded 7 . + 2970 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 970}] [ a r:Fact; r:gives {(970 2000) math:sum 2970}] - skolem:lemma1972 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1970 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma972 a r:Inference; +skolem:lemma971 a r:Inference; r:gives { - (2971 6174) :recursionsNeeded 7 . + 2971 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 971}] [ a r:Fact; r:gives {(971 2000) math:sum 2971}] - skolem:lemma1973 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1971 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma973 a r:Inference; +skolem:lemma972 a r:Inference; r:gives { - (2972 6174) :recursionsNeeded 5 . + 2972 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 972}] [ a r:Fact; r:gives {(972 2000) math:sum 2972}] - skolem:lemma1974 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1972 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma974 a r:Inference; +skolem:lemma973 a r:Inference; r:gives { - (2973 6174) :recursionsNeeded 3 . + 2973 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 973}] [ a r:Fact; r:gives {(973 2000) math:sum 2973}] - skolem:lemma1975 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1973 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma975 a r:Inference; +skolem:lemma974 a r:Inference; r:gives { - (2974 6174) :recursionsNeeded 6 . + 2974 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 974}] [ a r:Fact; r:gives {(974 2000) math:sum 2974}] - skolem:lemma1976 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1974 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma976 a r:Inference; +skolem:lemma975 a r:Inference; r:gives { - (2975 6174) :recursionsNeeded 5 . + 2975 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 975}] [ a r:Fact; r:gives {(975 2000) math:sum 2975}] - skolem:lemma1977 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1975 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma977 a r:Inference; +skolem:lemma976 a r:Inference; r:gives { - (2976 6174) :recursionsNeeded 3 . + 2976 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 976}] [ a r:Fact; r:gives {(976 2000) math:sum 2976}] - skolem:lemma1978 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1976 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma978 a r:Inference; +skolem:lemma977 a r:Inference; r:gives { - (2977 6174) :recursionsNeeded 4 . + 2977 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 977}] [ a r:Fact; r:gives {(977 2000) math:sum 2977}] - skolem:lemma1979 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1977 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma979 a r:Inference; +skolem:lemma978 a r:Inference; r:gives { - (2978 6174) :recursionsNeeded 3 . + 2978 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 978}] [ a r:Fact; r:gives {(978 2000) math:sum 2978}] - skolem:lemma1980 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1978 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma980 a r:Inference; +skolem:lemma979 a r:Inference; r:gives { - (2979 6174) :recursionsNeeded 5 . + 2979 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 979}] [ a r:Fact; r:gives {(979 2000) math:sum 2979}] - skolem:lemma1981 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1979 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma981 a r:Inference; +skolem:lemma980 a r:Inference; r:gives { - (2980 6174) :recursionsNeeded 7 . + 2980 :recursionCount 7 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 980}] [ a r:Fact; r:gives {(980 2000) math:sum 2980}] - skolem:lemma1982 - [ a r:Fact; r:gives {{ - :recursion :count 7. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1980 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma1001. -skolem:lemma982 a r:Inference; +skolem:lemma981 a r:Inference; r:gives { - (2981 6174) :recursionsNeeded 2 . + 2981 :recursionCount 2 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 981}] [ a r:Fact; r:gives {(981 2000) math:sum 2981}] - skolem:lemma1983 - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1981 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma1001. -skolem:lemma983 a r:Inference; +skolem:lemma982 a r:Inference; r:gives { - (2982 6174) :recursionsNeeded 3 . + 2982 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 982}] [ a r:Fact; r:gives {(982 2000) math:sum 2982}] - skolem:lemma1984 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1982 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma984 a r:Inference; +skolem:lemma983 a r:Inference; r:gives { - (2983 6174) :recursionsNeeded 5 . + 2983 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 983}] [ a r:Fact; r:gives {(983 2000) math:sum 2983}] - skolem:lemma1985 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1983 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma985 a r:Inference; +skolem:lemma984 a r:Inference; r:gives { - (2984 6174) :recursionsNeeded 3 . + 2984 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 984}] [ a r:Fact; r:gives {(984 2000) math:sum 2984}] - skolem:lemma1986 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1984 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma986 a r:Inference; +skolem:lemma985 a r:Inference; r:gives { - (2985 6174) :recursionsNeeded 6 . + 2985 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 985}] [ a r:Fact; r:gives {(985 2000) math:sum 2985}] - skolem:lemma1987 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1985 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma987 a r:Inference; +skolem:lemma986 a r:Inference; r:gives { - (2986 6174) :recursionsNeeded 5 . + 2986 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 986}] [ a r:Fact; r:gives {(986 2000) math:sum 2986}] - skolem:lemma1988 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1986 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma988 a r:Inference; +skolem:lemma987 a r:Inference; r:gives { - (2987 6174) :recursionsNeeded 3 . + 2987 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 987}] [ a r:Fact; r:gives {(987 2000) math:sum 2987}] - skolem:lemma1989 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1987 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma989 a r:Inference; +skolem:lemma988 a r:Inference; r:gives { - (2988 6174) :recursionsNeeded 4 . + 2988 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 988}] [ a r:Fact; r:gives {(988 2000) math:sum 2988}] - skolem:lemma1990 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1988 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma990 a r:Inference; +skolem:lemma989 a r:Inference; r:gives { - (2989 6174) :recursionsNeeded 3 . + 2989 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 989}] [ a r:Fact; r:gives {(989 2000) math:sum 2989}] - skolem:lemma1991 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1989 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma991 a r:Inference; +skolem:lemma990 a r:Inference; r:gives { - (2990 6174) :recursionsNeeded 3 . + 2990 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 990}] [ a r:Fact; r:gives {(990 2000) math:sum 2990}] - skolem:lemma1992 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1990 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma992 a r:Inference; +skolem:lemma991 a r:Inference; r:gives { - (2991 6174) :recursionsNeeded 5 . + 2991 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 991}] [ a r:Fact; r:gives {(991 2000) math:sum 2991}] - skolem:lemma1993 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1991 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma993 a r:Inference; +skolem:lemma992 a r:Inference; r:gives { - (2992 6174) :recursionsNeeded 6 . + 2992 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 992}] [ a r:Fact; r:gives {(992 2000) math:sum 2992}] - skolem:lemma1994 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1992 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma994 a r:Inference; +skolem:lemma993 a r:Inference; r:gives { - (2993 6174) :recursionsNeeded 3 . + 2993 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 993}] [ a r:Fact; r:gives {(993 2000) math:sum 2993}] - skolem:lemma1995 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1993 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma995 a r:Inference; +skolem:lemma994 a r:Inference; r:gives { - (2994 6174) :recursionsNeeded 5 . + 2994 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 994}] [ a r:Fact; r:gives {(994 2000) math:sum 2994}] - skolem:lemma1996 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1994 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma996 a r:Inference; +skolem:lemma995 a r:Inference; r:gives { - (2995 6174) :recursionsNeeded 3 . + 2995 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 995}] [ a r:Fact; r:gives {(995 2000) math:sum 2995}] - skolem:lemma1997 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1995 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma997 a r:Inference; +skolem:lemma996 a r:Inference; r:gives { - (2996 6174) :recursionsNeeded 6 . + 2996 :recursionCount 6 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 996}] [ a r:Fact; r:gives {(996 2000) math:sum 2996}] - skolem:lemma1998 - [ a r:Fact; r:gives {{ - :recursion :count 6. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1996 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma1001. -skolem:lemma998 a r:Inference; +skolem:lemma997 a r:Inference; r:gives { - (2997 6174) :recursionsNeeded 5 . + 2997 :recursionCount 5 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 997}] [ a r:Fact; r:gives {(997 2000) math:sum 2997}] - skolem:lemma1999 - [ a r:Fact; r:gives {{ - :recursion :count 5. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1997 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma1001. -skolem:lemma999 a r:Inference; +skolem:lemma998 a r:Inference; r:gives { - (2998 6174) :recursionsNeeded 3 . + 2998 :recursionCount 3 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 998}] [ a r:Fact; r:gives {(998 2000) math:sum 2998}] - skolem:lemma2000 - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1998 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma1001. -skolem:lemma1000 a r:Inference; +skolem:lemma999 a r:Inference; r:gives { - (2999 6174) :recursionsNeeded 4 . + 2999 :recursionCount 4 . }; r:evidence ( [ a r:Fact; r:gives {1000 log:repeat 999}] [ a r:Fact; r:gives {(999 2000) math:sum 2999}] - skolem:lemma2001 - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 0. - }}] + skolem:lemma1999 ); 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 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; - r:rule skolem:lemma1002. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma1001. -skolem:lemma1001 a r:Inference; +skolem:lemma1000 a r:Inference; r:gives { - 2000 :kaprekar 6174 . + 2000 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2003 - skolem:lemma2004 + [ a r:Fact; r:gives {2000 math:notEqualTo 0}] + skolem:lemma2000 + [ a r:Fact; r:gives {(2 0 0 0) list:quicksort (0 0 0 2)}] [ a r:Fact; r:gives {(0 0 0 2) list:reverse (2 0 0 0)}] - skolem:lemma2005 - skolem:lemma2006 + skolem:lemma2001 + skolem:lemma2002 [ a r:Fact; r:gives {(2000 2) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2000]; + 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 (0 0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:binding [ r:variable [ n3:uri "http://www.w3.org/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. -skolem:lemma1002 a r:Extraction; +skolem:lemma1001 a r:Extraction; r:gives { - @forAll var:x_0, var:x_1, var:x_2, var:x_3. { + @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 var:x_2. - { - :recursion :count var:x_3. - } log:becomes { - :recursion :count 0. - }. + var:x_1 :kaprekar (0 var:x_2). } => { - (var:x_1 var:x_2) :recursionsNeeded var:x_3. + var:x_1 :recursionCount var:x_2. }. }; r:because [ a r:Parsing; r:source ]. -skolem:lemma1003 a r:Inference; +skolem:lemma1002 a r:Inference; r:gives { - 2001 :kaprekar 6174 . + 2001 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2009 - skolem:lemma2010 + [ a r:Fact; r:gives {2001 math:notEqualTo 0}] + skolem:lemma2004 + [ a r:Fact; r:gives {(2 0 0 1) list:quicksort (0 0 1 2)}] [ a r:Fact; r:gives {(0 0 1 2) list:reverse (2 1 0 0)}] - skolem:lemma2011 - skolem:lemma2012 + skolem:lemma2005 + skolem:lemma2006 [ a r:Fact; r:gives {(2100 12) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2001]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 12]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1004 a r:Inference; +skolem:lemma1003 a r:Inference; r:gives { - 2002 :kaprekar 6174 . + 2002 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2013 - skolem:lemma2014 + [ a r:Fact; r:gives {2002 math:notEqualTo 0}] + skolem:lemma2007 + [ a r:Fact; r:gives {(2 0 0 2) list:quicksort (0 0 2 2)}] [ a r:Fact; r:gives {(0 0 2 2) list:reverse (2 2 0 0)}] - skolem:lemma2015 - skolem:lemma2016 + skolem:lemma2008 + skolem:lemma2009 [ a r:Fact; r:gives {(2200 22) math:difference 2178}] - [ a r:Fact; r:gives {2178 math:notEqualTo 6174}] - skolem:lemma1180 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2002]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 22]; - 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_8"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1005 a r:Inference; +skolem:lemma1004 a r:Inference; r:gives { - 2003 :kaprekar 6174 . + 2003 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2017 - skolem:lemma2018 + [ a r:Fact; r:gives {2003 math:notEqualTo 0}] + skolem:lemma2010 + [ a r:Fact; r:gives {(2 0 0 3) list:quicksort (0 0 2 3)}] [ a r:Fact; r:gives {(0 0 2 3) list:reverse (3 2 0 0)}] - skolem:lemma2019 - skolem:lemma2020 + skolem:lemma2011 + skolem:lemma2012 [ a r:Fact; r:gives {(3200 23) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2003]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 23]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1006 a r:Inference; +skolem:lemma1005 a r:Inference; r:gives { - 2004 :kaprekar 6174 . + 2004 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2022 - skolem:lemma2023 + [ a r:Fact; r:gives {2004 math:notEqualTo 0}] + skolem:lemma2013 + [ a r:Fact; r:gives {(2 0 0 4) list:quicksort (0 0 2 4)}] [ a r:Fact; r:gives {(0 0 2 4) list:reverse (4 2 0 0)}] - skolem:lemma2024 - skolem:lemma2025 + skolem:lemma2014 + skolem:lemma2015 [ a r:Fact; r:gives {(4200 24) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2004]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 24]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1007 a r:Inference; +skolem:lemma1006 a r:Inference; r:gives { - 2005 :kaprekar 6174 . + 2005 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2027 - skolem:lemma2028 + [ a r:Fact; r:gives {2005 math:notEqualTo 0}] + skolem:lemma2016 + [ a r:Fact; r:gives {(2 0 0 5) list:quicksort (0 0 2 5)}] [ a r:Fact; r:gives {(0 0 2 5) list:reverse (5 2 0 0)}] - skolem:lemma2029 - skolem:lemma2030 + skolem:lemma2017 + skolem:lemma2018 [ a r:Fact; r:gives {(5200 25) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2005]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 25]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1008 a r:Inference; +skolem:lemma1007 a r:Inference; r:gives { - 2006 :kaprekar 6174 . + 2006 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2006 math:notEqualTo 0}] + skolem:lemma2019 + [ a r:Fact; r:gives {(2 0 0 6) list:quicksort (0 0 2 6)}] + [ a r:Fact; r:gives {(0 0 2 6) list:reverse (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)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2006]; - r:rule skolem:lemma2032. + 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. -skolem:lemma1009 a r:Inference; +skolem:lemma1008 a r:Inference; r:gives { - 2007 :kaprekar 6174 . + 2007 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2033 - skolem:lemma2034 + [ a r:Fact; r:gives {2007 math:notEqualTo 0}] + skolem:lemma2022 + [ a r:Fact; r:gives {(2 0 0 7) list:quicksort (0 0 2 7)}] [ a r:Fact; r:gives {(0 0 2 7) list:reverse (7 2 0 0)}] - skolem:lemma2035 - skolem:lemma2036 + skolem:lemma2023 + skolem:lemma2024 [ a r:Fact; r:gives {(7200 27) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2007]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 27]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1010 a r:Inference; +skolem:lemma1009 a r:Inference; r:gives { - 2008 :kaprekar 6174 . + 2008 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2038 - skolem:lemma2039 + [ a r:Fact; r:gives {2008 math:notEqualTo 0}] + skolem:lemma2025 + [ a r:Fact; r:gives {(2 0 0 8) list:quicksort (0 0 2 8)}] [ a r:Fact; r:gives {(0 0 2 8) list:reverse (8 2 0 0)}] - skolem:lemma2040 - skolem:lemma2041 + skolem:lemma2026 + skolem:lemma2027 [ a r:Fact; r:gives {(8200 28) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2008]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 28]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1011 a r:Inference; +skolem:lemma1010 a r:Inference; r:gives { - 2009 :kaprekar 6174 . + 2009 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2043 - skolem:lemma2044 + [ a r:Fact; r:gives {2009 math:notEqualTo 0}] + skolem:lemma2028 + [ a r:Fact; r:gives {(2 0 0 9) list:quicksort (0 0 2 9)}] [ a r:Fact; r:gives {(0 0 2 9) list:reverse (9 2 0 0)}] - skolem:lemma2045 - skolem:lemma2046 + skolem:lemma2029 + skolem:lemma2030 [ a r:Fact; r:gives {(9200 29) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2009]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 29]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1012 a r:Inference; +skolem:lemma1011 a r:Inference; r:gives { - 2010 :kaprekar 6174 . + 2010 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2048 - skolem:lemma2049 + [ a r:Fact; r:gives {2010 math:notEqualTo 0}] + skolem:lemma2031 + [ a r:Fact; r:gives {(2 0 1 0) list:quicksort (0 0 1 2)}] [ a r:Fact; r:gives {(0 0 1 2) list:reverse (2 1 0 0)}] - skolem:lemma2011 - skolem:lemma2012 + skolem:lemma2005 + skolem:lemma2006 [ a r:Fact; r:gives {(2100 12) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2010]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 12]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1013 a r:Inference; +skolem:lemma1012 a r:Inference; r:gives { - 2011 :kaprekar 6174 . + 2011 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2050 - skolem:lemma2051 + [ a r:Fact; r:gives {2011 math:notEqualTo 0}] + skolem:lemma2032 + [ a r:Fact; r:gives {(2 0 1 1) list:quicksort (0 1 1 2)}] [ a r:Fact; r:gives {(0 1 1 2) list:reverse (2 1 1 0)}] - skolem:lemma2052 - skolem:lemma2053 + skolem:lemma2033 + skolem:lemma2034 [ a r:Fact; r:gives {(2110 112) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2011]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 112]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1014 a r:Inference; +skolem:lemma1013 a r:Inference; r:gives { - 2012 :kaprekar 6174 . + 2012 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2054 - skolem:lemma2055 + [ a r:Fact; r:gives {2012 math:notEqualTo 0}] + skolem:lemma2035 + [ a r:Fact; r:gives {(2 0 1 2) list:quicksort (0 1 2 2)}] [ a r:Fact; r:gives {(0 1 2 2) list:reverse (2 2 1 0)}] - skolem:lemma2056 - skolem:lemma2057 + skolem:lemma2036 + skolem:lemma2037 [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2012]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 122]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1015 a r:Inference; +skolem:lemma1014 a r:Inference; r:gives { - 2013 :kaprekar 6174 . + 2013 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2058 - skolem:lemma2059 + [ a r:Fact; r:gives {2013 math:notEqualTo 0}] + skolem:lemma2038 + [ a r:Fact; r:gives {(2 0 1 3) list:quicksort (0 1 2 3)}] [ a r:Fact; r:gives {(0 1 2 3) list:reverse (3 2 1 0)}] - skolem:lemma2060 - skolem:lemma2061 + skolem:lemma2039 + skolem:lemma2040 [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2013]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 123]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1016 a r:Inference; +skolem:lemma1015 a r:Inference; r:gives { - 2014 :kaprekar 6174 . + 2014 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2063 - skolem:lemma2064 + [ a r:Fact; r:gives {2014 math:notEqualTo 0}] + skolem:lemma2041 + [ a r:Fact; r:gives {(2 0 1 4) list:quicksort (0 1 2 4)}] [ a r:Fact; r:gives {(0 1 2 4) list:reverse (4 2 1 0)}] - skolem:lemma2065 - skolem:lemma2066 + skolem:lemma2042 + skolem:lemma2043 [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2014]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 124]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1017 a r:Inference; +skolem:lemma1016 a r:Inference; r:gives { - 2015 :kaprekar 6174 . + 2015 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2068 - skolem:lemma2069 + [ a r:Fact; r:gives {2015 math:notEqualTo 0}] + skolem:lemma2044 + [ a r:Fact; r:gives {(2 0 1 5) list:quicksort (0 1 2 5)}] [ a r:Fact; r:gives {(0 1 2 5) list:reverse (5 2 1 0)}] - skolem:lemma2070 - skolem:lemma2071 + skolem:lemma2045 + skolem:lemma2046 [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2015]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1018 a r:Inference; +skolem:lemma1017 a r:Inference; r:gives { - 2016 :kaprekar 6174 . + 2016 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2073 - skolem:lemma2074 + [ a r:Fact; r:gives {2016 math:notEqualTo 0}] + skolem:lemma2047 + [ a r:Fact; r:gives {(2 0 1 6) list:quicksort (0 1 2 6)}] [ a r:Fact; r:gives {(0 1 2 6) list:reverse (6 2 1 0)}] - skolem:lemma2075 - skolem:lemma2076 + skolem:lemma2048 + skolem:lemma2049 [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2016]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 126]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1019 a r:Inference; +skolem:lemma1018 a r:Inference; r:gives { - 2017 :kaprekar 6174 . + 2017 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2078 - skolem:lemma2079 + [ a r:Fact; r:gives {2017 math:notEqualTo 0}] + skolem:lemma2050 + [ a r:Fact; r:gives {(2 0 1 7) list:quicksort (0 1 2 7)}] [ a r:Fact; r:gives {(0 1 2 7) list:reverse (7 2 1 0)}] - skolem:lemma2080 - skolem:lemma2081 + skolem:lemma2051 + skolem:lemma2052 [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2017]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 127]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1020 a r:Inference; +skolem:lemma1019 a r:Inference; r:gives { - 2018 :kaprekar 6174 . + 2018 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2083 - skolem:lemma2084 + [ a r:Fact; r:gives {2018 math:notEqualTo 0}] + skolem:lemma2053 + [ a r:Fact; r:gives {(2 0 1 8) list:quicksort (0 1 2 8)}] [ a r:Fact; r:gives {(0 1 2 8) list:reverse (8 2 1 0)}] - skolem:lemma2085 - skolem:lemma2086 + skolem:lemma2054 + skolem:lemma2055 [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2018]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1021 a r:Inference; +skolem:lemma1020 a r:Inference; r:gives { - 2019 :kaprekar 6174 . + 2019 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2088 - skolem:lemma2089 + [ a r:Fact; r:gives {2019 math:notEqualTo 0}] + skolem:lemma2056 + [ a r:Fact; r:gives {(2 0 1 9) list:quicksort (0 1 2 9)}] [ a r:Fact; r:gives {(0 1 2 9) list:reverse (9 2 1 0)}] - skolem:lemma2090 - skolem:lemma2091 + skolem:lemma2057 + skolem:lemma2058 [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2019]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 129]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1022 a r:Inference; +skolem:lemma1021 a r:Inference; r:gives { - 2020 :kaprekar 6174 . + 2020 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2093 - skolem:lemma2094 + [ a r:Fact; r:gives {2020 math:notEqualTo 0}] + skolem:lemma2059 + [ a r:Fact; r:gives {(2 0 2 0) list:quicksort (0 0 2 2)}] [ a r:Fact; r:gives {(0 0 2 2) list:reverse (2 2 0 0)}] - skolem:lemma2015 - skolem:lemma2016 + skolem:lemma2008 + skolem:lemma2009 [ a r:Fact; r:gives {(2200 22) math:difference 2178}] - [ a r:Fact; r:gives {2178 math:notEqualTo 6174}] - skolem:lemma1180 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2020]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 22]; - 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_8"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1023 a r:Inference; +skolem:lemma1022 a r:Inference; r:gives { - 2021 :kaprekar 6174 . + 2021 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2095 - skolem:lemma2096 + [ a r:Fact; r:gives {2021 math:notEqualTo 0}] + skolem:lemma2060 + [ a r:Fact; r:gives {(2 0 2 1) list:quicksort (0 1 2 2)}] [ a r:Fact; r:gives {(0 1 2 2) list:reverse (2 2 1 0)}] - skolem:lemma2056 - skolem:lemma2057 + skolem:lemma2036 + skolem:lemma2037 [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2021]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 122]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1024 a r:Inference; +skolem:lemma1023 a r:Inference; r:gives { - 2022 :kaprekar 6174 . + 2022 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2097 - skolem:lemma2098 + [ a r:Fact; r:gives {2022 math:notEqualTo 0}] + skolem:lemma2061 + [ a r:Fact; r:gives {(2 0 2 2) list:quicksort (0 2 2 2)}] [ a r:Fact; r:gives {(0 2 2 2) list:reverse (2 2 2 0)}] - skolem:lemma2099 - skolem:lemma2100 + skolem:lemma2062 + skolem:lemma2063 [ a r:Fact; r:gives {(2220 222) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2022]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 222]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1025 a r:Inference; +skolem:lemma1024 a r:Inference; r:gives { - 2023 :kaprekar 6174 . + 2023 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2101 - skolem:lemma2102 + [ a r:Fact; r:gives {2023 math:notEqualTo 0}] + skolem:lemma2064 + [ a r:Fact; r:gives {(2 0 2 3) list:quicksort (0 2 2 3)}] [ a r:Fact; r:gives {(0 2 2 3) list:reverse (3 2 2 0)}] - skolem:lemma2103 - skolem:lemma2104 + skolem:lemma2065 + skolem:lemma2066 [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2023]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 223]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1026 a r:Inference; +skolem:lemma1025 a r:Inference; r:gives { - 2024 :kaprekar 6174 . + 2024 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2105 - skolem:lemma2106 + [ a r:Fact; r:gives {2024 math:notEqualTo 0}] + skolem:lemma2067 + [ a r:Fact; r:gives {(2 0 2 4) list:quicksort (0 2 2 4)}] [ a r:Fact; r:gives {(0 2 2 4) list:reverse (4 2 2 0)}] - skolem:lemma2107 - skolem:lemma2108 + skolem:lemma2068 + skolem:lemma2069 [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2024]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 224]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1027 a r:Inference; +skolem:lemma1026 a r:Inference; r:gives { - 2025 :kaprekar 6174 . + 2025 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2110 - skolem:lemma2111 + [ a r:Fact; r:gives {2025 math:notEqualTo 0}] + skolem:lemma2070 + [ a r:Fact; r:gives {(2 0 2 5) list:quicksort (0 2 2 5)}] [ a r:Fact; r:gives {(0 2 2 5) list:reverse (5 2 2 0)}] - skolem:lemma2112 - skolem:lemma2113 + skolem:lemma2071 + skolem:lemma2072 [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2025]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 225]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1028 a r:Inference; +skolem:lemma1027 a r:Inference; r:gives { - 2026 :kaprekar 6174 . + 2026 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2115 - skolem:lemma2116 + [ a r:Fact; r:gives {2026 math:notEqualTo 0}] + skolem:lemma2073 + [ a r:Fact; r:gives {(2 0 2 6) list:quicksort (0 2 2 6)}] [ a r:Fact; r:gives {(0 2 2 6) list:reverse (6 2 2 0)}] - skolem:lemma2117 - skolem:lemma2118 + skolem:lemma2074 + skolem:lemma2075 [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2026]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 226]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1029 a r:Inference; +skolem:lemma1028 a r:Inference; r:gives { - 2027 :kaprekar 6174 . + 2027 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2120 - skolem:lemma2121 + [ a r:Fact; r:gives {2027 math:notEqualTo 0}] + skolem:lemma2076 + [ a r:Fact; r:gives {(2 0 2 7) list:quicksort (0 2 2 7)}] [ a r:Fact; r:gives {(0 2 2 7) list:reverse (7 2 2 0)}] - skolem:lemma2122 - skolem:lemma2123 + skolem:lemma2077 + skolem:lemma2078 [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2027]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 227]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1030 a r:Inference; +skolem:lemma1029 a r:Inference; r:gives { - 2028 :kaprekar 6174 . + 2028 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2125 - skolem:lemma2126 + [ a r:Fact; r:gives {2028 math:notEqualTo 0}] + skolem:lemma2079 + [ a r:Fact; r:gives {(2 0 2 8) list:quicksort (0 2 2 8)}] [ a r:Fact; r:gives {(0 2 2 8) list:reverse (8 2 2 0)}] - skolem:lemma2127 - skolem:lemma2128 + skolem:lemma2080 + skolem:lemma2081 [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2028]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 228]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1031 a r:Inference; +skolem:lemma1030 a r:Inference; r:gives { - 2029 :kaprekar 6174 . + 2029 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2130 - skolem:lemma2131 + [ a r:Fact; r:gives {2029 math:notEqualTo 0}] + skolem:lemma2082 + [ a r:Fact; r:gives {(2 0 2 9) list:quicksort (0 2 2 9)}] [ a r:Fact; r:gives {(0 2 2 9) list:reverse (9 2 2 0)}] - skolem:lemma2132 - skolem:lemma2133 + skolem:lemma2083 + skolem:lemma2084 [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2029]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 229]; - 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_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1032 a r:Inference; +skolem:lemma1031 a r:Inference; r:gives { - 2030 :kaprekar 6174 . + 2030 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2135 - skolem:lemma2136 + [ a r:Fact; r:gives {2030 math:notEqualTo 0}] + skolem:lemma2085 + [ a r:Fact; r:gives {(2 0 3 0) list:quicksort (0 0 2 3)}] [ a r:Fact; r:gives {(0 0 2 3) list:reverse (3 2 0 0)}] - skolem:lemma2019 - skolem:lemma2020 + skolem:lemma2011 + skolem:lemma2012 [ a r:Fact; r:gives {(3200 23) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2030]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 23]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1033 a r:Inference; +skolem:lemma1032 a r:Inference; r:gives { - 2031 :kaprekar 6174 . + 2031 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2137 - skolem:lemma2138 + [ a r:Fact; r:gives {2031 math:notEqualTo 0}] + skolem:lemma2086 + [ a r:Fact; r:gives {(2 0 3 1) list:quicksort (0 1 2 3)}] [ a r:Fact; r:gives {(0 1 2 3) list:reverse (3 2 1 0)}] - skolem:lemma2060 - skolem:lemma2061 + skolem:lemma2039 + skolem:lemma2040 [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2031]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 123]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1034 a r:Inference; +skolem:lemma1033 a r:Inference; r:gives { - 2032 :kaprekar 6174 . + 2032 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2139 - skolem:lemma2140 + [ a r:Fact; r:gives {2032 math:notEqualTo 0}] + skolem:lemma2087 + [ a r:Fact; r:gives {(2 0 3 2) list:quicksort (0 2 2 3)}] [ a r:Fact; r:gives {(0 2 2 3) list:reverse (3 2 2 0)}] - skolem:lemma2103 - skolem:lemma2104 + skolem:lemma2065 + skolem:lemma2066 [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2032]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 223]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1035 a r:Inference; +skolem:lemma1034 a r:Inference; r:gives { - 2033 :kaprekar 6174 . + 2033 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2141 - skolem:lemma2142 + [ a r:Fact; r:gives {2033 math:notEqualTo 0}] + skolem:lemma2088 + [ a r:Fact; r:gives {(2 0 3 3) list:quicksort (0 2 3 3)}] [ a r:Fact; r:gives {(0 2 3 3) list:reverse (3 3 2 0)}] - skolem:lemma2143 - skolem:lemma2144 + skolem:lemma2089 + skolem:lemma2090 [ a r:Fact; r:gives {(3320 233) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2033]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 233]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1036 a r:Inference; +skolem:lemma1035 a r:Inference; r:gives { - 2034 :kaprekar 6174 . + 2034 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2145 - skolem:lemma2146 + [ a r:Fact; r:gives {2034 math:notEqualTo 0}] + skolem:lemma2091 + [ a r:Fact; r:gives {(2 0 3 4) list:quicksort (0 2 3 4)}] [ a r:Fact; r:gives {(0 2 3 4) list:reverse (4 3 2 0)}] - skolem:lemma2147 - skolem:lemma2148 + skolem:lemma2092 + skolem:lemma2093 [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2034]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 234]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1037 a r:Inference; +skolem:lemma1036 a r:Inference; r:gives { - 2035 :kaprekar 6174 . + 2035 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2149 - skolem:lemma2150 + [ a r:Fact; r:gives {2035 math:notEqualTo 0}] + skolem:lemma2094 + [ a r:Fact; r:gives {(2 0 3 5) list:quicksort (0 2 3 5)}] [ a r:Fact; r:gives {(0 2 3 5) list:reverse (5 3 2 0)}] - skolem:lemma2151 - skolem:lemma2152 + skolem:lemma2095 + skolem:lemma2096 [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2035]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 235]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1038 a r:Inference; +skolem:lemma1037 a r:Inference; r:gives { - 2036 :kaprekar 6174 . + 2036 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2153 - skolem:lemma2154 + [ a r:Fact; r:gives {2036 math:notEqualTo 0}] + skolem:lemma2097 + [ a r:Fact; r:gives {(2 0 3 6) list:quicksort (0 2 3 6)}] [ a r:Fact; r:gives {(0 2 3 6) list:reverse (6 3 2 0)}] - skolem:lemma2155 - skolem:lemma2156 + skolem:lemma2098 + skolem:lemma2099 [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2036]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 236]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1039 a r:Inference; +skolem:lemma1038 a r:Inference; r:gives { - 2037 :kaprekar 6174 . + 2037 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2157 - skolem:lemma2158 + [ a r:Fact; r:gives {2037 math:notEqualTo 0}] + skolem:lemma2100 + [ a r:Fact; r:gives {(2 0 3 7) list:quicksort (0 2 3 7)}] [ a r:Fact; r:gives {(0 2 3 7) list:reverse (7 3 2 0)}] - skolem:lemma2159 - skolem:lemma2160 + skolem:lemma2101 + skolem:lemma2102 [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2037]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 237]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1040 a r:Inference; +skolem:lemma1039 a r:Inference; r:gives { - 2038 :kaprekar 6174 . + 2038 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2161 - skolem:lemma2162 + [ a r:Fact; r:gives {2038 math:notEqualTo 0}] + skolem:lemma2103 + [ a r:Fact; r:gives {(2 0 3 8) list:quicksort (0 2 3 8)}] [ a r:Fact; r:gives {(0 2 3 8) list:reverse (8 3 2 0)}] - skolem:lemma2163 - skolem:lemma2164 + skolem:lemma2104 + skolem:lemma2105 [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2038]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 238]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1041 a r:Inference; +skolem:lemma1040 a r:Inference; r:gives { - 2039 :kaprekar 6174 . + 2039 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2165 - skolem:lemma2166 + [ a r:Fact; r:gives {2039 math:notEqualTo 0}] + skolem:lemma2106 + [ a r:Fact; r:gives {(2 0 3 9) list:quicksort (0 2 3 9)}] [ a r:Fact; r:gives {(0 2 3 9) list:reverse (9 3 2 0)}] - skolem:lemma2167 - skolem:lemma2168 + skolem:lemma2107 + skolem:lemma2108 [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2039]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 239]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1042 a r:Inference; +skolem:lemma1041 a r:Inference; r:gives { - 2040 :kaprekar 6174 . + 2040 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2169 - skolem:lemma2170 + [ a r:Fact; r:gives {2040 math:notEqualTo 0}] + skolem:lemma2109 + [ a r:Fact; r:gives {(2 0 4 0) list:quicksort (0 0 2 4)}] [ a r:Fact; r:gives {(0 0 2 4) list:reverse (4 2 0 0)}] - skolem:lemma2024 - skolem:lemma2025 + skolem:lemma2014 + skolem:lemma2015 [ a r:Fact; r:gives {(4200 24) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2040]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 24]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1043 a r:Inference; +skolem:lemma1042 a r:Inference; r:gives { - 2041 :kaprekar 6174 . + 2041 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2171 - skolem:lemma2172 + [ a r:Fact; r:gives {2041 math:notEqualTo 0}] + skolem:lemma2110 + [ a r:Fact; r:gives {(2 0 4 1) list:quicksort (0 1 2 4)}] [ a r:Fact; r:gives {(0 1 2 4) list:reverse (4 2 1 0)}] - skolem:lemma2065 - skolem:lemma2066 + skolem:lemma2042 + skolem:lemma2043 [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2041]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 124]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1044 a r:Inference; +skolem:lemma1043 a r:Inference; r:gives { - 2042 :kaprekar 6174 . + 2042 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2173 - skolem:lemma2174 + [ a r:Fact; r:gives {2042 math:notEqualTo 0}] + skolem:lemma2111 + [ a r:Fact; r:gives {(2 0 4 2) list:quicksort (0 2 2 4)}] [ a r:Fact; r:gives {(0 2 2 4) list:reverse (4 2 2 0)}] - skolem:lemma2107 - skolem:lemma2108 + skolem:lemma2068 + skolem:lemma2069 [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2042]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 224]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1045 a r:Inference; +skolem:lemma1044 a r:Inference; r:gives { - 2043 :kaprekar 6174 . + 2043 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2175 - skolem:lemma2176 + [ a r:Fact; r:gives {2043 math:notEqualTo 0}] + skolem:lemma2112 + [ a r:Fact; r:gives {(2 0 4 3) list:quicksort (0 2 3 4)}] [ a r:Fact; r:gives {(0 2 3 4) list:reverse (4 3 2 0)}] - skolem:lemma2147 - skolem:lemma2148 + skolem:lemma2092 + skolem:lemma2093 [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2043]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 234]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1046 a r:Inference; +skolem:lemma1045 a r:Inference; r:gives { - 2044 :kaprekar 6174 . + 2044 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2177 - skolem:lemma2178 + [ a r:Fact; r:gives {2044 math:notEqualTo 0}] + skolem:lemma2113 + [ a r:Fact; r:gives {(2 0 4 4) list:quicksort (0 2 4 4)}] [ a r:Fact; r:gives {(0 2 4 4) list:reverse (4 4 2 0)}] - skolem:lemma2179 - skolem:lemma2180 + skolem:lemma2114 + skolem:lemma2115 [ a r:Fact; r:gives {(4420 244) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2044]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 244]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1047 a r:Inference; +skolem:lemma1046 a r:Inference; r:gives { - 2045 :kaprekar 6174 . + 2045 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2181 - skolem:lemma2182 + [ a r:Fact; r:gives {2045 math:notEqualTo 0}] + skolem:lemma2116 + [ a r:Fact; r:gives {(2 0 4 5) list:quicksort (0 2 4 5)}] [ a r:Fact; r:gives {(0 2 4 5) list:reverse (5 4 2 0)}] - skolem:lemma2183 - skolem:lemma2184 + skolem:lemma2117 + skolem:lemma2118 [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2045]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 245]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1048 a r:Inference; +skolem:lemma1047 a r:Inference; r:gives { - 2046 :kaprekar 6174 . + 2046 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2046 math:notEqualTo 0}] + skolem:lemma2119 + [ a r:Fact; r:gives {(2 0 4 6) list:quicksort (0 2 4 6)}] + [ a r:Fact; r:gives {(0 2 4 6) list:reverse (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)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2046]; - r:rule skolem:lemma2032. + 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. -skolem:lemma1049 a r:Inference; +skolem:lemma1048 a r:Inference; r:gives { - 2047 :kaprekar 6174 . + 2047 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2185 - skolem:lemma2186 + [ a r:Fact; r:gives {2047 math:notEqualTo 0}] + skolem:lemma2122 + [ a r:Fact; r:gives {(2 0 4 7) list:quicksort (0 2 4 7)}] [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] - skolem:lemma2187 - skolem:lemma2188 + skolem:lemma2123 + skolem:lemma2124 [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2047]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 247]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1050 a r:Inference; +skolem:lemma1049 a r:Inference; r:gives { - 2048 :kaprekar 6174 . + 2048 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2189 - skolem:lemma2190 + [ a r:Fact; r:gives {2048 math:notEqualTo 0}] + skolem:lemma2125 + [ a r:Fact; r:gives {(2 0 4 8) list:quicksort (0 2 4 8)}] [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] - skolem:lemma2191 - skolem:lemma2192 + skolem:lemma2126 + skolem:lemma2127 [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2048]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 248]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1051 a r:Inference; +skolem:lemma1050 a r:Inference; r:gives { - 2049 :kaprekar 6174 . + 2049 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2193 - skolem:lemma2194 + [ a r:Fact; r:gives {2049 math:notEqualTo 0}] + skolem:lemma2128 + [ a r:Fact; r:gives {(2 0 4 9) list:quicksort (0 2 4 9)}] [ a r:Fact; r:gives {(0 2 4 9) list:reverse (9 4 2 0)}] - skolem:lemma2195 - skolem:lemma2196 + skolem:lemma2129 + skolem:lemma2130 [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2049]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 249]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1052 a r:Inference; +skolem:lemma1051 a r:Inference; r:gives { - 2050 :kaprekar 6174 . + 2050 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2197 - skolem:lemma2198 + [ a r:Fact; r:gives {2050 math:notEqualTo 0}] + skolem:lemma2131 + [ a r:Fact; r:gives {(2 0 5 0) list:quicksort (0 0 2 5)}] [ a r:Fact; r:gives {(0 0 2 5) list:reverse (5 2 0 0)}] - skolem:lemma2029 - skolem:lemma2030 + skolem:lemma2017 + skolem:lemma2018 [ a r:Fact; r:gives {(5200 25) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2050]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 25]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1053 a r:Inference; +skolem:lemma1052 a r:Inference; r:gives { - 2051 :kaprekar 6174 . + 2051 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2199 - skolem:lemma2200 + [ a r:Fact; r:gives {2051 math:notEqualTo 0}] + skolem:lemma2132 + [ a r:Fact; r:gives {(2 0 5 1) list:quicksort (0 1 2 5)}] [ a r:Fact; r:gives {(0 1 2 5) list:reverse (5 2 1 0)}] - skolem:lemma2070 - skolem:lemma2071 + skolem:lemma2045 + skolem:lemma2046 [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2051]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1054 a r:Inference; +skolem:lemma1053 a r:Inference; r:gives { - 2052 :kaprekar 6174 . + 2052 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2201 - skolem:lemma2202 + [ a r:Fact; r:gives {2052 math:notEqualTo 0}] + skolem:lemma2133 + [ a r:Fact; r:gives {(2 0 5 2) list:quicksort (0 2 2 5)}] [ a r:Fact; r:gives {(0 2 2 5) list:reverse (5 2 2 0)}] - skolem:lemma2112 - skolem:lemma2113 + skolem:lemma2071 + skolem:lemma2072 [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2052]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 225]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1055 a r:Inference; +skolem:lemma1054 a r:Inference; r:gives { - 2053 :kaprekar 6174 . + 2053 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2203 - skolem:lemma2204 + [ a r:Fact; r:gives {2053 math:notEqualTo 0}] + skolem:lemma2134 + [ a r:Fact; r:gives {(2 0 5 3) list:quicksort (0 2 3 5)}] [ a r:Fact; r:gives {(0 2 3 5) list:reverse (5 3 2 0)}] - skolem:lemma2151 - skolem:lemma2152 + skolem:lemma2095 + skolem:lemma2096 [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2053]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 235]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1056 a r:Inference; +skolem:lemma1055 a r:Inference; r:gives { - 2054 :kaprekar 6174 . + 2054 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2205 - skolem:lemma2206 + [ a r:Fact; r:gives {2054 math:notEqualTo 0}] + skolem:lemma2135 + [ a r:Fact; r:gives {(2 0 5 4) list:quicksort (0 2 4 5)}] [ a r:Fact; r:gives {(0 2 4 5) list:reverse (5 4 2 0)}] - skolem:lemma2183 - skolem:lemma2184 + skolem:lemma2117 + skolem:lemma2118 [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2054]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 245]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1057 a r:Inference; +skolem:lemma1056 a r:Inference; r:gives { - 2055 :kaprekar 6174 . + 2055 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2207 - skolem:lemma2208 + [ a r:Fact; r:gives {2055 math:notEqualTo 0}] + skolem:lemma2136 + [ a r:Fact; r:gives {(2 0 5 5) list:quicksort (0 2 5 5)}] [ a r:Fact; r:gives {(0 2 5 5) list:reverse (5 5 2 0)}] - skolem:lemma2209 - skolem:lemma2210 + skolem:lemma2137 + skolem:lemma2138 [ a r:Fact; r:gives {(5520 255) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2055]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 255]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1058 a r:Inference; +skolem:lemma1057 a r:Inference; r:gives { - 2056 :kaprekar 6174 . + 2056 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2212 - skolem:lemma2213 + [ a r:Fact; r:gives {2056 math:notEqualTo 0}] + skolem:lemma2139 + [ a r:Fact; r:gives {(2 0 5 6) list:quicksort (0 2 5 6)}] [ a r:Fact; r:gives {(0 2 5 6) list:reverse (6 5 2 0)}] - skolem:lemma2214 - skolem:lemma2215 + skolem:lemma2140 + skolem:lemma2141 [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2056]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1059 a r:Inference; +skolem:lemma1058 a r:Inference; r:gives { - 2057 :kaprekar 6174 . + 2057 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2217 - skolem:lemma2218 + [ a r:Fact; r:gives {2057 math:notEqualTo 0}] + skolem:lemma2142 + [ a r:Fact; r:gives {(2 0 5 7) list:quicksort (0 2 5 7)}] [ a r:Fact; r:gives {(0 2 5 7) list:reverse (7 5 2 0)}] - skolem:lemma2219 - skolem:lemma2220 + skolem:lemma2143 + skolem:lemma2144 [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2057]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 257]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1060 a r:Inference; +skolem:lemma1059 a r:Inference; r:gives { - 2058 :kaprekar 6174 . + 2058 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2222 - skolem:lemma2223 + [ a r:Fact; r:gives {2058 math:notEqualTo 0}] + skolem:lemma2145 + [ a r:Fact; r:gives {(2 0 5 8) list:quicksort (0 2 5 8)}] [ a r:Fact; r:gives {(0 2 5 8) list:reverse (8 5 2 0)}] - skolem:lemma2224 - skolem:lemma2225 + skolem:lemma2146 + skolem:lemma2147 [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2058]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 258]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1061 a r:Inference; +skolem:lemma1060 a r:Inference; r:gives { - 2059 :kaprekar 6174 . + 2059 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2227 - skolem:lemma2228 + [ a r:Fact; r:gives {2059 math:notEqualTo 0}] + skolem:lemma2148 + [ a r:Fact; r:gives {(2 0 5 9) list:quicksort (0 2 5 9)}] [ a r:Fact; r:gives {(0 2 5 9) list:reverse (9 5 2 0)}] - skolem:lemma2229 - skolem:lemma2230 + skolem:lemma2149 + skolem:lemma2150 [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {9261 math:notEqualTo 6174}] - skolem:lemma2231 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2059]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 259]; - 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_8"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1062 a r:Inference; +skolem:lemma1061 a r:Inference; r:gives { - 2060 :kaprekar 6174 . + 2060 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2060 math:notEqualTo 0}] + skolem:lemma2151 + [ a r:Fact; r:gives {(2 0 6 0) list:quicksort (0 0 2 6)}] + [ a r:Fact; r:gives {(0 0 2 6) list:reverse (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)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2060]; - r:rule skolem:lemma2032. + 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. -skolem:lemma1063 a r:Inference; +skolem:lemma1062 a r:Inference; r:gives { - 2061 :kaprekar 6174 . + 2061 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2232 - skolem:lemma2233 + [ a r:Fact; r:gives {2061 math:notEqualTo 0}] + skolem:lemma2152 + [ a r:Fact; r:gives {(2 0 6 1) list:quicksort (0 1 2 6)}] [ a r:Fact; r:gives {(0 1 2 6) list:reverse (6 2 1 0)}] - skolem:lemma2075 - skolem:lemma2076 + skolem:lemma2048 + skolem:lemma2049 [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2061]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 126]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1064 a r:Inference; +skolem:lemma1063 a r:Inference; r:gives { - 2062 :kaprekar 6174 . + 2062 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2234 - skolem:lemma2235 + [ a r:Fact; r:gives {2062 math:notEqualTo 0}] + skolem:lemma2153 + [ a r:Fact; r:gives {(2 0 6 2) list:quicksort (0 2 2 6)}] [ a r:Fact; r:gives {(0 2 2 6) list:reverse (6 2 2 0)}] - skolem:lemma2117 - skolem:lemma2118 + skolem:lemma2074 + skolem:lemma2075 [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2062]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 226]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1065 a r:Inference; +skolem:lemma1064 a r:Inference; r:gives { - 2063 :kaprekar 6174 . + 2063 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2236 - skolem:lemma2237 + [ a r:Fact; r:gives {2063 math:notEqualTo 0}] + skolem:lemma2154 + [ a r:Fact; r:gives {(2 0 6 3) list:quicksort (0 2 3 6)}] [ a r:Fact; r:gives {(0 2 3 6) list:reverse (6 3 2 0)}] - skolem:lemma2155 - skolem:lemma2156 + skolem:lemma2098 + skolem:lemma2099 [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2063]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 236]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1066 a r:Inference; +skolem:lemma1065 a r:Inference; r:gives { - 2064 :kaprekar 6174 . + 2064 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2064 math:notEqualTo 0}] + skolem:lemma2155 + [ a r:Fact; r:gives {(2 0 6 4) list:quicksort (0 2 4 6)}] + [ a r:Fact; r:gives {(0 2 4 6) list:reverse (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)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2064]; - r:rule skolem:lemma2032. + 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. -skolem:lemma1067 a r:Inference; +skolem:lemma1066 a r:Inference; r:gives { - 2065 :kaprekar 6174 . + 2065 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2238 - skolem:lemma2239 + [ a r:Fact; r:gives {2065 math:notEqualTo 0}] + skolem:lemma2156 + [ a r:Fact; r:gives {(2 0 6 5) list:quicksort (0 2 5 6)}] [ a r:Fact; r:gives {(0 2 5 6) list:reverse (6 5 2 0)}] - skolem:lemma2214 - skolem:lemma2215 + skolem:lemma2140 + skolem:lemma2141 [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2065]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1068 a r:Inference; +skolem:lemma1067 a r:Inference; r:gives { - 2066 :kaprekar 6174 . + 2066 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2240 - skolem:lemma2241 + [ a r:Fact; r:gives {2066 math:notEqualTo 0}] + skolem:lemma2157 + [ a r:Fact; r:gives {(2 0 6 6) list:quicksort (0 2 6 6)}] [ a r:Fact; r:gives {(0 2 6 6) list:reverse (6 6 2 0)}] - skolem:lemma2242 - skolem:lemma2243 + skolem:lemma2158 + skolem:lemma2159 [ a r:Fact; r:gives {(6620 266) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2066]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 266]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1069 a r:Inference; +skolem:lemma1068 a r:Inference; r:gives { - 2067 :kaprekar 6174 . + 2067 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2245 - skolem:lemma2246 + [ a r:Fact; r:gives {2067 math:notEqualTo 0}] + skolem:lemma2160 + [ a r:Fact; r:gives {(2 0 6 7) list:quicksort (0 2 6 7)}] [ a r:Fact; r:gives {(0 2 6 7) list:reverse (7 6 2 0)}] - skolem:lemma2247 - skolem:lemma2248 + skolem:lemma2161 + skolem:lemma2162 [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2067]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 267]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1070 a r:Inference; +skolem:lemma1069 a r:Inference; r:gives { - 2068 :kaprekar 6174 . + 2068 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2250 - skolem:lemma2251 + [ a r:Fact; r:gives {2068 math:notEqualTo 0}] + skolem:lemma2163 + [ a r:Fact; r:gives {(2 0 6 8) list:quicksort (0 2 6 8)}] [ a r:Fact; r:gives {(0 2 6 8) list:reverse (8 6 2 0)}] - skolem:lemma2252 - skolem:lemma2253 + skolem:lemma2164 + skolem:lemma2165 [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2068]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 268]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1071 a r:Inference; +skolem:lemma1070 a r:Inference; r:gives { - 2069 :kaprekar 6174 . + 2069 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2255 - skolem:lemma2256 + [ a r:Fact; r:gives {2069 math:notEqualTo 0}] + skolem:lemma2166 + [ a r:Fact; r:gives {(2 0 6 9) list:quicksort (0 2 6 9)}] [ a r:Fact; r:gives {(0 2 6 9) list:reverse (9 6 2 0)}] - skolem:lemma2257 - skolem:lemma2258 + skolem:lemma2167 + skolem:lemma2168 [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {9351 math:notEqualTo 6174}] - skolem:lemma2259 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2069]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 269]; - 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_8"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1072 a r:Inference; +skolem:lemma1071 a r:Inference; r:gives { - 2070 :kaprekar 6174 . + 2070 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2260 - skolem:lemma2261 + [ a r:Fact; r:gives {2070 math:notEqualTo 0}] + skolem:lemma2169 + [ a r:Fact; r:gives {(2 0 7 0) list:quicksort (0 0 2 7)}] [ a r:Fact; r:gives {(0 0 2 7) list:reverse (7 2 0 0)}] - skolem:lemma2035 - skolem:lemma2036 + skolem:lemma2023 + skolem:lemma2024 [ a r:Fact; r:gives {(7200 27) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2070]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 27]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1073 a r:Inference; +skolem:lemma1072 a r:Inference; r:gives { - 2071 :kaprekar 6174 . + 2071 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2262 - skolem:lemma2263 + [ a r:Fact; r:gives {2071 math:notEqualTo 0}] + skolem:lemma2170 + [ a r:Fact; r:gives {(2 0 7 1) list:quicksort (0 1 2 7)}] [ a r:Fact; r:gives {(0 1 2 7) list:reverse (7 2 1 0)}] - skolem:lemma2080 - skolem:lemma2081 + skolem:lemma2051 + skolem:lemma2052 [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2071]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 127]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1074 a r:Inference; +skolem:lemma1073 a r:Inference; r:gives { - 2072 :kaprekar 6174 . + 2072 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2264 - skolem:lemma2265 + [ a r:Fact; r:gives {2072 math:notEqualTo 0}] + skolem:lemma2171 + [ a r:Fact; r:gives {(2 0 7 2) list:quicksort (0 2 2 7)}] [ a r:Fact; r:gives {(0 2 2 7) list:reverse (7 2 2 0)}] - skolem:lemma2122 - skolem:lemma2123 + skolem:lemma2077 + skolem:lemma2078 [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2072]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 227]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1075 a r:Inference; +skolem:lemma1074 a r:Inference; r:gives { - 2073 :kaprekar 6174 . + 2073 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2266 - skolem:lemma2267 + [ a r:Fact; r:gives {2073 math:notEqualTo 0}] + skolem:lemma2172 + [ a r:Fact; r:gives {(2 0 7 3) list:quicksort (0 2 3 7)}] [ a r:Fact; r:gives {(0 2 3 7) list:reverse (7 3 2 0)}] - skolem:lemma2159 - skolem:lemma2160 + skolem:lemma2101 + skolem:lemma2102 [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2073]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 237]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1076 a r:Inference; +skolem:lemma1075 a r:Inference; r:gives { - 2074 :kaprekar 6174 . + 2074 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2268 - skolem:lemma2269 + [ a r:Fact; r:gives {2074 math:notEqualTo 0}] + skolem:lemma2173 + [ a r:Fact; r:gives {(2 0 7 4) list:quicksort (0 2 4 7)}] [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] - skolem:lemma2187 - skolem:lemma2188 + skolem:lemma2123 + skolem:lemma2124 [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2074]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 247]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1077 a r:Inference; +skolem:lemma1076 a r:Inference; r:gives { - 2075 :kaprekar 6174 . + 2075 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2270 - skolem:lemma2271 + [ a r:Fact; r:gives {2075 math:notEqualTo 0}] + skolem:lemma2174 + [ a r:Fact; r:gives {(2 0 7 5) list:quicksort (0 2 5 7)}] [ a r:Fact; r:gives {(0 2 5 7) list:reverse (7 5 2 0)}] - skolem:lemma2219 - skolem:lemma2220 + skolem:lemma2143 + skolem:lemma2144 [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2075]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 257]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1078 a r:Inference; +skolem:lemma1077 a r:Inference; r:gives { - 2076 :kaprekar 6174 . + 2076 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2272 - skolem:lemma2273 + [ a r:Fact; r:gives {2076 math:notEqualTo 0}] + skolem:lemma2175 + [ a r:Fact; r:gives {(2 0 7 6) list:quicksort (0 2 6 7)}] [ a r:Fact; r:gives {(0 2 6 7) list:reverse (7 6 2 0)}] - skolem:lemma2247 - skolem:lemma2248 + skolem:lemma2161 + skolem:lemma2162 [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2076]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 267]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1079 a r:Inference; +skolem:lemma1078 a r:Inference; r:gives { - 2077 :kaprekar 6174 . + 2077 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2274 - skolem:lemma2275 + [ a r:Fact; r:gives {2077 math:notEqualTo 0}] + skolem:lemma2176 + [ a r:Fact; r:gives {(2 0 7 7) list:quicksort (0 2 7 7)}] [ a r:Fact; r:gives {(0 2 7 7) list:reverse (7 7 2 0)}] - skolem:lemma2276 - skolem:lemma2277 + skolem:lemma2177 + skolem:lemma2178 [ a r:Fact; r:gives {(7720 277) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2077]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 277]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1080 a r:Inference; +skolem:lemma1079 a r:Inference; r:gives { - 2078 :kaprekar 6174 . + 2078 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2279 - skolem:lemma2280 + [ a r:Fact; r:gives {2078 math:notEqualTo 0}] + skolem:lemma2179 + [ a r:Fact; r:gives {(2 0 7 8) list:quicksort (0 2 7 8)}] [ a r:Fact; r:gives {(0 2 7 8) list:reverse (8 7 2 0)}] - skolem:lemma2281 - skolem:lemma2282 + skolem:lemma2180 + skolem:lemma2181 [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2078]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 278]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1081 a r:Inference; +skolem:lemma1080 a r:Inference; r:gives { - 2079 :kaprekar 6174 . + 2079 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2284 - skolem:lemma2285 + [ a r:Fact; r:gives {2079 math:notEqualTo 0}] + skolem:lemma2182 + [ a r:Fact; r:gives {(2 0 7 9) list:quicksort (0 2 7 9)}] [ a r:Fact; r:gives {(0 2 7 9) list:reverse (9 7 2 0)}] - skolem:lemma2286 - skolem:lemma2287 + skolem:lemma2183 + skolem:lemma2184 [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {9441 math:notEqualTo 6174}] - skolem:lemma2288 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2079]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 279]; - 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_8"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1082 a r:Inference; +skolem:lemma1081 a r:Inference; r:gives { - 2080 :kaprekar 6174 . + 2080 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2289 - skolem:lemma2290 + [ a r:Fact; r:gives {2080 math:notEqualTo 0}] + skolem:lemma2185 + [ a r:Fact; r:gives {(2 0 8 0) list:quicksort (0 0 2 8)}] [ a r:Fact; r:gives {(0 0 2 8) list:reverse (8 2 0 0)}] - skolem:lemma2040 - skolem:lemma2041 + skolem:lemma2026 + skolem:lemma2027 [ a r:Fact; r:gives {(8200 28) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2080]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 28]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1083 a r:Inference; +skolem:lemma1082 a r:Inference; r:gives { - 2081 :kaprekar 6174 . + 2081 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2291 - skolem:lemma2292 + [ a r:Fact; r:gives {2081 math:notEqualTo 0}] + skolem:lemma2186 + [ a r:Fact; r:gives {(2 0 8 1) list:quicksort (0 1 2 8)}] [ a r:Fact; r:gives {(0 1 2 8) list:reverse (8 2 1 0)}] - skolem:lemma2085 - skolem:lemma2086 + skolem:lemma2054 + skolem:lemma2055 [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1084 a r:Inference; +skolem:lemma1083 a r:Inference; r:gives { - 2082 :kaprekar 6174 . + 2082 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2293 - skolem:lemma2294 + [ a r:Fact; r:gives {2082 math:notEqualTo 0}] + skolem:lemma2187 + [ a r:Fact; r:gives {(2 0 8 2) list:quicksort (0 2 2 8)}] [ a r:Fact; r:gives {(0 2 2 8) list:reverse (8 2 2 0)}] - skolem:lemma2127 - skolem:lemma2128 + skolem:lemma2080 + skolem:lemma2081 [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 228]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1085 a r:Inference; +skolem:lemma1084 a r:Inference; r:gives { - 2083 :kaprekar 6174 . + 2083 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2295 - skolem:lemma2296 + [ a r:Fact; r:gives {2083 math:notEqualTo 0}] + skolem:lemma2188 + [ a r:Fact; r:gives {(2 0 8 3) list:quicksort (0 2 3 8)}] [ a r:Fact; r:gives {(0 2 3 8) list:reverse (8 3 2 0)}] - skolem:lemma2163 - skolem:lemma2164 + skolem:lemma2104 + skolem:lemma2105 [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 238]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1086 a r:Inference; +skolem:lemma1085 a r:Inference; r:gives { - 2084 :kaprekar 6174 . + 2084 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2297 - skolem:lemma2298 + [ a r:Fact; r:gives {2084 math:notEqualTo 0}] + skolem:lemma2189 + [ a r:Fact; r:gives {(2 0 8 4) list:quicksort (0 2 4 8)}] [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] - skolem:lemma2191 - skolem:lemma2192 + skolem:lemma2126 + skolem:lemma2127 [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 248]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1087 a r:Inference; +skolem:lemma1086 a r:Inference; r:gives { - 2085 :kaprekar 6174 . + 2085 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2299 - skolem:lemma2300 + [ a r:Fact; r:gives {2085 math:notEqualTo 0}] + skolem:lemma2190 + [ a r:Fact; r:gives {(2 0 8 5) list:quicksort (0 2 5 8)}] [ a r:Fact; r:gives {(0 2 5 8) list:reverse (8 5 2 0)}] - skolem:lemma2224 - skolem:lemma2225 + skolem:lemma2146 + skolem:lemma2147 [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 258]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1088 a r:Inference; +skolem:lemma1087 a r:Inference; r:gives { - 2086 :kaprekar 6174 . + 2086 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2301 - skolem:lemma2302 + [ a r:Fact; r:gives {2086 math:notEqualTo 0}] + skolem:lemma2191 + [ a r:Fact; r:gives {(2 0 8 6) list:quicksort (0 2 6 8)}] [ a r:Fact; r:gives {(0 2 6 8) list:reverse (8 6 2 0)}] - skolem:lemma2252 - skolem:lemma2253 + skolem:lemma2164 + skolem:lemma2165 [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 268]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1089 a r:Inference; +skolem:lemma1088 a r:Inference; r:gives { - 2087 :kaprekar 6174 . + 2087 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2303 - skolem:lemma2304 + [ a r:Fact; r:gives {2087 math:notEqualTo 0}] + skolem:lemma2192 + [ a r:Fact; r:gives {(2 0 8 7) list:quicksort (0 2 7 8)}] [ a r:Fact; r:gives {(0 2 7 8) list:reverse (8 7 2 0)}] - skolem:lemma2281 - skolem:lemma2282 + skolem:lemma2180 + skolem:lemma2181 [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 278]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1090 a r:Inference; +skolem:lemma1089 a r:Inference; r:gives { - 2088 :kaprekar 6174 . + 2088 :kaprekar (0 2). }; r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma2305 - skolem:lemma2306 + [ a r:Fact; r:gives {2088 math:notEqualTo 0}] + skolem:lemma2193 + [ a r:Fact; r:gives {(2 0 8 8) list:quicksort (0 2 8 8)}] [ a r:Fact; r:gives {(0 2 8 8) list:reverse (8 8 2 0)}] - skolem:lemma2307 - skolem:lemma2308 + skolem:lemma2194 + skolem:lemma2195 [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 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_2"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 288]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1091 a r:Inference; +skolem:lemma1090 a r:Inference; r:gives { - 2089 :kaprekar 6174 . + 2089 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2310 - skolem:lemma2311 + [ a r:Fact; r:gives {2089 math:notEqualTo 0}] + skolem:lemma2196 + [ a r:Fact; r:gives {(2 0 8 9) list:quicksort (0 2 8 9)}] [ a r:Fact; r:gives {(0 2 8 9) list:reverse (9 8 2 0)}] - skolem:lemma2312 - skolem:lemma2313 + skolem:lemma2197 + skolem:lemma2198 [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {9531 math:notEqualTo 6174}] - skolem:lemma2314 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 289]; - 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_8"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1092 a r:Inference; +skolem:lemma1091 a r:Inference; r:gives { - 2090 :kaprekar 6174 . + 2090 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2315 - skolem:lemma2316 + [ a r:Fact; r:gives {2090 math:notEqualTo 0}] + skolem:lemma2199 + [ a r:Fact; r:gives {(2 0 9 0) list:quicksort (0 0 2 9)}] [ a r:Fact; r:gives {(0 0 2 9) list:reverse (9 2 0 0)}] - skolem:lemma2045 - skolem:lemma2046 + skolem:lemma2029 + skolem:lemma2030 [ a r:Fact; r:gives {(9200 29) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2090]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 29]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1093 a r:Inference; +skolem:lemma1092 a r:Inference; r:gives { - 2091 :kaprekar 6174 . + 2091 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2317 - skolem:lemma2318 + [ a r:Fact; r:gives {2091 math:notEqualTo 0}] + skolem:lemma2200 + [ a r:Fact; r:gives {(2 0 9 1) list:quicksort (0 1 2 9)}] [ a r:Fact; r:gives {(0 1 2 9) list:reverse (9 2 1 0)}] - skolem:lemma2090 - skolem:lemma2091 + skolem:lemma2057 + skolem:lemma2058 [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2091]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 129]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1094 a r:Inference; +skolem:lemma1093 a r:Inference; r:gives { - 2092 :kaprekar 6174 . + 2092 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2319 - skolem:lemma2320 + [ a r:Fact; r:gives {2092 math:notEqualTo 0}] + skolem:lemma2201 + [ a r:Fact; r:gives {(2 0 9 2) list:quicksort (0 2 2 9)}] [ a r:Fact; r:gives {(0 2 2 9) list:reverse (9 2 2 0)}] - skolem:lemma2132 - skolem:lemma2133 + skolem:lemma2083 + skolem:lemma2084 [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2092]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 229]; - 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_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1095 a r:Inference; +skolem:lemma1094 a r:Inference; r:gives { - 2093 :kaprekar 6174 . + 2093 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2321 - skolem:lemma2322 + [ a r:Fact; r:gives {2093 math:notEqualTo 0}] + skolem:lemma2202 + [ a r:Fact; r:gives {(2 0 9 3) list:quicksort (0 2 3 9)}] [ a r:Fact; r:gives {(0 2 3 9) list:reverse (9 3 2 0)}] - skolem:lemma2167 - skolem:lemma2168 + skolem:lemma2107 + skolem:lemma2108 [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2093]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 239]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1096 a r:Inference; +skolem:lemma1095 a r:Inference; r:gives { - 2094 :kaprekar 6174 . + 2094 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2323 - skolem:lemma2324 + [ a r:Fact; r:gives {2094 math:notEqualTo 0}] + skolem:lemma2203 + [ a r:Fact; r:gives {(2 0 9 4) list:quicksort (0 2 4 9)}] [ a r:Fact; r:gives {(0 2 4 9) list:reverse (9 4 2 0)}] - skolem:lemma2195 - skolem:lemma2196 + skolem:lemma2129 + skolem:lemma2130 [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2094]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 249]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1097 a r:Inference; +skolem:lemma1096 a r:Inference; r:gives { - 2095 :kaprekar 6174 . + 2095 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2325 - skolem:lemma2326 + [ a r:Fact; r:gives {2095 math:notEqualTo 0}] + skolem:lemma2204 + [ a r:Fact; r:gives {(2 0 9 5) list:quicksort (0 2 5 9)}] [ a r:Fact; r:gives {(0 2 5 9) list:reverse (9 5 2 0)}] - skolem:lemma2229 - skolem:lemma2230 + skolem:lemma2149 + skolem:lemma2150 [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {9261 math:notEqualTo 6174}] - skolem:lemma2231 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2095]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 259]; - 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_8"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1098 a r:Inference; +skolem:lemma1097 a r:Inference; r:gives { - 2096 :kaprekar 6174 . + 2096 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2327 - skolem:lemma2328 + [ a r:Fact; r:gives {2096 math:notEqualTo 0}] + skolem:lemma2205 + [ a r:Fact; r:gives {(2 0 9 6) list:quicksort (0 2 6 9)}] [ a r:Fact; r:gives {(0 2 6 9) list:reverse (9 6 2 0)}] - skolem:lemma2257 - skolem:lemma2258 + skolem:lemma2167 + skolem:lemma2168 [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {9351 math:notEqualTo 6174}] - skolem:lemma2259 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2096]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 269]; - 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_8"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1099 a r:Inference; +skolem:lemma1098 a r:Inference; r:gives { - 2097 :kaprekar 6174 . + 2097 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2329 - skolem:lemma2330 + [ a r:Fact; r:gives {2097 math:notEqualTo 0}] + skolem:lemma2206 + [ a r:Fact; r:gives {(2 0 9 7) list:quicksort (0 2 7 9)}] [ a r:Fact; r:gives {(0 2 7 9) list:reverse (9 7 2 0)}] - skolem:lemma2286 - skolem:lemma2287 + skolem:lemma2183 + skolem:lemma2184 [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {9441 math:notEqualTo 6174}] - skolem:lemma2288 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2097]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 279]; - 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_8"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1100 a r:Inference; +skolem:lemma1099 a r:Inference; r:gives { - 2098 :kaprekar 6174 . + 2098 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2331 - skolem:lemma2332 + [ a r:Fact; r:gives {2098 math:notEqualTo 0}] + skolem:lemma2207 + [ a r:Fact; r:gives {(2 0 9 8) list:quicksort (0 2 8 9)}] [ a r:Fact; r:gives {(0 2 8 9) list:reverse (9 8 2 0)}] - skolem:lemma2312 - skolem:lemma2313 + skolem:lemma2197 + skolem:lemma2198 [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {9531 math:notEqualTo 6174}] - skolem:lemma2314 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2098]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 289]; - 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_8"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1101 a r:Inference; +skolem:lemma1100 a r:Inference; r:gives { - 2099 :kaprekar 6174 . + 2099 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2333 - skolem:lemma2334 + [ a r:Fact; r:gives {2099 math:notEqualTo 0}] + skolem:lemma2208 + [ a r:Fact; r:gives {(2 0 9 9) list:quicksort (0 2 9 9)}] [ a r:Fact; r:gives {(0 2 9 9) list:reverse (9 9 2 0)}] - skolem:lemma2335 - skolem:lemma2336 + skolem:lemma2209 + skolem:lemma2210 [ a r:Fact; r:gives {(9920 299) math:difference 9621}] - [ a r:Fact; r:gives {9621 math:notEqualTo 6174}] - skolem:lemma2337 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2099]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 299]; - 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_8"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1102 a r:Inference; +skolem:lemma1101 a r:Inference; r:gives { - 2100 :kaprekar 6174 . + 2100 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2338 - skolem:lemma2339 + [ a r:Fact; r:gives {2100 math:notEqualTo 0}] + skolem:lemma2211 + [ a r:Fact; r:gives {(2 1 0 0) list:quicksort (0 0 1 2)}] [ a r:Fact; r:gives {(0 0 1 2) list:reverse (2 1 0 0)}] - skolem:lemma2011 - skolem:lemma2012 + skolem:lemma2005 + skolem:lemma2006 [ a r:Fact; r:gives {(2100 12) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2100]; + 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 (0 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 12]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1103 a r:Inference; +skolem:lemma1102 a r:Inference; r:gives { - 2101 :kaprekar 6174 . + 2101 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2340 - skolem:lemma2341 + [ a r:Fact; r:gives {2101 math:notEqualTo 0}] + skolem:lemma2212 + [ a r:Fact; r:gives {(2 1 0 1) list:quicksort (0 1 1 2)}] [ a r:Fact; r:gives {(0 1 1 2) list:reverse (2 1 1 0)}] - skolem:lemma2052 - skolem:lemma2053 + skolem:lemma2033 + skolem:lemma2034 [ a r:Fact; r:gives {(2110 112) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2101]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 112]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma1104 a r:Inference; + 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. + +skolem:lemma1103 a r:Inference; r:gives { - 2102 :kaprekar 6174 . + 2102 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2342 - skolem:lemma2343 + [ a r:Fact; r:gives {2102 math:notEqualTo 0}] + skolem:lemma2213 + [ a r:Fact; r:gives {(2 1 0 2) list:quicksort (0 1 2 2)}] [ a r:Fact; r:gives {(0 1 2 2) list:reverse (2 2 1 0)}] - skolem:lemma2056 - skolem:lemma2057 + skolem:lemma2036 + skolem:lemma2037 [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2102]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 122]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1105 a r:Inference; +skolem:lemma1104 a r:Inference; r:gives { - 2103 :kaprekar 6174 . + 2103 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2344 - skolem:lemma2345 + [ a r:Fact; r:gives {2103 math:notEqualTo 0}] + skolem:lemma2214 + [ a r:Fact; r:gives {(2 1 0 3) list:quicksort (0 1 2 3)}] [ a r:Fact; r:gives {(0 1 2 3) list:reverse (3 2 1 0)}] - skolem:lemma2060 - skolem:lemma2061 + skolem:lemma2039 + skolem:lemma2040 [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2103]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 123]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1106 a r:Inference; +skolem:lemma1105 a r:Inference; r:gives { - 2104 :kaprekar 6174 . + 2104 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2346 - skolem:lemma2347 + [ a r:Fact; r:gives {2104 math:notEqualTo 0}] + skolem:lemma2215 + [ a r:Fact; r:gives {(2 1 0 4) list:quicksort (0 1 2 4)}] [ a r:Fact; r:gives {(0 1 2 4) list:reverse (4 2 1 0)}] - skolem:lemma2065 - skolem:lemma2066 + skolem:lemma2042 + skolem:lemma2043 [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2104]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 124]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1107 a r:Inference; +skolem:lemma1106 a r:Inference; r:gives { - 2105 :kaprekar 6174 . + 2105 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2348 - skolem:lemma2349 + [ a r:Fact; r:gives {2105 math:notEqualTo 0}] + skolem:lemma2216 + [ a r:Fact; r:gives {(2 1 0 5) list:quicksort (0 1 2 5)}] [ a r:Fact; r:gives {(0 1 2 5) list:reverse (5 2 1 0)}] - skolem:lemma2070 - skolem:lemma2071 + skolem:lemma2045 + skolem:lemma2046 [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2105]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1108 a r:Inference; +skolem:lemma1107 a r:Inference; r:gives { - 2106 :kaprekar 6174 . + 2106 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2350 - skolem:lemma2351 + [ a r:Fact; r:gives {2106 math:notEqualTo 0}] + skolem:lemma2217 + [ a r:Fact; r:gives {(2 1 0 6) list:quicksort (0 1 2 6)}] [ a r:Fact; r:gives {(0 1 2 6) list:reverse (6 2 1 0)}] - skolem:lemma2075 - skolem:lemma2076 + skolem:lemma2048 + skolem:lemma2049 [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2106]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 126]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1109 a r:Inference; +skolem:lemma1108 a r:Inference; r:gives { - 2107 :kaprekar 6174 . + 2107 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2352 - skolem:lemma2353 + [ a r:Fact; r:gives {2107 math:notEqualTo 0}] + skolem:lemma2218 + [ a r:Fact; r:gives {(2 1 0 7) list:quicksort (0 1 2 7)}] [ a r:Fact; r:gives {(0 1 2 7) list:reverse (7 2 1 0)}] - skolem:lemma2080 - skolem:lemma2081 + skolem:lemma2051 + skolem:lemma2052 [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2107]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 127]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1110 a r:Inference; +skolem:lemma1109 a r:Inference; r:gives { - 2108 :kaprekar 6174 . + 2108 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2354 - skolem:lemma2355 + [ a r:Fact; r:gives {2108 math:notEqualTo 0}] + skolem:lemma2219 + [ a r:Fact; r:gives {(2 1 0 8) list:quicksort (0 1 2 8)}] [ a r:Fact; r:gives {(0 1 2 8) list:reverse (8 2 1 0)}] - skolem:lemma2085 - skolem:lemma2086 + skolem:lemma2054 + skolem:lemma2055 [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2108]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1111 a r:Inference; +skolem:lemma1110 a r:Inference; r:gives { - 2109 :kaprekar 6174 . + 2109 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2356 - skolem:lemma2357 + [ a r:Fact; r:gives {2109 math:notEqualTo 0}] + skolem:lemma2220 + [ a r:Fact; r:gives {(2 1 0 9) list:quicksort (0 1 2 9)}] [ a r:Fact; r:gives {(0 1 2 9) list:reverse (9 2 1 0)}] - skolem:lemma2090 - skolem:lemma2091 + skolem:lemma2057 + skolem:lemma2058 [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2109]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 129]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1112 a r:Inference; +skolem:lemma1111 a r:Inference; r:gives { - 2110 :kaprekar 6174 . + 2110 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2358 - skolem:lemma2359 + [ a r:Fact; r:gives {2110 math:notEqualTo 0}] + skolem:lemma2221 + [ a r:Fact; r:gives {(2 1 1 0) list:quicksort (0 1 1 2)}] [ a r:Fact; r:gives {(0 1 1 2) list:reverse (2 1 1 0)}] - skolem:lemma2052 - skolem:lemma2053 + skolem:lemma2033 + skolem:lemma2034 [ a r:Fact; r:gives {(2110 112) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2110]; + 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 (0 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 112]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1113 a r:Inference; +skolem:lemma1112 a r:Inference; r:gives { - 2111 :kaprekar 6174 . + 2111 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2360 - skolem:lemma2361 + [ a r:Fact; r:gives {2111 math:notEqualTo 0}] + skolem:lemma2222 + [ a r:Fact; r:gives {(2 1 1 1) list:quicksort (1 1 1 2)}] [ a r:Fact; r:gives {(1 1 1 2) list:reverse (2 1 1 1)}] - skolem:lemma2362 - skolem:lemma2363 + skolem:lemma2223 + skolem:lemma2224 [ a r:Fact; r:gives {(2111 1112) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2111]; + 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 (1 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1112]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1114 a r:Inference; +skolem:lemma1113 a r:Inference; r:gives { - 2112 :kaprekar 6174 . + 2112 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2365 - skolem:lemma2366 + [ a r:Fact; r:gives {2112 math:notEqualTo 0}] + skolem:lemma2225 + [ a r:Fact; r:gives {(2 1 1 2) list:quicksort (1 1 2 2)}] [ a r:Fact; r:gives {(1 1 2 2) list:reverse (2 2 1 1)}] - skolem:lemma2367 - skolem:lemma2368 + skolem:lemma2226 + skolem:lemma2227 [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1122]; - 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_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1115 a r:Inference; +skolem:lemma1114 a r:Inference; r:gives { - 2113 :kaprekar 6174 . + 2113 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2370 - skolem:lemma2371 + [ a r:Fact; r:gives {2113 math:notEqualTo 0}] + skolem:lemma2228 + [ a r:Fact; r:gives {(2 1 1 3) list:quicksort (1 1 2 3)}] [ a r:Fact; r:gives {(1 1 2 3) list:reverse (3 2 1 1)}] - skolem:lemma2372 - skolem:lemma2373 + skolem:lemma2229 + skolem:lemma2230 [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2113]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1123]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1116 a r:Inference; +skolem:lemma1115 a r:Inference; r:gives { - 2114 :kaprekar 6174 . + 2114 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2374 - skolem:lemma2375 + [ a r:Fact; r:gives {2114 math:notEqualTo 0}] + skolem:lemma2231 + [ a r:Fact; r:gives {(2 1 1 4) list:quicksort (1 1 2 4)}] [ a r:Fact; r:gives {(1 1 2 4) list:reverse (4 2 1 1)}] - skolem:lemma2376 - skolem:lemma2377 + skolem:lemma2232 + skolem:lemma2233 [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2114]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1124]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1117 a r:Inference; +skolem:lemma1116 a r:Inference; r:gives { - 2115 :kaprekar 6174 . + 2115 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2378 - skolem:lemma2379 + [ a r:Fact; r:gives {2115 math:notEqualTo 0}] + skolem:lemma2234 + [ a r:Fact; r:gives {(2 1 1 5) list:quicksort (1 1 2 5)}] [ a r:Fact; r:gives {(1 1 2 5) list:reverse (5 2 1 1)}] - skolem:lemma2380 - skolem:lemma2381 + skolem:lemma2235 + skolem:lemma2236 [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2115]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1125]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1118 a r:Inference; +skolem:lemma1117 a r:Inference; r:gives { - 2116 :kaprekar 6174 . + 2116 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2382 - skolem:lemma2383 + [ a r:Fact; r:gives {2116 math:notEqualTo 0}] + skolem:lemma2237 + [ a r:Fact; r:gives {(2 1 1 6) list:quicksort (1 1 2 6)}] [ a r:Fact; r:gives {(1 1 2 6) list:reverse (6 2 1 1)}] - skolem:lemma2384 - skolem:lemma2385 + skolem:lemma2238 + skolem:lemma2239 [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2116]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1126]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1119 a r:Inference; +skolem:lemma1118 a r:Inference; r:gives { - 2117 :kaprekar 6174 . + 2117 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2386 - skolem:lemma2387 + [ a r:Fact; r:gives {2117 math:notEqualTo 0}] + skolem:lemma2240 + [ a r:Fact; r:gives {(2 1 1 7) list:quicksort (1 1 2 7)}] [ a r:Fact; r:gives {(1 1 2 7) list:reverse (7 2 1 1)}] - skolem:lemma2388 - skolem:lemma2389 + skolem:lemma2241 + skolem:lemma2242 [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2117]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1127]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1120 a r:Inference; +skolem:lemma1119 a r:Inference; r:gives { - 2118 :kaprekar 6174 . + 2118 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2390 - skolem:lemma2391 + [ a r:Fact; r:gives {2118 math:notEqualTo 0}] + skolem:lemma2243 + [ a r:Fact; r:gives {(2 1 1 8) list:quicksort (1 1 2 8)}] [ a r:Fact; r:gives {(1 1 2 8) list:reverse (8 2 1 1)}] - skolem:lemma2392 - skolem:lemma2393 + skolem:lemma2244 + skolem:lemma2245 [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2118]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1128]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1121 a r:Inference; +skolem:lemma1120 a r:Inference; r:gives { - 2119 :kaprekar 6174 . + 2119 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2394 - skolem:lemma2395 + [ a r:Fact; r:gives {2119 math:notEqualTo 0}] + skolem:lemma2246 + [ a r:Fact; r:gives {(2 1 1 9) list:quicksort (1 1 2 9)}] [ a r:Fact; r:gives {(1 1 2 9) list:reverse (9 2 1 1)}] - skolem:lemma2396 - skolem:lemma2397 + skolem:lemma2247 + skolem:lemma2248 [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2119]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1129]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1122 a r:Inference; +skolem:lemma1121 a r:Inference; r:gives { - 2120 :kaprekar 6174 . + 2120 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2398 - skolem:lemma2399 + [ a r:Fact; r:gives {2120 math:notEqualTo 0}] + skolem:lemma2249 + [ a r:Fact; r:gives {(2 1 2 0) list:quicksort (0 1 2 2)}] [ a r:Fact; r:gives {(0 1 2 2) list:reverse (2 2 1 0)}] - skolem:lemma2056 - skolem:lemma2057 + skolem:lemma2036 + skolem:lemma2037 [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2120]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 122]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1123 a r:Inference; +skolem:lemma1122 a r:Inference; r:gives { - 2121 :kaprekar 6174 . + 2121 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2400 - skolem:lemma2401 + [ a r:Fact; r:gives {2121 math:notEqualTo 0}] + skolem:lemma2250 + [ a r:Fact; r:gives {(2 1 2 1) list:quicksort (1 1 2 2)}] [ a r:Fact; r:gives {(1 1 2 2) list:reverse (2 2 1 1)}] - skolem:lemma2367 - skolem:lemma2368 + skolem:lemma2226 + skolem:lemma2227 [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2121]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1122]; - 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_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1124 a r:Inference; +skolem:lemma1123 a r:Inference; r:gives { - 2122 :kaprekar 6174 . + 2122 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2402 - skolem:lemma2403 + [ a r:Fact; r:gives {2122 math:notEqualTo 0}] + skolem:lemma2251 + [ a r:Fact; r:gives {(2 1 2 2) list:quicksort (1 2 2 2)}] [ a r:Fact; r:gives {(1 2 2 2) list:reverse (2 2 2 1)}] - skolem:lemma2404 - skolem:lemma2405 + skolem:lemma2252 + skolem:lemma2253 [ a r:Fact; r:gives {(2221 1222) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1222]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1125 a r:Inference; +skolem:lemma1124 a r:Inference; r:gives { - 2123 :kaprekar 6174 . + 2123 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2406 - skolem:lemma2407 + [ a r:Fact; r:gives {2123 math:notEqualTo 0}] + skolem:lemma2254 + [ a r:Fact; r:gives {(2 1 2 3) list:quicksort (1 2 2 3)}] [ a r:Fact; r:gives {(1 2 2 3) list:reverse (3 2 2 1)}] - skolem:lemma2408 - skolem:lemma2409 + skolem:lemma2255 + skolem:lemma2256 [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1223]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1126 a r:Inference; +skolem:lemma1125 a r:Inference; r:gives { - 2124 :kaprekar 6174 . + 2124 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2410 - skolem:lemma2411 + [ a r:Fact; r:gives {2124 math:notEqualTo 0}] + skolem:lemma2257 + [ a r:Fact; r:gives {(2 1 2 4) list:quicksort (1 2 2 4)}] [ a r:Fact; r:gives {(1 2 2 4) list:reverse (4 2 2 1)}] - skolem:lemma2412 - skolem:lemma2413 + skolem:lemma2258 + skolem:lemma2259 [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1224]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1127 a r:Inference; +skolem:lemma1126 a r:Inference; r:gives { - 2125 :kaprekar 6174 . + 2125 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2414 - skolem:lemma2415 + [ a r:Fact; r:gives {2125 math:notEqualTo 0}] + skolem:lemma2260 + [ a r:Fact; r:gives {(2 1 2 5) list:quicksort (1 2 2 5)}] [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] - skolem:lemma2416 - skolem:lemma2417 + skolem:lemma2261 + skolem:lemma2262 [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1225]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1128 a r:Inference; +skolem:lemma1127 a r:Inference; r:gives { - 2126 :kaprekar 6174 . + 2126 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2418 - skolem:lemma2419 + [ a r:Fact; r:gives {2126 math:notEqualTo 0}] + skolem:lemma2263 + [ a r:Fact; r:gives {(2 1 2 6) list:quicksort (1 2 2 6)}] [ a r:Fact; r:gives {(1 2 2 6) list:reverse (6 2 2 1)}] - skolem:lemma2420 - skolem:lemma2421 + skolem:lemma2264 + skolem:lemma2265 [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1226]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1129 a r:Inference; +skolem:lemma1128 a r:Inference; r:gives { - 2127 :kaprekar 6174 . + 2127 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2422 - skolem:lemma2423 + [ a r:Fact; r:gives {2127 math:notEqualTo 0}] + skolem:lemma2266 + [ a r:Fact; r:gives {(2 1 2 7) list:quicksort (1 2 2 7)}] [ a r:Fact; r:gives {(1 2 2 7) list:reverse (7 2 2 1)}] - skolem:lemma2424 - skolem:lemma2425 + skolem:lemma2267 + skolem:lemma2268 [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1227]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1130 a r:Inference; +skolem:lemma1129 a r:Inference; r:gives { - 2128 :kaprekar 6174 . + 2128 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2426 - skolem:lemma2427 + [ a r:Fact; r:gives {2128 math:notEqualTo 0}] + skolem:lemma2269 + [ a r:Fact; r:gives {(2 1 2 8) list:quicksort (1 2 2 8)}] [ a r:Fact; r:gives {(1 2 2 8) list:reverse (8 2 2 1)}] - skolem:lemma2428 - skolem:lemma2429 + skolem:lemma2270 + skolem:lemma2271 [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1228]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1131 a r:Inference; +skolem:lemma1130 a r:Inference; r:gives { - 2129 :kaprekar 6174 . + 2129 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2430 - skolem:lemma2431 + [ a r:Fact; r:gives {2129 math:notEqualTo 0}] + skolem:lemma2272 + [ a r:Fact; r:gives {(2 1 2 9) list:quicksort (1 2 2 9)}] [ a r:Fact; r:gives {(1 2 2 9) list:reverse (9 2 2 1)}] - skolem:lemma2432 - skolem:lemma2433 + skolem:lemma2273 + skolem:lemma2274 [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1229]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1132 a r:Inference; +skolem:lemma1131 a r:Inference; r:gives { - 2130 :kaprekar 6174 . + 2130 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2434 - skolem:lemma2435 + [ a r:Fact; r:gives {2130 math:notEqualTo 0}] + skolem:lemma2275 + [ a r:Fact; r:gives {(2 1 3 0) list:quicksort (0 1 2 3)}] [ a r:Fact; r:gives {(0 1 2 3) list:reverse (3 2 1 0)}] - skolem:lemma2060 - skolem:lemma2061 + skolem:lemma2039 + skolem:lemma2040 [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2130]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 123]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1133 a r:Inference; +skolem:lemma1132 a r:Inference; r:gives { - 2131 :kaprekar 6174 . + 2131 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2436 - skolem:lemma2437 + [ a r:Fact; r:gives {2131 math:notEqualTo 0}] + skolem:lemma2276 + [ a r:Fact; r:gives {(2 1 3 1) list:quicksort (1 1 2 3)}] [ a r:Fact; r:gives {(1 1 2 3) list:reverse (3 2 1 1)}] - skolem:lemma2372 - skolem:lemma2373 + skolem:lemma2229 + skolem:lemma2230 [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2131]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1123]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1134 a r:Inference; +skolem:lemma1133 a r:Inference; r:gives { - 2132 :kaprekar 6174 . + 2132 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2438 - skolem:lemma2439 + [ a r:Fact; r:gives {2132 math:notEqualTo 0}] + skolem:lemma2277 + [ a r:Fact; r:gives {(2 1 3 2) list:quicksort (1 2 2 3)}] [ a r:Fact; r:gives {(1 2 2 3) list:reverse (3 2 2 1)}] - skolem:lemma2408 - skolem:lemma2409 + skolem:lemma2255 + skolem:lemma2256 [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2132]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1223]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1135 a r:Inference; +skolem:lemma1134 a r:Inference; r:gives { - 2133 :kaprekar 6174 . + 2133 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2440 - skolem:lemma2441 + [ a r:Fact; r:gives {2133 math:notEqualTo 0}] + skolem:lemma2278 + [ a r:Fact; r:gives {(2 1 3 3) list:quicksort (1 2 3 3)}] [ a r:Fact; r:gives {(1 2 3 3) list:reverse (3 3 2 1)}] - skolem:lemma2442 - skolem:lemma2443 + skolem:lemma2279 + skolem:lemma2280 [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2133]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1233]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1136 a r:Inference; +skolem:lemma1135 a r:Inference; r:gives { - 2134 :kaprekar 6174 . + 2134 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2444 - skolem:lemma2445 + [ a r:Fact; r:gives {2134 math:notEqualTo 0}] + skolem:lemma2281 + [ a r:Fact; r:gives {(2 1 3 4) list:quicksort (1 2 3 4)}] [ a r:Fact; r:gives {(1 2 3 4) list:reverse (4 3 2 1)}] - skolem:lemma2446 - skolem:lemma2447 + skolem:lemma2282 + skolem:lemma2283 [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2134]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1234]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1137 a r:Inference; +skolem:lemma1136 a r:Inference; r:gives { - 2135 :kaprekar 6174 . + 2135 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2448 - skolem:lemma2449 + [ a r:Fact; r:gives {2135 math:notEqualTo 0}] + skolem:lemma2284 + [ a r:Fact; r:gives {(2 1 3 5) list:quicksort (1 2 3 5)}] [ a r:Fact; r:gives {(1 2 3 5) list:reverse (5 3 2 1)}] - skolem:lemma2450 - skolem:lemma2451 + skolem:lemma2285 + skolem:lemma2286 [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2135]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1235]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1138 a r:Inference; +skolem:lemma1137 a r:Inference; r:gives { - 2136 :kaprekar 6174 . + 2136 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2452 - skolem:lemma2453 + [ a r:Fact; r:gives {2136 math:notEqualTo 0}] + skolem:lemma2287 + [ a r:Fact; r:gives {(2 1 3 6) list:quicksort (1 2 3 6)}] [ a r:Fact; r:gives {(1 2 3 6) list:reverse (6 3 2 1)}] - skolem:lemma2454 - skolem:lemma2455 + skolem:lemma2288 + skolem:lemma2289 [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2136]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1236]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1139 a r:Inference; +skolem:lemma1138 a r:Inference; r:gives { - 2137 :kaprekar 6174 . + 2137 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2456 - skolem:lemma2457 + [ a r:Fact; r:gives {2137 math:notEqualTo 0}] + skolem:lemma2290 + [ a r:Fact; r:gives {(2 1 3 7) list:quicksort (1 2 3 7)}] [ a r:Fact; r:gives {(1 2 3 7) list:reverse (7 3 2 1)}] - skolem:lemma2458 - skolem:lemma2459 + skolem:lemma2291 + skolem:lemma2292 [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2137]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1237]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1140 a r:Inference; +skolem:lemma1139 a r:Inference; r:gives { - 2138 :kaprekar 6174 . + 2138 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2460 - skolem:lemma2461 + [ a r:Fact; r:gives {2138 math:notEqualTo 0}] + skolem:lemma2293 + [ a r:Fact; r:gives {(2 1 3 8) list:quicksort (1 2 3 8)}] [ a r:Fact; r:gives {(1 2 3 8) list:reverse (8 3 2 1)}] - skolem:lemma2462 - skolem:lemma2463 + skolem:lemma2294 + skolem:lemma2295 [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2138]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1238]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1141 a r:Inference; +skolem:lemma1140 a r:Inference; r:gives { - 2139 :kaprekar 6174 . + 2139 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2464 - skolem:lemma2465 + [ a r:Fact; r:gives {2139 math:notEqualTo 0}] + skolem:lemma2296 + [ a r:Fact; r:gives {(2 1 3 9) list:quicksort (1 2 3 9)}] [ a r:Fact; r:gives {(1 2 3 9) list:reverse (9 3 2 1)}] - skolem:lemma2466 - skolem:lemma2467 + skolem:lemma2297 + skolem:lemma2298 [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2139]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1239]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1142 a r:Inference; +skolem:lemma1141 a r:Inference; r:gives { - 2140 :kaprekar 6174 . + 2140 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2468 - skolem:lemma2469 + [ a r:Fact; r:gives {2140 math:notEqualTo 0}] + skolem:lemma2299 + [ a r:Fact; r:gives {(2 1 4 0) list:quicksort (0 1 2 4)}] [ a r:Fact; r:gives {(0 1 2 4) list:reverse (4 2 1 0)}] - skolem:lemma2065 - skolem:lemma2066 + skolem:lemma2042 + skolem:lemma2043 [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2140]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 124]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1143 a r:Inference; +skolem:lemma1142 a r:Inference; r:gives { - 2141 :kaprekar 6174 . + 2141 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2470 - skolem:lemma2471 + [ a r:Fact; r:gives {2141 math:notEqualTo 0}] + skolem:lemma2300 + [ a r:Fact; r:gives {(2 1 4 1) list:quicksort (1 1 2 4)}] [ a r:Fact; r:gives {(1 1 2 4) list:reverse (4 2 1 1)}] - skolem:lemma2376 - skolem:lemma2377 + skolem:lemma2232 + skolem:lemma2233 [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2141]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1124]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1144 a r:Inference; +skolem:lemma1143 a r:Inference; r:gives { - 2142 :kaprekar 6174 . + 2142 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2472 - skolem:lemma2473 + [ a r:Fact; r:gives {2142 math:notEqualTo 0}] + skolem:lemma2301 + [ a r:Fact; r:gives {(2 1 4 2) list:quicksort (1 2 2 4)}] [ a r:Fact; r:gives {(1 2 2 4) list:reverse (4 2 2 1)}] - skolem:lemma2412 - skolem:lemma2413 + skolem:lemma2258 + skolem:lemma2259 [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2142]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1224]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1145 a r:Inference; +skolem:lemma1144 a r:Inference; r:gives { - 2143 :kaprekar 6174 . + 2143 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2474 - skolem:lemma2475 + [ a r:Fact; r:gives {2143 math:notEqualTo 0}] + skolem:lemma2302 + [ a r:Fact; r:gives {(2 1 4 3) list:quicksort (1 2 3 4)}] [ a r:Fact; r:gives {(1 2 3 4) list:reverse (4 3 2 1)}] - skolem:lemma2446 - skolem:lemma2447 + skolem:lemma2282 + skolem:lemma2283 [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2143]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1234]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1146 a r:Inference; +skolem:lemma1145 a r:Inference; r:gives { - 2144 :kaprekar 6174 . + 2144 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2476 - skolem:lemma2477 + [ a r:Fact; r:gives {2144 math:notEqualTo 0}] + skolem:lemma2303 + [ a r:Fact; r:gives {(2 1 4 4) list:quicksort (1 2 4 4)}] [ a r:Fact; r:gives {(1 2 4 4) list:reverse (4 4 2 1)}] - skolem:lemma2478 - skolem:lemma2479 + skolem:lemma2304 + skolem:lemma2305 [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2144]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1244]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1147 a r:Inference; +skolem:lemma1146 a r:Inference; r:gives { - 2145 :kaprekar 6174 . + 2145 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2480 - skolem:lemma2481 + [ a r:Fact; r:gives {2145 math:notEqualTo 0}] + skolem:lemma2306 + [ a r:Fact; r:gives {(2 1 4 5) list:quicksort (1 2 4 5)}] [ a r:Fact; r:gives {(1 2 4 5) list:reverse (5 4 2 1)}] - skolem:lemma2482 - skolem:lemma2483 + skolem:lemma2307 + skolem:lemma2308 [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2145]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1245]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1148 a r:Inference; +skolem:lemma1147 a r:Inference; r:gives { - 2146 :kaprekar 6174 . + 2146 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2484 - skolem:lemma2485 + [ a r:Fact; r:gives {2146 math:notEqualTo 0}] + skolem:lemma2309 + [ a r:Fact; r:gives {(2 1 4 6) list:quicksort (1 2 4 6)}] [ a r:Fact; r:gives {(1 2 4 6) list:reverse (6 4 2 1)}] - skolem:lemma2486 - skolem:lemma2487 + skolem:lemma2310 + skolem:lemma2311 [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2146]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1246]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1149 a r:Inference; +skolem:lemma1148 a r:Inference; r:gives { - 2147 :kaprekar 6174 . + 2147 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2147 math:notEqualTo 0}] + skolem:lemma2312 + [ a r:Fact; r:gives {(2 1 4 7) list:quicksort (1 2 4 7)}] + [ a r:Fact; r:gives {(1 2 4 7) list:reverse (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)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147]; - r:rule skolem:lemma2032. + 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. -skolem:lemma1150 a r:Inference; +skolem:lemma1149 a r:Inference; r:gives { - 2148 :kaprekar 6174 . + 2148 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2488 - skolem:lemma2489 + [ a r:Fact; r:gives {2148 math:notEqualTo 0}] + skolem:lemma2315 + [ a r:Fact; r:gives {(2 1 4 8) list:quicksort (1 2 4 8)}] [ a r:Fact; r:gives {(1 2 4 8) list:reverse (8 4 2 1)}] - skolem:lemma2490 - skolem:lemma2491 + skolem:lemma2316 + skolem:lemma2317 [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2148]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1248]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1151 a r:Inference; +skolem:lemma1150 a r:Inference; r:gives { - 2149 :kaprekar 6174 . + 2149 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2492 - skolem:lemma2493 + [ a r:Fact; r:gives {2149 math:notEqualTo 0}] + skolem:lemma2318 + [ a r:Fact; r:gives {(2 1 4 9) list:quicksort (1 2 4 9)}] [ a r:Fact; r:gives {(1 2 4 9) list:reverse (9 4 2 1)}] - skolem:lemma2494 - skolem:lemma2495 + skolem:lemma2319 + skolem:lemma2320 [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2149]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1249]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1152 a r:Inference; +skolem:lemma1151 a r:Inference; r:gives { - 2150 :kaprekar 6174 . + 2150 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2496 - skolem:lemma2497 + [ a r:Fact; r:gives {2150 math:notEqualTo 0}] + skolem:lemma2321 + [ a r:Fact; r:gives {(2 1 5 0) list:quicksort (0 1 2 5)}] [ a r:Fact; r:gives {(0 1 2 5) list:reverse (5 2 1 0)}] - skolem:lemma2070 - skolem:lemma2071 + skolem:lemma2045 + skolem:lemma2046 [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2150]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1153 a r:Inference; +skolem:lemma1152 a r:Inference; r:gives { - 2151 :kaprekar 6174 . + 2151 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2498 - skolem:lemma2499 + [ a r:Fact; r:gives {2151 math:notEqualTo 0}] + skolem:lemma2322 + [ a r:Fact; r:gives {(2 1 5 1) list:quicksort (1 1 2 5)}] [ a r:Fact; r:gives {(1 1 2 5) list:reverse (5 2 1 1)}] - skolem:lemma2380 - skolem:lemma2381 + skolem:lemma2235 + skolem:lemma2236 [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2151]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1125]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1154 a r:Inference; +skolem:lemma1153 a r:Inference; r:gives { - 2152 :kaprekar 6174 . + 2152 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2500 - skolem:lemma2501 + [ a r:Fact; r:gives {2152 math:notEqualTo 0}] + skolem:lemma2323 + [ a r:Fact; r:gives {(2 1 5 2) list:quicksort (1 2 2 5)}] [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] - skolem:lemma2416 - skolem:lemma2417 + skolem:lemma2261 + skolem:lemma2262 [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2152]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1225]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1155 a r:Inference; +skolem:lemma1154 a r:Inference; r:gives { - 2153 :kaprekar 6174 . + 2153 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2502 - skolem:lemma2503 + [ a r:Fact; r:gives {2153 math:notEqualTo 0}] + skolem:lemma2324 + [ a r:Fact; r:gives {(2 1 5 3) list:quicksort (1 2 3 5)}] [ a r:Fact; r:gives {(1 2 3 5) list:reverse (5 3 2 1)}] - skolem:lemma2450 - skolem:lemma2451 + skolem:lemma2285 + skolem:lemma2286 [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2153]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1235]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1156 a r:Inference; +skolem:lemma1155 a r:Inference; r:gives { - 2154 :kaprekar 6174 . + 2154 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2504 - skolem:lemma2505 + [ a r:Fact; r:gives {2154 math:notEqualTo 0}] + skolem:lemma2325 + [ a r:Fact; r:gives {(2 1 5 4) list:quicksort (1 2 4 5)}] [ a r:Fact; r:gives {(1 2 4 5) list:reverse (5 4 2 1)}] - skolem:lemma2482 - skolem:lemma2483 + skolem:lemma2307 + skolem:lemma2308 [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2154]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1245]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1157 a r:Inference; +skolem:lemma1156 a r:Inference; r:gives { - 2155 :kaprekar 6174 . + 2155 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2506 - skolem:lemma2507 + [ a r:Fact; r:gives {2155 math:notEqualTo 0}] + skolem:lemma2326 + [ a r:Fact; r:gives {(2 1 5 5) list:quicksort (1 2 5 5)}] [ a r:Fact; r:gives {(1 2 5 5) list:reverse (5 5 2 1)}] - skolem:lemma2508 - skolem:lemma2509 + skolem:lemma2327 + skolem:lemma2328 [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2155]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1255]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1158 a r:Inference; +skolem:lemma1157 a r:Inference; r:gives { - 2156 :kaprekar 6174 . + 2156 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2511 - skolem:lemma2512 + [ a r:Fact; r:gives {2156 math:notEqualTo 0}] + skolem:lemma2329 + [ a r:Fact; r:gives {(2 1 5 6) list:quicksort (1 2 5 6)}] [ a r:Fact; r:gives {(1 2 5 6) list:reverse (6 5 2 1)}] - skolem:lemma2513 - skolem:lemma2514 + skolem:lemma2330 + skolem:lemma2331 [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2156]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1256]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1159 a r:Inference; +skolem:lemma1158 a r:Inference; r:gives { - 2157 :kaprekar 6174 . + 2157 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2515 - skolem:lemma2516 + [ a r:Fact; r:gives {2157 math:notEqualTo 0}] + skolem:lemma2332 + [ a r:Fact; r:gives {(2 1 5 7) list:quicksort (1 2 5 7)}] [ a r:Fact; r:gives {(1 2 5 7) list:reverse (7 5 2 1)}] - skolem:lemma2517 - skolem:lemma2518 + skolem:lemma2333 + skolem:lemma2334 [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2157]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1257]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1160 a r:Inference; +skolem:lemma1159 a r:Inference; r:gives { - 2158 :kaprekar 6174 . + 2158 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2519 - skolem:lemma2520 + [ a r:Fact; r:gives {2158 math:notEqualTo 0}] + skolem:lemma2335 + [ a r:Fact; r:gives {(2 1 5 8) list:quicksort (1 2 5 8)}] [ a r:Fact; r:gives {(1 2 5 8) list:reverse (8 5 2 1)}] - skolem:lemma2521 - skolem:lemma2522 + skolem:lemma2336 + skolem:lemma2337 [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2158]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1258]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1161 a r:Inference; +skolem:lemma1160 a r:Inference; r:gives { - 2159 :kaprekar 6174 . + 2159 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2523 - skolem:lemma2524 + [ a r:Fact; r:gives {2159 math:notEqualTo 0}] + skolem:lemma2338 + [ a r:Fact; r:gives {(2 1 5 9) list:quicksort (1 2 5 9)}] [ a r:Fact; r:gives {(1 2 5 9) list:reverse (9 5 2 1)}] - skolem:lemma2525 - skolem:lemma2526 + skolem:lemma2339 + skolem:lemma2340 [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2159]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1259]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1162 a r:Inference; +skolem:lemma1161 a r:Inference; r:gives { - 2160 :kaprekar 6174 . + 2160 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2527 - skolem:lemma2528 + [ a r:Fact; r:gives {2160 math:notEqualTo 0}] + skolem:lemma2341 + [ a r:Fact; r:gives {(2 1 6 0) list:quicksort (0 1 2 6)}] [ a r:Fact; r:gives {(0 1 2 6) list:reverse (6 2 1 0)}] - skolem:lemma2075 - skolem:lemma2076 + skolem:lemma2048 + skolem:lemma2049 [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2160]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 126]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1163 a r:Inference; +skolem:lemma1162 a r:Inference; r:gives { - 2161 :kaprekar 6174 . + 2161 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2529 - skolem:lemma2530 + [ a r:Fact; r:gives {2161 math:notEqualTo 0}] + skolem:lemma2342 + [ a r:Fact; r:gives {(2 1 6 1) list:quicksort (1 1 2 6)}] [ a r:Fact; r:gives {(1 1 2 6) list:reverse (6 2 1 1)}] - skolem:lemma2384 - skolem:lemma2385 + skolem:lemma2238 + skolem:lemma2239 [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2161]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1126]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1164 a r:Inference; +skolem:lemma1163 a r:Inference; r:gives { - 2162 :kaprekar 6174 . + 2162 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2531 - skolem:lemma2532 + [ a r:Fact; r:gives {2162 math:notEqualTo 0}] + skolem:lemma2343 + [ a r:Fact; r:gives {(2 1 6 2) list:quicksort (1 2 2 6)}] [ a r:Fact; r:gives {(1 2 2 6) list:reverse (6 2 2 1)}] - skolem:lemma2420 - skolem:lemma2421 + skolem:lemma2264 + skolem:lemma2265 [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2162]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1226]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1165 a r:Inference; +skolem:lemma1164 a r:Inference; r:gives { - 2163 :kaprekar 6174 . + 2163 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2533 - skolem:lemma2534 + [ a r:Fact; r:gives {2163 math:notEqualTo 0}] + skolem:lemma2344 + [ a r:Fact; r:gives {(2 1 6 3) list:quicksort (1 2 3 6)}] [ a r:Fact; r:gives {(1 2 3 6) list:reverse (6 3 2 1)}] - skolem:lemma2454 - skolem:lemma2455 + skolem:lemma2288 + skolem:lemma2289 [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2163]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1236]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1166 a r:Inference; +skolem:lemma1165 a r:Inference; r:gives { - 2164 :kaprekar 6174 . + 2164 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2535 - skolem:lemma2536 + [ a r:Fact; r:gives {2164 math:notEqualTo 0}] + skolem:lemma2345 + [ a r:Fact; r:gives {(2 1 6 4) list:quicksort (1 2 4 6)}] [ a r:Fact; r:gives {(1 2 4 6) list:reverse (6 4 2 1)}] - skolem:lemma2486 - skolem:lemma2487 + skolem:lemma2310 + skolem:lemma2311 [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2164]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1246]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1167 a r:Inference; +skolem:lemma1166 a r:Inference; r:gives { - 2165 :kaprekar 6174 . + 2165 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2537 - skolem:lemma2538 + [ a r:Fact; r:gives {2165 math:notEqualTo 0}] + skolem:lemma2346 + [ a r:Fact; r:gives {(2 1 6 5) list:quicksort (1 2 5 6)}] [ a r:Fact; r:gives {(1 2 5 6) list:reverse (6 5 2 1)}] - skolem:lemma2513 - skolem:lemma2514 + skolem:lemma2330 + skolem:lemma2331 [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2165]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1256]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1168 a r:Inference; +skolem:lemma1167 a r:Inference; r:gives { - 2166 :kaprekar 6174 . + 2166 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2539 - skolem:lemma2540 + [ a r:Fact; r:gives {2166 math:notEqualTo 0}] + skolem:lemma2347 + [ a r:Fact; r:gives {(2 1 6 6) list:quicksort (1 2 6 6)}] [ a r:Fact; r:gives {(1 2 6 6) list:reverse (6 6 2 1)}] - skolem:lemma2541 - skolem:lemma2542 + skolem:lemma2348 + skolem:lemma2349 [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2166]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1266]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1169 a r:Inference; +skolem:lemma1168 a r:Inference; r:gives { - 2167 :kaprekar 6174 . + 2167 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2544 - skolem:lemma2545 + [ a r:Fact; r:gives {2167 math:notEqualTo 0}] + skolem:lemma2350 + [ a r:Fact; r:gives {(2 1 6 7) list:quicksort (1 2 6 7)}] [ a r:Fact; r:gives {(1 2 6 7) list:reverse (7 6 2 1)}] - skolem:lemma2546 - skolem:lemma2547 + skolem:lemma2351 + skolem:lemma2352 [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2167]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1267]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1170 a r:Inference; +skolem:lemma1169 a r:Inference; r:gives { - 2168 :kaprekar 6174 . + 2168 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2548 - skolem:lemma2549 + [ a r:Fact; r:gives {2168 math:notEqualTo 0}] + skolem:lemma2353 + [ a r:Fact; r:gives {(2 1 6 8) list:quicksort (1 2 6 8)}] [ a r:Fact; r:gives {(1 2 6 8) list:reverse (8 6 2 1)}] - skolem:lemma2550 - skolem:lemma2551 + skolem:lemma2354 + skolem:lemma2355 [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2168]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1268]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1171 a r:Inference; +skolem:lemma1170 a r:Inference; r:gives { - 2169 :kaprekar 6174 . + 2169 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2552 - skolem:lemma2553 + [ a r:Fact; r:gives {2169 math:notEqualTo 0}] + skolem:lemma2356 + [ a r:Fact; r:gives {(2 1 6 9) list:quicksort (1 2 6 9)}] [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 + skolem:lemma2357 + skolem:lemma2358 [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2169]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1172 a r:Inference; +skolem:lemma1171 a r:Inference; r:gives { - 2170 :kaprekar 6174 . + 2170 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2556 - skolem:lemma2557 + [ a r:Fact; r:gives {2170 math:notEqualTo 0}] + skolem:lemma2359 + [ a r:Fact; r:gives {(2 1 7 0) list:quicksort (0 1 2 7)}] [ a r:Fact; r:gives {(0 1 2 7) list:reverse (7 2 1 0)}] - skolem:lemma2080 - skolem:lemma2081 + skolem:lemma2051 + skolem:lemma2052 [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2170]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 127]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1173 a r:Inference; +skolem:lemma1172 a r:Inference; r:gives { - 2171 :kaprekar 6174 . + 2171 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2558 - skolem:lemma2559 + [ a r:Fact; r:gives {2171 math:notEqualTo 0}] + skolem:lemma2360 + [ a r:Fact; r:gives {(2 1 7 1) list:quicksort (1 1 2 7)}] [ a r:Fact; r:gives {(1 1 2 7) list:reverse (7 2 1 1)}] - skolem:lemma2388 - skolem:lemma2389 + skolem:lemma2241 + skolem:lemma2242 [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1127]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1174 a r:Inference; +skolem:lemma1173 a r:Inference; r:gives { - 2172 :kaprekar 6174 . + 2172 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2560 - skolem:lemma2561 + [ a r:Fact; r:gives {2172 math:notEqualTo 0}] + skolem:lemma2361 + [ a r:Fact; r:gives {(2 1 7 2) list:quicksort (1 2 2 7)}] [ a r:Fact; r:gives {(1 2 2 7) list:reverse (7 2 2 1)}] - skolem:lemma2424 - skolem:lemma2425 + skolem:lemma2267 + skolem:lemma2268 [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1227]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1175 a r:Inference; +skolem:lemma1174 a r:Inference; r:gives { - 2173 :kaprekar 6174 . + 2173 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2562 - skolem:lemma2563 + [ a r:Fact; r:gives {2173 math:notEqualTo 0}] + skolem:lemma2362 + [ a r:Fact; r:gives {(2 1 7 3) list:quicksort (1 2 3 7)}] [ a r:Fact; r:gives {(1 2 3 7) list:reverse (7 3 2 1)}] - skolem:lemma2458 - skolem:lemma2459 + skolem:lemma2291 + skolem:lemma2292 [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1237]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1176 a r:Inference; +skolem:lemma1175 a r:Inference; r:gives { - 2174 :kaprekar 6174 . + 2174 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2174 math:notEqualTo 0}] + skolem:lemma2363 + [ a r:Fact; r:gives {(2 1 7 4) list:quicksort (1 2 4 7)}] + [ a r:Fact; r:gives {(1 2 4 7) list:reverse (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)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2174]; - r:rule skolem:lemma2032. + 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. -skolem:lemma1177 a r:Inference; +skolem:lemma1176 a r:Inference; r:gives { - 2175 :kaprekar 6174 . + 2175 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2564 - skolem:lemma2565 + [ a r:Fact; r:gives {2175 math:notEqualTo 0}] + skolem:lemma2364 + [ a r:Fact; r:gives {(2 1 7 5) list:quicksort (1 2 5 7)}] [ a r:Fact; r:gives {(1 2 5 7) list:reverse (7 5 2 1)}] - skolem:lemma2517 - skolem:lemma2518 + skolem:lemma2333 + skolem:lemma2334 [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1257]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1178 a r:Inference; +skolem:lemma1177 a r:Inference; r:gives { - 2176 :kaprekar 6174 . + 2176 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2566 - skolem:lemma2567 + [ a r:Fact; r:gives {2176 math:notEqualTo 0}] + skolem:lemma2365 + [ a r:Fact; r:gives {(2 1 7 6) list:quicksort (1 2 6 7)}] [ a r:Fact; r:gives {(1 2 6 7) list:reverse (7 6 2 1)}] - skolem:lemma2546 - skolem:lemma2547 + skolem:lemma2351 + skolem:lemma2352 [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1267]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1179 a r:Inference; +skolem:lemma1178 a r:Inference; r:gives { - 2177 :kaprekar 6174 . + 2177 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2568 - skolem:lemma2569 + [ a r:Fact; r:gives {2177 math:notEqualTo 0}] + skolem:lemma2366 + [ a r:Fact; r:gives {(2 1 7 7) list:quicksort (1 2 7 7)}] [ a r:Fact; r:gives {(1 2 7 7) list:reverse (7 7 2 1)}] - skolem:lemma2570 - skolem:lemma2571 + skolem:lemma2367 + skolem:lemma2368 [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1277]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1180 a r:Inference; +skolem:lemma1179 a r:Inference; r:gives { - 2178 :kaprekar 6174 . + 2178 :kaprekar (0 5). }; r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma2573 - skolem:lemma2574 + [ a r:Fact; r:gives {2178 math:notEqualTo 0}] + skolem:lemma2369 + [ a r:Fact; r:gives {(2 1 7 8) list:quicksort (1 2 7 8)}] [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 + skolem:lemma2370 + skolem:lemma2371 [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 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_2"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1181 a r:Inference; +skolem:lemma1180 a r:Inference; r:gives { - 2179 :kaprekar 6174 . + 2179 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2577 - skolem:lemma2578 + [ a r:Fact; r:gives {2179 math:notEqualTo 0}] + skolem:lemma2372 + [ a r:Fact; r:gives {(2 1 7 9) list:quicksort (1 2 7 9)}] [ a r:Fact; r:gives {(1 2 7 9) list:reverse (9 7 2 1)}] - skolem:lemma2579 - skolem:lemma2580 + skolem:lemma2373 + skolem:lemma2374 [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2179]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1279]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1182 a r:Inference; +skolem:lemma1181 a r:Inference; r:gives { - 2180 :kaprekar 6174 . + 2180 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2581 - skolem:lemma2582 + [ a r:Fact; r:gives {2180 math:notEqualTo 0}] + skolem:lemma2375 + [ a r:Fact; r:gives {(2 1 8 0) list:quicksort (0 1 2 8)}] [ a r:Fact; r:gives {(0 1 2 8) list:reverse (8 2 1 0)}] - skolem:lemma2085 - skolem:lemma2086 + skolem:lemma2054 + skolem:lemma2055 [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2180]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1183 a r:Inference; +skolem:lemma1182 a r:Inference; r:gives { - 2181 :kaprekar 6174 . + 2181 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2583 - skolem:lemma2584 + [ a r:Fact; r:gives {2181 math:notEqualTo 0}] + skolem:lemma2376 + [ a r:Fact; r:gives {(2 1 8 1) list:quicksort (1 1 2 8)}] [ a r:Fact; r:gives {(1 1 2 8) list:reverse (8 2 1 1)}] - skolem:lemma2392 - skolem:lemma2393 + skolem:lemma2244 + skolem:lemma2245 [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2181]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1128]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1184 a r:Inference; +skolem:lemma1183 a r:Inference; r:gives { - 2182 :kaprekar 6174 . + 2182 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2585 - skolem:lemma2586 + [ a r:Fact; r:gives {2182 math:notEqualTo 0}] + skolem:lemma2377 + [ a r:Fact; r:gives {(2 1 8 2) list:quicksort (1 2 2 8)}] [ a r:Fact; r:gives {(1 2 2 8) list:reverse (8 2 2 1)}] - skolem:lemma2428 - skolem:lemma2429 + skolem:lemma2270 + skolem:lemma2271 [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2182]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1228]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1185 a r:Inference; +skolem:lemma1184 a r:Inference; r:gives { - 2183 :kaprekar 6174 . + 2183 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2587 - skolem:lemma2588 + [ a r:Fact; r:gives {2183 math:notEqualTo 0}] + skolem:lemma2378 + [ a r:Fact; r:gives {(2 1 8 3) list:quicksort (1 2 3 8)}] [ a r:Fact; r:gives {(1 2 3 8) list:reverse (8 3 2 1)}] - skolem:lemma2462 - skolem:lemma2463 + skolem:lemma2294 + skolem:lemma2295 [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2183]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1238]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1186 a r:Inference; +skolem:lemma1185 a r:Inference; r:gives { - 2184 :kaprekar 6174 . + 2184 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2589 - skolem:lemma2590 + [ a r:Fact; r:gives {2184 math:notEqualTo 0}] + skolem:lemma2379 + [ a r:Fact; r:gives {(2 1 8 4) list:quicksort (1 2 4 8)}] [ a r:Fact; r:gives {(1 2 4 8) list:reverse (8 4 2 1)}] - skolem:lemma2490 - skolem:lemma2491 + skolem:lemma2316 + skolem:lemma2317 [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2184]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1248]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1187 a r:Inference; +skolem:lemma1186 a r:Inference; r:gives { - 2185 :kaprekar 6174 . + 2185 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2591 - skolem:lemma2592 + [ a r:Fact; r:gives {2185 math:notEqualTo 0}] + skolem:lemma2380 + [ a r:Fact; r:gives {(2 1 8 5) list:quicksort (1 2 5 8)}] [ a r:Fact; r:gives {(1 2 5 8) list:reverse (8 5 2 1)}] - skolem:lemma2521 - skolem:lemma2522 + skolem:lemma2336 + skolem:lemma2337 [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2185]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1258]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1188 a r:Inference; +skolem:lemma1187 a r:Inference; r:gives { - 2186 :kaprekar 6174 . + 2186 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2593 - skolem:lemma2594 + [ a r:Fact; r:gives {2186 math:notEqualTo 0}] + skolem:lemma2381 + [ a r:Fact; r:gives {(2 1 8 6) list:quicksort (1 2 6 8)}] [ a r:Fact; r:gives {(1 2 6 8) list:reverse (8 6 2 1)}] - skolem:lemma2550 - skolem:lemma2551 + skolem:lemma2354 + skolem:lemma2355 [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2186]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1268]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1189 a r:Inference; +skolem:lemma1188 a r:Inference; r:gives { - 2187 :kaprekar 6174 . + 2187 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2595 - skolem:lemma2596 + [ a r:Fact; r:gives {2187 math:notEqualTo 0}] + skolem:lemma2382 + [ a r:Fact; r:gives {(2 1 8 7) list:quicksort (1 2 7 8)}] [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 + skolem:lemma2370 + skolem:lemma2371 [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2187]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1190 a r:Inference; +skolem:lemma1189 a r:Inference; r:gives { - 2188 :kaprekar 6174 . + 2188 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2597 - skolem:lemma2598 + [ a r:Fact; r:gives {2188 math:notEqualTo 0}] + skolem:lemma2383 + [ a r:Fact; r:gives {(2 1 8 8) list:quicksort (1 2 8 8)}] [ a r:Fact; r:gives {(1 2 8 8) list:reverse (8 8 2 1)}] - skolem:lemma2599 - skolem:lemma2600 + skolem:lemma2384 + skolem:lemma2385 [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2188]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1288]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1191 a r:Inference; +skolem:lemma1190 a r:Inference; r:gives { - 2189 :kaprekar 6174 . + 2189 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2602 - skolem:lemma2603 + [ a r:Fact; r:gives {2189 math:notEqualTo 0}] + skolem:lemma2386 + [ a r:Fact; r:gives {(2 1 8 9) list:quicksort (1 2 8 9)}] [ a r:Fact; r:gives {(1 2 8 9) list:reverse (9 8 2 1)}] - skolem:lemma2604 - skolem:lemma2605 + skolem:lemma2387 + skolem:lemma2388 [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2189]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1289]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1192 a r:Inference; +skolem:lemma1191 a r:Inference; r:gives { - 2190 :kaprekar 6174 . + 2190 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2606 - skolem:lemma2607 + [ a r:Fact; r:gives {2190 math:notEqualTo 0}] + skolem:lemma2389 + [ a r:Fact; r:gives {(2 1 9 0) list:quicksort (0 1 2 9)}] [ a r:Fact; r:gives {(0 1 2 9) list:reverse (9 2 1 0)}] - skolem:lemma2090 - skolem:lemma2091 + skolem:lemma2057 + skolem:lemma2058 [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2190]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 129]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1193 a r:Inference; +skolem:lemma1192 a r:Inference; r:gives { - 2191 :kaprekar 6174 . + 2191 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2608 - skolem:lemma2609 + [ a r:Fact; r:gives {2191 math:notEqualTo 0}] + skolem:lemma2390 + [ a r:Fact; r:gives {(2 1 9 1) list:quicksort (1 1 2 9)}] [ a r:Fact; r:gives {(1 1 2 9) list:reverse (9 2 1 1)}] - skolem:lemma2396 - skolem:lemma2397 + skolem:lemma2247 + skolem:lemma2248 [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2191]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1129]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1194 a r:Inference; +skolem:lemma1193 a r:Inference; r:gives { - 2192 :kaprekar 6174 . + 2192 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2610 - skolem:lemma2611 + [ a r:Fact; r:gives {2192 math:notEqualTo 0}] + skolem:lemma2391 + [ a r:Fact; r:gives {(2 1 9 2) list:quicksort (1 2 2 9)}] [ a r:Fact; r:gives {(1 2 2 9) list:reverse (9 2 2 1)}] - skolem:lemma2432 - skolem:lemma2433 + skolem:lemma2273 + skolem:lemma2274 [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2192]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1229]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1195 a r:Inference; +skolem:lemma1194 a r:Inference; r:gives { - 2193 :kaprekar 6174 . + 2193 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2612 - skolem:lemma2613 + [ a r:Fact; r:gives {2193 math:notEqualTo 0}] + skolem:lemma2392 + [ a r:Fact; r:gives {(2 1 9 3) list:quicksort (1 2 3 9)}] [ a r:Fact; r:gives {(1 2 3 9) list:reverse (9 3 2 1)}] - skolem:lemma2466 - skolem:lemma2467 + skolem:lemma2297 + skolem:lemma2298 [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2193]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1239]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1196 a r:Inference; +skolem:lemma1195 a r:Inference; r:gives { - 2194 :kaprekar 6174 . + 2194 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2614 - skolem:lemma2615 + [ a r:Fact; r:gives {2194 math:notEqualTo 0}] + skolem:lemma2393 + [ a r:Fact; r:gives {(2 1 9 4) list:quicksort (1 2 4 9)}] [ a r:Fact; r:gives {(1 2 4 9) list:reverse (9 4 2 1)}] - skolem:lemma2494 - skolem:lemma2495 + skolem:lemma2319 + skolem:lemma2320 [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2194]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1249]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1197 a r:Inference; +skolem:lemma1196 a r:Inference; r:gives { - 2195 :kaprekar 6174 . + 2195 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2616 - skolem:lemma2617 + [ a r:Fact; r:gives {2195 math:notEqualTo 0}] + skolem:lemma2394 + [ a r:Fact; r:gives {(2 1 9 5) list:quicksort (1 2 5 9)}] [ a r:Fact; r:gives {(1 2 5 9) list:reverse (9 5 2 1)}] - skolem:lemma2525 - skolem:lemma2526 + skolem:lemma2339 + skolem:lemma2340 [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2195]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1259]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1198 a r:Inference; +skolem:lemma1197 a r:Inference; r:gives { - 2196 :kaprekar 6174 . + 2196 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2618 - skolem:lemma2619 + [ a r:Fact; r:gives {2196 math:notEqualTo 0}] + skolem:lemma2395 + [ a r:Fact; r:gives {(2 1 9 6) list:quicksort (1 2 6 9)}] [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 + skolem:lemma2357 + skolem:lemma2358 [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2196]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1199 a r:Inference; +skolem:lemma1198 a r:Inference; r:gives { - 2197 :kaprekar 6174 . + 2197 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2620 - skolem:lemma2621 + [ a r:Fact; r:gives {2197 math:notEqualTo 0}] + skolem:lemma2396 + [ a r:Fact; r:gives {(2 1 9 7) list:quicksort (1 2 7 9)}] [ a r:Fact; r:gives {(1 2 7 9) list:reverse (9 7 2 1)}] - skolem:lemma2579 - skolem:lemma2580 + skolem:lemma2373 + skolem:lemma2374 [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2197]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1279]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1200 a r:Inference; +skolem:lemma1199 a r:Inference; r:gives { - 2198 :kaprekar 6174 . + 2198 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2622 - skolem:lemma2623 + [ a r:Fact; r:gives {2198 math:notEqualTo 0}] + skolem:lemma2397 + [ a r:Fact; r:gives {(2 1 9 8) list:quicksort (1 2 8 9)}] [ a r:Fact; r:gives {(1 2 8 9) list:reverse (9 8 2 1)}] - skolem:lemma2604 - skolem:lemma2605 + skolem:lemma2387 + skolem:lemma2388 [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2198]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1289]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1201 a r:Inference; +skolem:lemma1200 a r:Inference; r:gives { - 2199 :kaprekar 6174 . + 2199 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2624 - skolem:lemma2625 + [ a r:Fact; r:gives {2199 math:notEqualTo 0}] + skolem:lemma2398 + [ a r:Fact; r:gives {(2 1 9 9) list:quicksort (1 2 9 9)}] [ a r:Fact; r:gives {(1 2 9 9) list:reverse (9 9 2 1)}] - skolem:lemma2626 - skolem:lemma2627 + skolem:lemma2399 + skolem:lemma2400 [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] - [ a r:Fact; r:gives {8622 math:notEqualTo 6174}] - skolem:lemma2628 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2199]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1299]; - 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_8"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1202 a r:Inference; +skolem:lemma1201 a r:Inference; r:gives { - 2200 :kaprekar 6174 . + 2200 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2629 - skolem:lemma2630 + [ a r:Fact; r:gives {2200 math:notEqualTo 0}] + skolem:lemma2401 + [ a r:Fact; r:gives {(2 2 0 0) list:quicksort (0 0 2 2)}] [ a r:Fact; r:gives {(0 0 2 2) list:reverse (2 2 0 0)}] - skolem:lemma2015 - skolem:lemma2016 + skolem:lemma2008 + skolem:lemma2009 [ a r:Fact; r:gives {(2200 22) math:difference 2178}] - [ a r:Fact; r:gives {2178 math:notEqualTo 6174}] - skolem:lemma1180 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2200]; + 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 (0 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 22]; - 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_8"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1203 a r:Inference; +skolem:lemma1202 a r:Inference; r:gives { - 2201 :kaprekar 6174 . + 2201 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2631 - skolem:lemma2632 + [ a r:Fact; r:gives {2201 math:notEqualTo 0}] + skolem:lemma2402 + [ a r:Fact; r:gives {(2 2 0 1) list:quicksort (0 1 2 2)}] [ a r:Fact; r:gives {(0 1 2 2) list:reverse (2 2 1 0)}] - skolem:lemma2056 - skolem:lemma2057 + skolem:lemma2036 + skolem:lemma2037 [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2201]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 122]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1204 a r:Inference; +skolem:lemma1203 a r:Inference; r:gives { - 2202 :kaprekar 6174 . + 2202 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2633 - skolem:lemma2634 + [ a r:Fact; r:gives {2202 math:notEqualTo 0}] + skolem:lemma2403 + [ a r:Fact; r:gives {(2 2 0 2) list:quicksort (0 2 2 2)}] [ a r:Fact; r:gives {(0 2 2 2) list:reverse (2 2 2 0)}] - skolem:lemma2099 - skolem:lemma2100 + skolem:lemma2062 + skolem:lemma2063 [ a r:Fact; r:gives {(2220 222) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2202]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 222]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1205 a r:Inference; +skolem:lemma1204 a r:Inference; r:gives { - 2203 :kaprekar 6174 . + 2203 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2635 - skolem:lemma2636 + [ a r:Fact; r:gives {2203 math:notEqualTo 0}] + skolem:lemma2404 + [ a r:Fact; r:gives {(2 2 0 3) list:quicksort (0 2 2 3)}] [ a r:Fact; r:gives {(0 2 2 3) list:reverse (3 2 2 0)}] - skolem:lemma2103 - skolem:lemma2104 + skolem:lemma2065 + skolem:lemma2066 [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2203]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 223]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1206 a r:Inference; +skolem:lemma1205 a r:Inference; r:gives { - 2204 :kaprekar 6174 . + 2204 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2637 - skolem:lemma2638 + [ a r:Fact; r:gives {2204 math:notEqualTo 0}] + skolem:lemma2405 + [ a r:Fact; r:gives {(2 2 0 4) list:quicksort (0 2 2 4)}] [ a r:Fact; r:gives {(0 2 2 4) list:reverse (4 2 2 0)}] - skolem:lemma2107 - skolem:lemma2108 + skolem:lemma2068 + skolem:lemma2069 [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2204]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 224]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1207 a r:Inference; +skolem:lemma1206 a r:Inference; r:gives { - 2205 :kaprekar 6174 . + 2205 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2639 - skolem:lemma2640 + [ a r:Fact; r:gives {2205 math:notEqualTo 0}] + skolem:lemma2406 + [ a r:Fact; r:gives {(2 2 0 5) list:quicksort (0 2 2 5)}] [ a r:Fact; r:gives {(0 2 2 5) list:reverse (5 2 2 0)}] - skolem:lemma2112 - skolem:lemma2113 + skolem:lemma2071 + skolem:lemma2072 [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2205]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 225]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1208 a r:Inference; +skolem:lemma1207 a r:Inference; r:gives { - 2206 :kaprekar 6174 . + 2206 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2641 - skolem:lemma2642 + [ a r:Fact; r:gives {2206 math:notEqualTo 0}] + skolem:lemma2407 + [ a r:Fact; r:gives {(2 2 0 6) list:quicksort (0 2 2 6)}] [ a r:Fact; r:gives {(0 2 2 6) list:reverse (6 2 2 0)}] - skolem:lemma2117 - skolem:lemma2118 + skolem:lemma2074 + skolem:lemma2075 [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2206]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 226]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1209 a r:Inference; +skolem:lemma1208 a r:Inference; r:gives { - 2207 :kaprekar 6174 . + 2207 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2643 - skolem:lemma2644 + [ a r:Fact; r:gives {2207 math:notEqualTo 0}] + skolem:lemma2408 + [ a r:Fact; r:gives {(2 2 0 7) list:quicksort (0 2 2 7)}] [ a r:Fact; r:gives {(0 2 2 7) list:reverse (7 2 2 0)}] - skolem:lemma2122 - skolem:lemma2123 + skolem:lemma2077 + skolem:lemma2078 [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2207]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 227]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1210 a r:Inference; +skolem:lemma1209 a r:Inference; r:gives { - 2208 :kaprekar 6174 . + 2208 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2645 - skolem:lemma2646 + [ a r:Fact; r:gives {2208 math:notEqualTo 0}] + skolem:lemma2409 + [ a r:Fact; r:gives {(2 2 0 8) list:quicksort (0 2 2 8)}] [ a r:Fact; r:gives {(0 2 2 8) list:reverse (8 2 2 0)}] - skolem:lemma2127 - skolem:lemma2128 + skolem:lemma2080 + skolem:lemma2081 [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2208]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 228]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1211 a r:Inference; +skolem:lemma1210 a r:Inference; r:gives { - 2209 :kaprekar 6174 . + 2209 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2647 - skolem:lemma2648 + [ a r:Fact; r:gives {2209 math:notEqualTo 0}] + skolem:lemma2410 + [ a r:Fact; r:gives {(2 2 0 9) list:quicksort (0 2 2 9)}] [ a r:Fact; r:gives {(0 2 2 9) list:reverse (9 2 2 0)}] - skolem:lemma2132 - skolem:lemma2133 + skolem:lemma2083 + skolem:lemma2084 [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2209]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 229]; - 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_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1212 a r:Inference; +skolem:lemma1211 a r:Inference; r:gives { - 2210 :kaprekar 6174 . + 2210 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2649 - skolem:lemma2650 + [ a r:Fact; r:gives {2210 math:notEqualTo 0}] + skolem:lemma2411 + [ a r:Fact; r:gives {(2 2 1 0) list:quicksort (0 1 2 2)}] [ a r:Fact; r:gives {(0 1 2 2) list:reverse (2 2 1 0)}] - skolem:lemma2056 - skolem:lemma2057 + skolem:lemma2036 + skolem:lemma2037 [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2210]; + 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 (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 122]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1213 a r:Inference; +skolem:lemma1212 a r:Inference; r:gives { - 2211 :kaprekar 6174 . + 2211 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2651 - skolem:lemma2652 + [ a r:Fact; r:gives {2211 math:notEqualTo 0}] + skolem:lemma2412 + [ a r:Fact; r:gives {(2 2 1 1) list:quicksort (1 1 2 2)}] [ a r:Fact; r:gives {(1 1 2 2) list:reverse (2 2 1 1)}] - skolem:lemma2367 - skolem:lemma2368 + skolem:lemma2226 + skolem:lemma2227 [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2211]; + 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 (1 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1122]; - 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_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1214 a r:Inference; +skolem:lemma1213 a r:Inference; r:gives { - 2212 :kaprekar 6174 . + 2212 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2653 - skolem:lemma2654 + [ a r:Fact; r:gives {2212 math:notEqualTo 0}] + skolem:lemma2413 + [ a r:Fact; r:gives {(2 2 1 2) list:quicksort (1 2 2 2)}] [ a r:Fact; r:gives {(1 2 2 2) list:reverse (2 2 2 1)}] - skolem:lemma2404 - skolem:lemma2405 + skolem:lemma2252 + skolem:lemma2253 [ a r:Fact; r:gives {(2221 1222) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2212]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1222]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1215 a r:Inference; +skolem:lemma1214 a r:Inference; r:gives { - 2213 :kaprekar 6174 . + 2213 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2655 - skolem:lemma2656 + [ a r:Fact; r:gives {2213 math:notEqualTo 0}] + skolem:lemma2414 + [ a r:Fact; r:gives {(2 2 1 3) list:quicksort (1 2 2 3)}] [ a r:Fact; r:gives {(1 2 2 3) list:reverse (3 2 2 1)}] - skolem:lemma2408 - skolem:lemma2409 + skolem:lemma2255 + skolem:lemma2256 [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2213]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1223]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1216 a r:Inference; +skolem:lemma1215 a r:Inference; r:gives { - 2214 :kaprekar 6174 . + 2214 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2657 - skolem:lemma2658 + [ a r:Fact; r:gives {2214 math:notEqualTo 0}] + skolem:lemma2415 + [ a r:Fact; r:gives {(2 2 1 4) list:quicksort (1 2 2 4)}] [ a r:Fact; r:gives {(1 2 2 4) list:reverse (4 2 2 1)}] - skolem:lemma2412 - skolem:lemma2413 + skolem:lemma2258 + skolem:lemma2259 [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2214]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1224]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1217 a r:Inference; +skolem:lemma1216 a r:Inference; r:gives { - 2215 :kaprekar 6174 . + 2215 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2659 - skolem:lemma2660 - [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] + [ a r:Fact; r:gives {2215 math:notEqualTo 0}] skolem:lemma2416 - skolem:lemma2417 + [ a r:Fact; r:gives {(2 2 1 5) list:quicksort (1 2 2 5)}] + [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] + skolem:lemma2261 + skolem:lemma2262 [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2215]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1225]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1218 a r:Inference; +skolem:lemma1217 a r:Inference; r:gives { - 2216 :kaprekar 6174 . + 2216 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2661 - skolem:lemma2662 + [ a r:Fact; r:gives {2216 math:notEqualTo 0}] + skolem:lemma2417 + [ a r:Fact; r:gives {(2 2 1 6) list:quicksort (1 2 2 6)}] [ a r:Fact; r:gives {(1 2 2 6) list:reverse (6 2 2 1)}] - skolem:lemma2420 - skolem:lemma2421 + skolem:lemma2264 + skolem:lemma2265 [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2216]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1226]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1219 a r:Inference; +skolem:lemma1218 a r:Inference; r:gives { - 2217 :kaprekar 6174 . + 2217 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2663 - skolem:lemma2664 + [ a r:Fact; r:gives {2217 math:notEqualTo 0}] + skolem:lemma2418 + [ a r:Fact; r:gives {(2 2 1 7) list:quicksort (1 2 2 7)}] [ a r:Fact; r:gives {(1 2 2 7) list:reverse (7 2 2 1)}] - skolem:lemma2424 - skolem:lemma2425 + skolem:lemma2267 + skolem:lemma2268 [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2217]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1227]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1220 a r:Inference; +skolem:lemma1219 a r:Inference; r:gives { - 2218 :kaprekar 6174 . + 2218 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2665 - skolem:lemma2666 + [ a r:Fact; r:gives {2218 math:notEqualTo 0}] + skolem:lemma2419 + [ a r:Fact; r:gives {(2 2 1 8) list:quicksort (1 2 2 8)}] [ a r:Fact; r:gives {(1 2 2 8) list:reverse (8 2 2 1)}] - skolem:lemma2428 - skolem:lemma2429 + skolem:lemma2270 + skolem:lemma2271 [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2218]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1228]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1221 a r:Inference; +skolem:lemma1220 a r:Inference; r:gives { - 2219 :kaprekar 6174 . + 2219 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2667 - skolem:lemma2668 + [ a r:Fact; r:gives {2219 math:notEqualTo 0}] + skolem:lemma2420 + [ a r:Fact; r:gives {(2 2 1 9) list:quicksort (1 2 2 9)}] [ a r:Fact; r:gives {(1 2 2 9) list:reverse (9 2 2 1)}] - skolem:lemma2432 - skolem:lemma2433 + skolem:lemma2273 + skolem:lemma2274 [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2219]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1229]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1222 a r:Inference; +skolem:lemma1221 a r:Inference; r:gives { - 2220 :kaprekar 6174 . + 2220 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2669 - skolem:lemma2670 + [ a r:Fact; r:gives {2220 math:notEqualTo 0}] + skolem:lemma2421 + [ a r:Fact; r:gives {(2 2 2 0) list:quicksort (0 2 2 2)}] [ a r:Fact; r:gives {(0 2 2 2) list:reverse (2 2 2 0)}] - skolem:lemma2099 - skolem:lemma2100 + skolem:lemma2062 + skolem:lemma2063 [ a r:Fact; r:gives {(2220 222) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2220]; + 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 (0 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 222]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma1223 a r:Inference; +skolem:lemma1222 a r:Inference; r:gives { - 2221 :kaprekar 6174 . + 2221 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2671 - skolem:lemma2672 + [ a r:Fact; r:gives {2221 math:notEqualTo 0}] + skolem:lemma2422 + [ a r:Fact; r:gives {(2 2 2 1) list:quicksort (1 2 2 2)}] [ a r:Fact; r:gives {(1 2 2 2) list:reverse (2 2 2 1)}] - skolem:lemma2404 - skolem:lemma2405 + skolem:lemma2252 + skolem:lemma2253 [ a r:Fact; r:gives {(2221 1222) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2221]; + 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 (1 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1222]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. + +skolem:lemma1223 a r:Inference; + r:gives { + 2223 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2223 math:notEqualTo 0}] + skolem:lemma2423 + [ a r:Fact; r:gives {(2 2 2 3) list:quicksort (2 2 2 3)}] + [ a r:Fact; r:gives {(2 2 2 3) list:reverse (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)}] + ); + 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. skolem:lemma1224 a r:Inference; r:gives { - 2222 :kaprekar 0 . + 2224 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2224 math:notEqualTo 0}] + skolem:lemma2426 + [ a r:Fact; r:gives {(2 2 2 4) list:quicksort (2 2 2 4)}] + [ a r:Fact; r:gives {(2 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2673 - skolem:lemma2674 - [ a r:Fact; r:gives {(2 2 2 2) list:reverse (2 2 2 2)}] - skolem:lemma2675 - skolem:lemma2675 - [ a r:Fact; r:gives {(2222 2222) math:difference 0}] - [ a r:Fact; r:gives {0 math:notEqualTo 6174}] - skolem:lemma2676 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 0]; - r:rule skolem:lemma2008. + 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. skolem:lemma1225 a r:Inference; r:gives { - 2223 :kaprekar 6174 . + 2225 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2225 math:notEqualTo 0}] + skolem:lemma2429 + [ a r:Fact; r:gives {(2 2 2 5) list:quicksort (2 2 2 5)}] + [ a r:Fact; r:gives {(2 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2677 - skolem:lemma2678 - [ a r:Fact; r:gives {(2 2 2 3) list:reverse (3 2 2 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(3222 2223) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2223]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1226 a r:Inference; r:gives { - 2224 :kaprekar 6174 . + 2226 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2226 math:notEqualTo 0}] + skolem:lemma2432 + [ a r:Fact; r:gives {(2 2 2 6) list:quicksort (2 2 2 6)}] + [ a r:Fact; r:gives {(2 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2681 - skolem:lemma2682 - [ a r:Fact; r:gives {(2 2 2 4) list:reverse (4 2 2 2)}] - skolem:lemma2683 - skolem:lemma2684 - [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2224]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1227 a r:Inference; r:gives { - 2225 :kaprekar 6174 . + 2227 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2227 math:notEqualTo 0}] + skolem:lemma2435 + [ a r:Fact; r:gives {(2 2 2 7) list:quicksort (2 2 2 7)}] + [ a r:Fact; r:gives {(2 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2685 - skolem:lemma2686 - [ a r:Fact; r:gives {(2 2 2 5) list:reverse (5 2 2 2)}] - skolem:lemma2687 - skolem:lemma2688 - [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2225]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1228 a r:Inference; r:gives { - 2226 :kaprekar 6174 . + 2228 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2228 math:notEqualTo 0}] + skolem:lemma2438 + [ a r:Fact; r:gives {(2 2 2 8) list:quicksort (2 2 2 8)}] + [ a r:Fact; r:gives {(2 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2689 - skolem:lemma2690 - [ a r:Fact; r:gives {(2 2 2 6) list:reverse (6 2 2 2)}] - skolem:lemma2691 - skolem:lemma2692 - [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2226]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1229 a r:Inference; r:gives { - 2227 :kaprekar 6174 . + 2229 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2229 math:notEqualTo 0}] + skolem:lemma2441 + [ a r:Fact; r:gives {(2 2 2 9) list:quicksort (2 2 2 9)}] + [ a r:Fact; r:gives {(2 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2693 - skolem:lemma2694 - [ a r:Fact; r:gives {(2 2 2 7) list:reverse (7 2 2 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2227]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1230 a r:Inference; r:gives { - 2228 :kaprekar 6174 . + 2230 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2230 math:notEqualTo 0}] + skolem:lemma2444 + [ a r:Fact; r:gives {(2 2 3 0) list:quicksort (0 2 2 3)}] + [ a r:Fact; r:gives {(0 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2697 - skolem:lemma2698 - [ a r:Fact; r:gives {(2 2 2 8) list:reverse (8 2 2 2)}] - skolem:lemma2699 - skolem:lemma2700 - [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2228]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1231 a r:Inference; r:gives { - 2229 :kaprekar 6174 . + 2231 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2231 math:notEqualTo 0}] + skolem:lemma2445 + [ a r:Fact; r:gives {(2 2 3 1) list:quicksort (1 2 2 3)}] + [ a r:Fact; r:gives {(1 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2701 - skolem:lemma2702 - [ a r:Fact; r:gives {(2 2 2 9) list:reverse (9 2 2 2)}] - skolem:lemma2703 - skolem:lemma2704 - [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2229]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1232 a r:Inference; r:gives { - 2230 :kaprekar 6174 . + 2232 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2232 math:notEqualTo 0}] + skolem:lemma2446 + [ a r:Fact; r:gives {(2 2 3 2) list:quicksort (2 2 2 3)}] + [ a r:Fact; r:gives {(2 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2705 - skolem:lemma2706 - [ a r:Fact; r:gives {(0 2 2 3) list:reverse (3 2 2 0)}] - skolem:lemma2103 - skolem:lemma2104 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2230]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 223]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1233 a r:Inference; r:gives { - 2231 :kaprekar 6174 . + 2233 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2233 math:notEqualTo 0}] + skolem:lemma2447 + [ a r:Fact; r:gives {(2 2 3 3) list:quicksort (2 2 3 3)}] + [ a r:Fact; r:gives {(2 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2707 - skolem:lemma2708 - [ a r:Fact; r:gives {(1 2 2 3) list:reverse (3 2 2 1)}] - skolem:lemma2408 - skolem:lemma2409 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2231]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1223]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1234 a r:Inference; r:gives { - 2232 :kaprekar 6174 . + 2234 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2234 math:notEqualTo 0}] + skolem:lemma2450 + [ a r:Fact; r:gives {(2 2 3 4) list:quicksort (2 2 3 4)}] + [ a r:Fact; r:gives {(2 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2709 - skolem:lemma2710 - [ a r:Fact; r:gives {(2 2 2 3) list:reverse (3 2 2 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(3222 2223) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2232]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2223]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1235 a r:Inference; r:gives { - 2233 :kaprekar 6174 . + 2235 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2235 math:notEqualTo 0}] + skolem:lemma2453 + [ a r:Fact; r:gives {(2 2 3 5) list:quicksort (2 2 3 5)}] + [ a r:Fact; r:gives {(2 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2711 - skolem:lemma2712 - [ a r:Fact; r:gives {(2 2 3 3) list:reverse (3 3 2 2)}] - skolem:lemma2713 - skolem:lemma2714 - [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2233]; - 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_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1236 a r:Inference; r:gives { - 2234 :kaprekar 6174 . + 2236 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2236 math:notEqualTo 0}] + skolem:lemma2456 + [ a r:Fact; r:gives {(2 2 3 6) list:quicksort (2 2 3 6)}] + [ a r:Fact; r:gives {(2 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2715 - skolem:lemma2716 - [ a r:Fact; r:gives {(2 2 3 4) list:reverse (4 3 2 2)}] - skolem:lemma2717 - skolem:lemma2718 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2234]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1237 a r:Inference; r:gives { - 2235 :kaprekar 6174 . + 2237 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2237 math:notEqualTo 0}] + skolem:lemma2459 + [ a r:Fact; r:gives {(2 2 3 7) list:quicksort (2 2 3 7)}] + [ a r:Fact; r:gives {(2 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2719 - skolem:lemma2720 - [ a r:Fact; r:gives {(2 2 3 5) list:reverse (5 3 2 2)}] - skolem:lemma2721 - skolem:lemma2722 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2235]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1238 a r:Inference; r:gives { - 2236 :kaprekar 6174 . + 2238 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2238 math:notEqualTo 0}] + skolem:lemma2462 + [ a r:Fact; r:gives {(2 2 3 8) list:quicksort (2 2 3 8)}] + [ a r:Fact; r:gives {(2 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2723 - skolem:lemma2724 - [ a r:Fact; r:gives {(2 2 3 6) list:reverse (6 3 2 2)}] - skolem:lemma2725 - skolem:lemma2726 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2236]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1239 a r:Inference; r:gives { - 2237 :kaprekar 6174 . + 2239 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2239 math:notEqualTo 0}] + skolem:lemma2465 + [ a r:Fact; r:gives {(2 2 3 9) list:quicksort (2 2 3 9)}] + [ a r:Fact; r:gives {(2 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2727 - skolem:lemma2728 - [ a r:Fact; r:gives {(2 2 3 7) list:reverse (7 3 2 2)}] - skolem:lemma2729 - skolem:lemma2730 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2237]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1240 a r:Inference; r:gives { - 2238 :kaprekar 6174 . + 2240 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2240 math:notEqualTo 0}] + skolem:lemma2468 + [ a r:Fact; r:gives {(2 2 4 0) list:quicksort (0 2 2 4)}] + [ a r:Fact; r:gives {(0 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2731 - skolem:lemma2732 - [ a r:Fact; r:gives {(2 2 3 8) list:reverse (8 3 2 2)}] - skolem:lemma2733 - skolem:lemma2734 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2238]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1241 a r:Inference; r:gives { - 2239 :kaprekar 6174 . + 2241 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2241 math:notEqualTo 0}] + skolem:lemma2469 + [ a r:Fact; r:gives {(2 2 4 1) list:quicksort (1 2 2 4)}] + [ a r:Fact; r:gives {(1 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2735 - skolem:lemma2736 - [ a r:Fact; r:gives {(2 2 3 9) list:reverse (9 3 2 2)}] - skolem:lemma2737 - skolem:lemma2738 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2239]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1242 a r:Inference; r:gives { - 2240 :kaprekar 6174 . + 2242 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2242 math:notEqualTo 0}] + skolem:lemma2470 + [ a r:Fact; r:gives {(2 2 4 2) list:quicksort (2 2 2 4)}] + [ a r:Fact; r:gives {(2 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2739 - skolem:lemma2740 - [ a r:Fact; r:gives {(0 2 2 4) list:reverse (4 2 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2240]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 224]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1243 a r:Inference; r:gives { - 2241 :kaprekar 6174 . + 2243 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2243 math:notEqualTo 0}] + skolem:lemma2471 + [ a r:Fact; r:gives {(2 2 4 3) list:quicksort (2 2 3 4)}] + [ a r:Fact; r:gives {(2 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2741 - skolem:lemma2742 - [ a r:Fact; r:gives {(1 2 2 4) list:reverse (4 2 2 1)}] - skolem:lemma2412 - skolem:lemma2413 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2241]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1224]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1244 a r:Inference; r:gives { - 2242 :kaprekar 6174 . + 2244 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2244 math:notEqualTo 0}] + skolem:lemma2472 + [ a r:Fact; r:gives {(2 2 4 4) list:quicksort (2 2 4 4)}] + [ a r:Fact; r:gives {(2 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2743 - skolem:lemma2744 - [ a r:Fact; r:gives {(2 2 2 4) list:reverse (4 2 2 2)}] - skolem:lemma2683 - skolem:lemma2684 - [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2242]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2224]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1245 a r:Inference; r:gives { - 2243 :kaprekar 6174 . + 2245 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2245 math:notEqualTo 0}] + skolem:lemma2475 + [ a r:Fact; r:gives {(2 2 4 5) list:quicksort (2 2 4 5)}] + [ a r:Fact; r:gives {(2 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2745 - skolem:lemma2746 - [ a r:Fact; r:gives {(2 2 3 4) list:reverse (4 3 2 2)}] - skolem:lemma2717 - skolem:lemma2718 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2243]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2234]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1246 a r:Inference; r:gives { - 2244 :kaprekar 6174 . + 2246 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2246 math:notEqualTo 0}] + skolem:lemma2478 + [ a r:Fact; r:gives {(2 2 4 6) list:quicksort (2 2 4 6)}] + [ a r:Fact; r:gives {(2 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2747 - skolem:lemma2748 - [ a r:Fact; r:gives {(2 2 4 4) list:reverse (4 4 2 2)}] - skolem:lemma2749 - skolem:lemma2750 - [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] - [ a r:Fact; r:gives {2178 math:notEqualTo 6174}] - skolem:lemma1180 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2244]; - 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_8"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1247 a r:Inference; r:gives { - 2245 :kaprekar 6174 . + 2247 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2247 math:notEqualTo 0}] + skolem:lemma2481 + [ a r:Fact; r:gives {(2 2 4 7) list:quicksort (2 2 4 7)}] + [ a r:Fact; r:gives {(2 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2751 - skolem:lemma2752 - [ a r:Fact; r:gives {(2 2 4 5) list:reverse (5 4 2 2)}] - skolem:lemma2753 - skolem:lemma2754 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2245]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1248 a r:Inference; r:gives { - 2246 :kaprekar 6174 . + 2248 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2248 math:notEqualTo 0}] + skolem:lemma2484 + [ a r:Fact; r:gives {(2 2 4 8) list:quicksort (2 2 4 8)}] + [ a r:Fact; r:gives {(2 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2755 - skolem:lemma2756 - [ a r:Fact; r:gives {(2 2 4 6) list:reverse (6 4 2 2)}] - skolem:lemma2757 - skolem:lemma2758 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2246]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1249 a r:Inference; r:gives { - 2247 :kaprekar 6174 . + 2249 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2249 math:notEqualTo 0}] + skolem:lemma2487 + [ a r:Fact; r:gives {(2 2 4 9) list:quicksort (2 2 4 9)}] + [ a r:Fact; r:gives {(2 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2759 - skolem:lemma2760 - [ a r:Fact; r:gives {(2 2 4 7) list:reverse (7 4 2 2)}] - skolem:lemma2761 - skolem:lemma2762 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2247]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1250 a r:Inference; r:gives { - 2248 :kaprekar 6174 . + 2250 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2250 math:notEqualTo 0}] + skolem:lemma2490 + [ a r:Fact; r:gives {(2 2 5 0) list:quicksort (0 2 2 5)}] + [ a r:Fact; r:gives {(0 2 2 5) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2248]; - r:rule skolem:lemma2032. + 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. skolem:lemma1251 a r:Inference; r:gives { - 2249 :kaprekar 6174 . + 2251 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2251 math:notEqualTo 0}] + skolem:lemma2491 + [ a r:Fact; r:gives {(2 2 5 1) list:quicksort (1 2 2 5)}] + [ a r:Fact; r:gives {(1 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2763 - skolem:lemma2764 - [ a r:Fact; r:gives {(2 2 4 9) list:reverse (9 4 2 2)}] - skolem:lemma2765 - skolem:lemma2766 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2249]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1252 a r:Inference; r:gives { - 2250 :kaprekar 6174 . + 2252 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2252 math:notEqualTo 0}] + skolem:lemma2492 + [ a r:Fact; r:gives {(2 2 5 2) list:quicksort (2 2 2 5)}] + [ a r:Fact; r:gives {(2 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2767 - skolem:lemma2768 - [ a r:Fact; r:gives {(0 2 2 5) list:reverse (5 2 2 0)}] - skolem:lemma2112 - skolem:lemma2113 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2250]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 225]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1253 a r:Inference; r:gives { - 2251 :kaprekar 6174 . + 2253 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2253 math:notEqualTo 0}] + skolem:lemma2493 + [ a r:Fact; r:gives {(2 2 5 3) list:quicksort (2 2 3 5)}] + [ a r:Fact; r:gives {(2 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2769 - skolem:lemma2770 - [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] - skolem:lemma2416 - skolem:lemma2417 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2251]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1225]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1254 a r:Inference; r:gives { - 2252 :kaprekar 6174 . + 2254 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2254 math:notEqualTo 0}] + skolem:lemma2494 + [ a r:Fact; r:gives {(2 2 5 4) list:quicksort (2 2 4 5)}] + [ a r:Fact; r:gives {(2 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2771 - skolem:lemma2772 - [ a r:Fact; r:gives {(2 2 2 5) list:reverse (5 2 2 2)}] - skolem:lemma2687 - skolem:lemma2688 - [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2252]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2225]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1255 a r:Inference; r:gives { - 2253 :kaprekar 6174 . + 2255 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2255 math:notEqualTo 0}] + skolem:lemma2495 + [ a r:Fact; r:gives {(2 2 5 5) list:quicksort (2 2 5 5)}] + [ a r:Fact; r:gives {(2 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2773 - skolem:lemma2774 - [ a r:Fact; r:gives {(2 2 3 5) list:reverse (5 3 2 2)}] - skolem:lemma2721 - skolem:lemma2722 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2253]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2235]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1256 a r:Inference; r:gives { - 2254 :kaprekar 6174 . + 2256 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2256 math:notEqualTo 0}] + skolem:lemma2498 + [ a r:Fact; r:gives {(2 2 5 6) list:quicksort (2 2 5 6)}] + [ a r:Fact; r:gives {(2 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2775 - skolem:lemma2776 - [ a r:Fact; r:gives {(2 2 4 5) list:reverse (5 4 2 2)}] - skolem:lemma2753 - skolem:lemma2754 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2254]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2245]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1257 a r:Inference; r:gives { - 2255 :kaprekar 6174 . + 2257 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2257 math:notEqualTo 0}] + skolem:lemma2501 + [ a r:Fact; r:gives {(2 2 5 7) list:quicksort (2 2 5 7)}] + [ a r:Fact; r:gives {(2 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2777 - skolem:lemma2778 - [ a r:Fact; r:gives {(2 2 5 5) list:reverse (5 5 2 2)}] - skolem:lemma2779 - skolem:lemma2780 - [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] - [ a r:Fact; r:gives {3267 math:notEqualTo 6174}] - skolem:lemma2781 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2255]; - 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_8"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1258 a r:Inference; r:gives { - 2256 :kaprekar 6174 . + 2258 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2258 math:notEqualTo 0}] + skolem:lemma2504 + [ a r:Fact; r:gives {(2 2 5 8) list:quicksort (2 2 5 8)}] + [ a r:Fact; r:gives {(2 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2782 - skolem:lemma2783 - [ a r:Fact; r:gives {(2 2 5 6) list:reverse (6 5 2 2)}] - skolem:lemma2784 - skolem:lemma2785 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2256]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1259 a r:Inference; r:gives { - 2257 :kaprekar 6174 . + 2259 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2259 math:notEqualTo 0}] + skolem:lemma2507 + [ a r:Fact; r:gives {(2 2 5 9) list:quicksort (2 2 5 9)}] + [ a r:Fact; r:gives {(2 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2786 - skolem:lemma2787 - [ a r:Fact; r:gives {(2 2 5 7) list:reverse (7 5 2 2)}] - skolem:lemma2788 - skolem:lemma2789 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2257]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1260 a r:Inference; r:gives { - 2258 :kaprekar 6174 . + 2260 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2260 math:notEqualTo 0}] + skolem:lemma2510 + [ a r:Fact; r:gives {(2 2 6 0) list:quicksort (0 2 2 6)}] + [ a r:Fact; r:gives {(0 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2790 - skolem:lemma2791 - [ a r:Fact; r:gives {(2 2 5 8) list:reverse (8 5 2 2)}] - skolem:lemma2792 - skolem:lemma2793 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2258]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1261 a r:Inference; r:gives { - 2259 :kaprekar 6174 . + 2261 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2261 math:notEqualTo 0}] + skolem:lemma2511 + [ a r:Fact; r:gives {(2 2 6 1) list:quicksort (1 2 2 6)}] + [ a r:Fact; r:gives {(1 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2794 - skolem:lemma2795 - [ a r:Fact; r:gives {(2 2 5 9) list:reverse (9 5 2 2)}] - skolem:lemma2796 - skolem:lemma2797 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2259]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1262 a r:Inference; r:gives { - 2260 :kaprekar 6174 . + 2262 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2262 math:notEqualTo 0}] + skolem:lemma2512 + [ a r:Fact; r:gives {(2 2 6 2) list:quicksort (2 2 2 6)}] + [ a r:Fact; r:gives {(2 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2798 - skolem:lemma2799 - [ a r:Fact; r:gives {(0 2 2 6) list:reverse (6 2 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2260]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 226]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1263 a r:Inference; r:gives { - 2261 :kaprekar 6174 . + 2263 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2263 math:notEqualTo 0}] + skolem:lemma2513 + [ a r:Fact; r:gives {(2 2 6 3) list:quicksort (2 2 3 6)}] + [ a r:Fact; r:gives {(2 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(1 2 2 6) list:reverse (6 2 2 1)}] - skolem:lemma2420 - skolem:lemma2421 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1226]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1264 a r:Inference; r:gives { - 2262 :kaprekar 6174 . + 2264 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2802 - skolem:lemma2803 - [ a r:Fact; r:gives {(2 2 2 6) list:reverse (6 2 2 2)}] - skolem:lemma2691 - skolem:lemma2692 - [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ a r:Fact; r:gives {2264 math:notEqualTo 0}] + skolem:lemma2514 + [ a r:Fact; r:gives {(2 2 6 4) list:quicksort (2 2 4 6)}] + [ a r:Fact; r:gives {(2 2 4 6) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2226]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1265 a r:Inference; r:gives { - 2263 :kaprekar 6174 . + 2265 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2265 math:notEqualTo 0}] + skolem:lemma2515 + [ a r:Fact; r:gives {(2 2 6 5) list:quicksort (2 2 5 6)}] + [ a r:Fact; r:gives {(2 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2804 - skolem:lemma2805 - [ a r:Fact; r:gives {(2 2 3 6) list:reverse (6 3 2 2)}] - skolem:lemma2725 - skolem:lemma2726 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2236]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1266 a r:Inference; r:gives { - 2264 :kaprekar 6174 . + 2266 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2266 math:notEqualTo 0}] + skolem:lemma2516 + [ a r:Fact; r:gives {(2 2 6 6) list:quicksort (2 2 6 6)}] + [ a r:Fact; r:gives {(2 2 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(2 2 4 6) list:reverse (6 4 2 2)}] - skolem:lemma2757 - skolem:lemma2758 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2246]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1267 a r:Inference; r:gives { - 2265 :kaprekar 6174 . + 2267 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2267 math:notEqualTo 0}] + skolem:lemma2519 + [ a r:Fact; r:gives {(2 2 6 7) list:quicksort (2 2 6 7)}] + [ a r:Fact; r:gives {(2 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2808 - skolem:lemma2809 - [ a r:Fact; r:gives {(2 2 5 6) list:reverse (6 5 2 2)}] - skolem:lemma2784 - skolem:lemma2785 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2256]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1268 a r:Inference; r:gives { - 2266 :kaprekar 6174 . + 2268 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2268 math:notEqualTo 0}] + skolem:lemma2522 + [ a r:Fact; r:gives {(2 2 6 8) list:quicksort (2 2 6 8)}] + [ a r:Fact; r:gives {(2 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2810 - skolem:lemma2811 - [ a r:Fact; r:gives {(2 2 6 6) list:reverse (6 6 2 2)}] - skolem:lemma2812 - skolem:lemma2813 - [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] - [ a r:Fact; r:gives {4356 math:notEqualTo 6174}] - skolem:lemma2814 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2266]; - 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_8"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1269 a r:Inference; r:gives { - 2267 :kaprekar 6174 . + 2269 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2269 math:notEqualTo 0}] + skolem:lemma2525 + [ a r:Fact; r:gives {(2 2 6 9) list:quicksort (2 2 6 9)}] + [ a r:Fact; r:gives {(2 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2815 - skolem:lemma2816 - [ a r:Fact; r:gives {(2 2 6 7) list:reverse (7 6 2 2)}] - skolem:lemma2817 - skolem:lemma2818 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2267]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1270 a r:Inference; r:gives { - 2268 :kaprekar 6174 . + 2270 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2270 math:notEqualTo 0}] + skolem:lemma2528 + [ a r:Fact; r:gives {(2 2 7 0) list:quicksort (0 2 2 7)}] + [ a r:Fact; r:gives {(0 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2819 - skolem:lemma2820 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1271 a r:Inference; r:gives { - 2269 :kaprekar 6174 . + 2271 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2271 math:notEqualTo 0}] + skolem:lemma2529 + [ a r:Fact; r:gives {(2 2 7 1) list:quicksort (1 2 2 7)}] + [ a r:Fact; r:gives {(1 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2823 - skolem:lemma2824 - [ a r:Fact; r:gives {(2 2 6 9) list:reverse (9 6 2 2)}] - skolem:lemma2825 - skolem:lemma2826 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2269]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1272 a r:Inference; r:gives { - 2270 :kaprekar 6174 . + 2272 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2272 math:notEqualTo 0}] + skolem:lemma2530 + [ a r:Fact; r:gives {(2 2 7 2) list:quicksort (2 2 2 7)}] + [ a r:Fact; r:gives {(2 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2827 - skolem:lemma2828 - [ a r:Fact; r:gives {(0 2 2 7) list:reverse (7 2 2 0)}] - skolem:lemma2122 - skolem:lemma2123 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2270]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 227]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1273 a r:Inference; r:gives { - 2271 :kaprekar 6174 . + 2273 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2273 math:notEqualTo 0}] + skolem:lemma2531 + [ a r:Fact; r:gives {(2 2 7 3) list:quicksort (2 2 3 7)}] + [ a r:Fact; r:gives {(2 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2829 - skolem:lemma2830 - [ a r:Fact; r:gives {(1 2 2 7) list:reverse (7 2 2 1)}] - skolem:lemma2424 - skolem:lemma2425 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2271]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1227]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1274 a r:Inference; r:gives { - 2272 :kaprekar 6174 . + 2274 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2274 math:notEqualTo 0}] + skolem:lemma2532 + [ a r:Fact; r:gives {(2 2 7 4) list:quicksort (2 2 4 7)}] + [ a r:Fact; r:gives {(2 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2831 - skolem:lemma2832 - [ a r:Fact; r:gives {(2 2 2 7) list:reverse (7 2 2 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2272]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2227]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1275 a r:Inference; r:gives { - 2273 :kaprekar 6174 . + 2275 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2275 math:notEqualTo 0}] + skolem:lemma2533 + [ a r:Fact; r:gives {(2 2 7 5) list:quicksort (2 2 5 7)}] + [ a r:Fact; r:gives {(2 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2833 - skolem:lemma2834 - [ a r:Fact; r:gives {(2 2 3 7) list:reverse (7 3 2 2)}] - skolem:lemma2729 - skolem:lemma2730 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2273]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2237]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1276 a r:Inference; r:gives { - 2274 :kaprekar 6174 . + 2276 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2276 math:notEqualTo 0}] + skolem:lemma2534 + [ a r:Fact; r:gives {(2 2 7 6) list:quicksort (2 2 6 7)}] + [ a r:Fact; r:gives {(2 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2835 - skolem:lemma2836 - [ a r:Fact; r:gives {(2 2 4 7) list:reverse (7 4 2 2)}] - skolem:lemma2761 - skolem:lemma2762 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2274]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2247]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1277 a r:Inference; r:gives { - 2275 :kaprekar 6174 . + 2277 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2277 math:notEqualTo 0}] + skolem:lemma2535 + [ a r:Fact; r:gives {(2 2 7 7) list:quicksort (2 2 7 7)}] + [ a r:Fact; r:gives {(2 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(2 2 5 7) list:reverse (7 5 2 2)}] - skolem:lemma2788 - skolem:lemma2789 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2275]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2257]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1278 a r:Inference; r:gives { - 2276 :kaprekar 6174 . + 2278 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2278 math:notEqualTo 0}] + skolem:lemma2538 + [ a r:Fact; r:gives {(2 2 7 8) list:quicksort (2 2 7 8)}] + [ a r:Fact; r:gives {(2 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2839 - skolem:lemma2840 - [ a r:Fact; r:gives {(2 2 6 7) list:reverse (7 6 2 2)}] - skolem:lemma2817 - skolem:lemma2818 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2276]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2267]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1279 a r:Inference; r:gives { - 2277 :kaprekar 6174 . + 2279 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2279 math:notEqualTo 0}] + skolem:lemma2541 + [ a r:Fact; r:gives {(2 2 7 9) list:quicksort (2 2 7 9)}] + [ a r:Fact; r:gives {(2 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2841 - skolem:lemma2842 - [ a r:Fact; r:gives {(2 2 7 7) list:reverse (7 7 2 2)}] - skolem:lemma2843 - skolem:lemma2844 - [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] - [ a r:Fact; r:gives {5445 math:notEqualTo 6174}] - skolem:lemma2845 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2277]; - 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_8"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1280 a r:Inference; r:gives { - 2278 :kaprekar 6174 . + 2280 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2280 math:notEqualTo 0}] + skolem:lemma2544 + [ a r:Fact; r:gives {(2 2 8 0) list:quicksort (0 2 2 8)}] + [ a r:Fact; r:gives {(0 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2846 - skolem:lemma2847 - [ a r:Fact; r:gives {(2 2 7 8) list:reverse (8 7 2 2)}] - skolem:lemma2848 - skolem:lemma2849 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2278]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1281 a r:Inference; r:gives { - 2279 :kaprekar 6174 . + 2281 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2281 math:notEqualTo 0}] + skolem:lemma2545 + [ a r:Fact; r:gives {(2 2 8 1) list:quicksort (1 2 2 8)}] + [ a r:Fact; r:gives {(1 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2850 - skolem:lemma2851 - [ a r:Fact; r:gives {(2 2 7 9) list:reverse (9 7 2 2)}] - skolem:lemma2852 - skolem:lemma2853 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2279]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1282 a r:Inference; r:gives { - 2280 :kaprekar 6174 . + 2282 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2282 math:notEqualTo 0}] + skolem:lemma2546 + [ a r:Fact; r:gives {(2 2 8 2) list:quicksort (2 2 2 8)}] + [ a r:Fact; r:gives {(2 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(0 2 2 8) list:reverse (8 2 2 0)}] - skolem:lemma2127 - skolem:lemma2128 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2280]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 228]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1283 a r:Inference; r:gives { - 2281 :kaprekar 6174 . + 2283 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2283 math:notEqualTo 0}] + skolem:lemma2547 + [ a r:Fact; r:gives {(2 2 8 3) list:quicksort (2 2 3 8)}] + [ a r:Fact; r:gives {(2 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2856 - skolem:lemma2857 - [ a r:Fact; r:gives {(1 2 2 8) list:reverse (8 2 2 1)}] - skolem:lemma2428 - skolem:lemma2429 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2281]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1228]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1284 a r:Inference; r:gives { - 2282 :kaprekar 6174 . + 2284 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2284 math:notEqualTo 0}] + skolem:lemma2548 + [ a r:Fact; r:gives {(2 2 8 4) list:quicksort (2 2 4 8)}] + [ a r:Fact; r:gives {(2 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2858 - skolem:lemma2859 - [ a r:Fact; r:gives {(2 2 2 8) list:reverse (8 2 2 2)}] - skolem:lemma2699 - skolem:lemma2700 - [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2282]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2228]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1285 a r:Inference; r:gives { - 2283 :kaprekar 6174 . + 2285 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2285 math:notEqualTo 0}] + skolem:lemma2549 + [ a r:Fact; r:gives {(2 2 8 5) list:quicksort (2 2 5 8)}] + [ a r:Fact; r:gives {(2 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2860 - skolem:lemma2861 - [ a r:Fact; r:gives {(2 2 3 8) list:reverse (8 3 2 2)}] - skolem:lemma2733 - skolem:lemma2734 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2283]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2238]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1286 a r:Inference; r:gives { - 2284 :kaprekar 6174 . + 2286 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2286 math:notEqualTo 0}] + skolem:lemma2550 + [ a r:Fact; r:gives {(2 2 8 6) list:quicksort (2 2 6 8)}] + [ a r:Fact; r:gives {(2 2 6 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2284]; - r:rule skolem:lemma2032. + 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. skolem:lemma1287 a r:Inference; r:gives { - 2285 :kaprekar 6174 . + 2287 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2287 math:notEqualTo 0}] + skolem:lemma2551 + [ a r:Fact; r:gives {(2 2 8 7) list:quicksort (2 2 7 8)}] + [ a r:Fact; r:gives {(2 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2862 - skolem:lemma2863 - [ a r:Fact; r:gives {(2 2 5 8) list:reverse (8 5 2 2)}] - skolem:lemma2792 - skolem:lemma2793 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2285]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2258]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1288 a r:Inference; r:gives { - 2286 :kaprekar 6174 . + 2288 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2288 math:notEqualTo 0}] + skolem:lemma2552 + [ a r:Fact; r:gives {(2 2 8 8) list:quicksort (2 2 8 8)}] + [ a r:Fact; r:gives {(2 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2864 - skolem:lemma2865 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2286]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1289 a r:Inference; r:gives { - 2287 :kaprekar 6174 . + 2289 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2289 math:notEqualTo 0}] + skolem:lemma2555 + [ a r:Fact; r:gives {(2 2 8 9) list:quicksort (2 2 8 9)}] + [ a r:Fact; r:gives {(2 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2866 - skolem:lemma2867 - [ a r:Fact; r:gives {(2 2 7 8) list:reverse (8 7 2 2)}] - skolem:lemma2848 - skolem:lemma2849 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2287]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2278]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1290 a r:Inference; r:gives { - 2288 :kaprekar 6174 . + 2290 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2290 math:notEqualTo 0}] + skolem:lemma2558 + [ a r:Fact; r:gives {(2 2 9 0) list:quicksort (0 2 2 9)}] + [ a r:Fact; r:gives {(0 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2868 - skolem:lemma2869 - [ a r:Fact; r:gives {(2 2 8 8) list:reverse (8 8 2 2)}] - skolem:lemma2870 - skolem:lemma2871 - [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] - [ a r:Fact; r:gives {6534 math:notEqualTo 6174}] - skolem:lemma2872 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2288]; - 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_8"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1291 a r:Inference; r:gives { - 2289 :kaprekar 6174 . + 2291 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2291 math:notEqualTo 0}] + skolem:lemma2559 + [ a r:Fact; r:gives {(2 2 9 1) list:quicksort (1 2 2 9)}] + [ a r:Fact; r:gives {(1 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2873 - skolem:lemma2874 - [ a r:Fact; r:gives {(2 2 8 9) list:reverse (9 8 2 2)}] - skolem:lemma2875 - skolem:lemma2876 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2289]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1292 a r:Inference; r:gives { - 2290 :kaprekar 6174 . + 2292 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2292 math:notEqualTo 0}] + skolem:lemma2560 + [ a r:Fact; r:gives {(2 2 9 2) list:quicksort (2 2 2 9)}] + [ a r:Fact; r:gives {(2 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2877 - skolem:lemma2878 - [ a r:Fact; r:gives {(0 2 2 9) list:reverse (9 2 2 0)}] - skolem:lemma2132 - skolem:lemma2133 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2290]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 229]; - 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_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1293 a r:Inference; r:gives { - 2291 :kaprekar 6174 . + 2293 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2293 math:notEqualTo 0}] + skolem:lemma2561 + [ a r:Fact; r:gives {(2 2 9 3) list:quicksort (2 2 3 9)}] + [ a r:Fact; r:gives {(2 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2879 - skolem:lemma2880 - [ a r:Fact; r:gives {(1 2 2 9) list:reverse (9 2 2 1)}] - skolem:lemma2432 - skolem:lemma2433 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2291]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1229]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1294 a r:Inference; r:gives { - 2292 :kaprekar 6174 . + 2294 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2294 math:notEqualTo 0}] + skolem:lemma2562 + [ a r:Fact; r:gives {(2 2 9 4) list:quicksort (2 2 4 9)}] + [ a r:Fact; r:gives {(2 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2881 - skolem:lemma2882 - [ a r:Fact; r:gives {(2 2 2 9) list:reverse (9 2 2 2)}] - skolem:lemma2703 - skolem:lemma2704 - [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2292]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2229]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1295 a r:Inference; r:gives { - 2293 :kaprekar 6174 . + 2295 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2295 math:notEqualTo 0}] + skolem:lemma2563 + [ a r:Fact; r:gives {(2 2 9 5) list:quicksort (2 2 5 9)}] + [ a r:Fact; r:gives {(2 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2883 - skolem:lemma2884 - [ a r:Fact; r:gives {(2 2 3 9) list:reverse (9 3 2 2)}] - skolem:lemma2737 - skolem:lemma2738 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2293]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2239]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1296 a r:Inference; r:gives { - 2294 :kaprekar 6174 . + 2296 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2296 math:notEqualTo 0}] + skolem:lemma2564 + [ a r:Fact; r:gives {(2 2 9 6) list:quicksort (2 2 6 9)}] + [ a r:Fact; r:gives {(2 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2885 - skolem:lemma2886 - [ a r:Fact; r:gives {(2 2 4 9) list:reverse (9 4 2 2)}] - skolem:lemma2765 - skolem:lemma2766 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2294]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2249]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1297 a r:Inference; r:gives { - 2295 :kaprekar 6174 . + 2297 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2297 math:notEqualTo 0}] + skolem:lemma2565 + [ a r:Fact; r:gives {(2 2 9 7) list:quicksort (2 2 7 9)}] + [ a r:Fact; r:gives {(2 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2887 - skolem:lemma2888 - [ a r:Fact; r:gives {(2 2 5 9) list:reverse (9 5 2 2)}] - skolem:lemma2796 - skolem:lemma2797 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2295]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2259]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1298 a r:Inference; r:gives { - 2296 :kaprekar 6174 . + 2298 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2298 math:notEqualTo 0}] + skolem:lemma2566 + [ a r:Fact; r:gives {(2 2 9 8) list:quicksort (2 2 8 9)}] + [ a r:Fact; r:gives {(2 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2889 - skolem:lemma2890 - [ a r:Fact; r:gives {(2 2 6 9) list:reverse (9 6 2 2)}] - skolem:lemma2825 - skolem:lemma2826 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2296]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2269]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1299 a r:Inference; r:gives { - 2297 :kaprekar 6174 . + 2299 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2299 math:notEqualTo 0}] + skolem:lemma2567 + [ a r:Fact; r:gives {(2 2 9 9) list:quicksort (2 2 9 9)}] + [ a r:Fact; r:gives {(2 2 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2891 - skolem:lemma2892 - [ a r:Fact; r:gives {(2 2 7 9) list:reverse (9 7 2 2)}] - skolem:lemma2852 - skolem:lemma2853 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2297]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2279]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1300 a r:Inference; r:gives { - 2298 :kaprekar 6174 . + 2300 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2300 math:notEqualTo 0}] + skolem:lemma2570 + [ a r:Fact; r:gives {(2 3 0 0) list:quicksort (0 0 2 3)}] + [ a r:Fact; r:gives {(0 0 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2893 - skolem:lemma2894 - [ a r:Fact; r:gives {(2 2 8 9) list:reverse (9 8 2 2)}] - skolem:lemma2875 - skolem:lemma2876 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2298]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2289]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1301 a r:Inference; r:gives { - 2299 :kaprekar 6174 . + 2301 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2301 math:notEqualTo 0}] + skolem:lemma2571 + [ a r:Fact; r:gives {(2 3 0 1) list:quicksort (0 1 2 3)}] + [ a r:Fact; r:gives {(0 1 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2895 - skolem:lemma2896 - [ a r:Fact; r:gives {(2 2 9 9) list:reverse (9 9 2 2)}] - skolem:lemma2897 - skolem:lemma2898 - [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] - [ a r:Fact; r:gives {7623 math:notEqualTo 6174}] - skolem:lemma2899 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2299]; - 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_8"]; r:boundTo 7623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1302 a r:Inference; r:gives { - 2300 :kaprekar 6174 . + 2302 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2302 math:notEqualTo 0}] + skolem:lemma2572 + [ a r:Fact; r:gives {(2 3 0 2) list:quicksort (0 2 2 3)}] + [ a r:Fact; r:gives {(0 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2900 - skolem:lemma2901 - [ a r:Fact; r:gives {(0 0 2 3) list:reverse (3 2 0 0)}] - skolem:lemma2019 - skolem:lemma2020 - [ a r:Fact; r:gives {(3200 23) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 23]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1303 a r:Inference; r:gives { - 2301 :kaprekar 6174 . + 2303 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2303 math:notEqualTo 0}] + skolem:lemma2573 + [ a r:Fact; r:gives {(2 3 0 3) list:quicksort (0 2 3 3)}] + [ a r:Fact; r:gives {(0 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2902 - skolem:lemma2903 - [ a r:Fact; r:gives {(0 1 2 3) list:reverse (3 2 1 0)}] - skolem:lemma2060 - skolem:lemma2061 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2301]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 123]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1304 a r:Inference; r:gives { - 2302 :kaprekar 6174 . + 2304 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2304 math:notEqualTo 0}] + skolem:lemma2574 + [ a r:Fact; r:gives {(2 3 0 4) list:quicksort (0 2 3 4)}] + [ a r:Fact; r:gives {(0 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2904 - skolem:lemma2905 - [ a r:Fact; r:gives {(0 2 2 3) list:reverse (3 2 2 0)}] - skolem:lemma2103 - skolem:lemma2104 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2302]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 223]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1305 a r:Inference; r:gives { - 2303 :kaprekar 6174 . + 2305 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2305 math:notEqualTo 0}] + skolem:lemma2575 + [ a r:Fact; r:gives {(2 3 0 5) list:quicksort (0 2 3 5)}] + [ a r:Fact; r:gives {(0 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2906 - skolem:lemma2907 - [ a r:Fact; r:gives {(0 2 3 3) list:reverse (3 3 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(3320 233) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2303]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 233]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1306 a r:Inference; r:gives { - 2304 :kaprekar 6174 . + 2306 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2306 math:notEqualTo 0}] + skolem:lemma2576 + [ a r:Fact; r:gives {(2 3 0 6) list:quicksort (0 2 3 6)}] + [ a r:Fact; r:gives {(0 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2908 - skolem:lemma2909 - [ a r:Fact; r:gives {(0 2 3 4) list:reverse (4 3 2 0)}] - skolem:lemma2147 - skolem:lemma2148 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2304]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 234]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1307 a r:Inference; r:gives { - 2305 :kaprekar 6174 . + 2307 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2307 math:notEqualTo 0}] + skolem:lemma2577 + [ a r:Fact; r:gives {(2 3 0 7) list:quicksort (0 2 3 7)}] + [ a r:Fact; r:gives {(0 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2910 - skolem:lemma2911 - [ a r:Fact; r:gives {(0 2 3 5) list:reverse (5 3 2 0)}] - skolem:lemma2151 - skolem:lemma2152 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2305]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 235]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1308 a r:Inference; r:gives { - 2306 :kaprekar 6174 . + 2308 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2308 math:notEqualTo 0}] + skolem:lemma2578 + [ a r:Fact; r:gives {(2 3 0 8) list:quicksort (0 2 3 8)}] + [ a r:Fact; r:gives {(0 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2912 - skolem:lemma2913 - [ a r:Fact; r:gives {(0 2 3 6) list:reverse (6 3 2 0)}] - skolem:lemma2155 - skolem:lemma2156 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2306]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 236]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1309 a r:Inference; r:gives { - 2307 :kaprekar 6174 . + 2309 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2309 math:notEqualTo 0}] + skolem:lemma2579 + [ a r:Fact; r:gives {(2 3 0 9) list:quicksort (0 2 3 9)}] + [ a r:Fact; r:gives {(0 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2914 - skolem:lemma2915 - [ a r:Fact; r:gives {(0 2 3 7) list:reverse (7 3 2 0)}] - skolem:lemma2159 - skolem:lemma2160 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2307]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 237]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1310 a r:Inference; r:gives { - 2308 :kaprekar 6174 . + 2310 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2310 math:notEqualTo 0}] + skolem:lemma2580 + [ a r:Fact; r:gives {(2 3 1 0) list:quicksort (0 1 2 3)}] + [ a r:Fact; r:gives {(0 1 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2916 - skolem:lemma2917 - [ a r:Fact; r:gives {(0 2 3 8) list:reverse (8 3 2 0)}] - skolem:lemma2163 - skolem:lemma2164 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2308]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 238]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1311 a r:Inference; r:gives { - 2309 :kaprekar 6174 . + 2311 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2311 math:notEqualTo 0}] + skolem:lemma2581 + [ a r:Fact; r:gives {(2 3 1 1) list:quicksort (1 1 2 3)}] + [ a r:Fact; r:gives {(1 1 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2918 - skolem:lemma2919 - [ a r:Fact; r:gives {(0 2 3 9) list:reverse (9 3 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2309]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 239]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1312 a r:Inference; r:gives { - 2310 :kaprekar 6174 . + 2312 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2312 math:notEqualTo 0}] + skolem:lemma2582 + [ a r:Fact; r:gives {(2 3 1 2) list:quicksort (1 2 2 3)}] + [ a r:Fact; r:gives {(1 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2920 - skolem:lemma2921 - [ a r:Fact; r:gives {(0 1 2 3) list:reverse (3 2 1 0)}] - skolem:lemma2060 - skolem:lemma2061 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2310]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 123]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1313 a r:Inference; r:gives { - 2311 :kaprekar 6174 . + 2313 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2313 math:notEqualTo 0}] + skolem:lemma2583 + [ a r:Fact; r:gives {(2 3 1 3) list:quicksort (1 2 3 3)}] + [ a r:Fact; r:gives {(1 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2922 - skolem:lemma2923 - [ a r:Fact; r:gives {(1 1 2 3) list:reverse (3 2 1 1)}] - skolem:lemma2372 - skolem:lemma2373 - [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2311]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1123]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1314 a r:Inference; r:gives { - 2312 :kaprekar 6174 . + 2314 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2314 math:notEqualTo 0}] + skolem:lemma2584 + [ a r:Fact; r:gives {(2 3 1 4) list:quicksort (1 2 3 4)}] + [ a r:Fact; r:gives {(1 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2924 - skolem:lemma2925 - [ a r:Fact; r:gives {(1 2 2 3) list:reverse (3 2 2 1)}] - skolem:lemma2408 - skolem:lemma2409 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2312]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1223]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1315 a r:Inference; r:gives { - 2313 :kaprekar 6174 . + 2315 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2315 math:notEqualTo 0}] + skolem:lemma2585 + [ a r:Fact; r:gives {(2 3 1 5) list:quicksort (1 2 3 5)}] + [ a r:Fact; r:gives {(1 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2926 - skolem:lemma2927 - [ a r:Fact; r:gives {(1 2 3 3) list:reverse (3 3 2 1)}] - skolem:lemma2442 - skolem:lemma2443 - [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2313]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1233]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1316 a r:Inference; r:gives { - 2314 :kaprekar 6174 . + 2316 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2316 math:notEqualTo 0}] + skolem:lemma2586 + [ a r:Fact; r:gives {(2 3 1 6) list:quicksort (1 2 3 6)}] + [ a r:Fact; r:gives {(1 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2928 - skolem:lemma2929 - [ a r:Fact; r:gives {(1 2 3 4) list:reverse (4 3 2 1)}] - skolem:lemma2446 - skolem:lemma2447 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2314]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1234]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1317 a r:Inference; r:gives { - 2315 :kaprekar 6174 . + 2317 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2317 math:notEqualTo 0}] + skolem:lemma2587 + [ a r:Fact; r:gives {(2 3 1 7) list:quicksort (1 2 3 7)}] + [ a r:Fact; r:gives {(1 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2930 - skolem:lemma2931 - [ a r:Fact; r:gives {(1 2 3 5) list:reverse (5 3 2 1)}] - skolem:lemma2450 - skolem:lemma2451 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2315]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1235]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1318 a r:Inference; r:gives { - 2316 :kaprekar 6174 . + 2318 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2318 math:notEqualTo 0}] + skolem:lemma2588 + [ a r:Fact; r:gives {(2 3 1 8) list:quicksort (1 2 3 8)}] + [ a r:Fact; r:gives {(1 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2932 - skolem:lemma2933 - [ a r:Fact; r:gives {(1 2 3 6) list:reverse (6 3 2 1)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2316]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1236]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1319 a r:Inference; r:gives { - 2317 :kaprekar 6174 . + 2319 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2319 math:notEqualTo 0}] + skolem:lemma2589 + [ a r:Fact; r:gives {(2 3 1 9) list:quicksort (1 2 3 9)}] + [ a r:Fact; r:gives {(1 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2934 - skolem:lemma2935 - [ a r:Fact; r:gives {(1 2 3 7) list:reverse (7 3 2 1)}] - skolem:lemma2458 - skolem:lemma2459 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2317]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1237]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1320 a r:Inference; r:gives { - 2318 :kaprekar 6174 . + 2320 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2320 math:notEqualTo 0}] + skolem:lemma2590 + [ a r:Fact; r:gives {(2 3 2 0) list:quicksort (0 2 2 3)}] + [ a r:Fact; r:gives {(0 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2936 - skolem:lemma2937 - [ a r:Fact; r:gives {(1 2 3 8) list:reverse (8 3 2 1)}] - skolem:lemma2462 - skolem:lemma2463 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2318]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1238]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1321 a r:Inference; r:gives { - 2319 :kaprekar 6174 . + 2321 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2321 math:notEqualTo 0}] + skolem:lemma2591 + [ a r:Fact; r:gives {(2 3 2 1) list:quicksort (1 2 2 3)}] + [ a r:Fact; r:gives {(1 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2938 - skolem:lemma2939 - [ a r:Fact; r:gives {(1 2 3 9) list:reverse (9 3 2 1)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2319]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1239]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1322 a r:Inference; r:gives { - 2320 :kaprekar 6174 . + 2322 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2322 math:notEqualTo 0}] + skolem:lemma2592 + [ a r:Fact; r:gives {(2 3 2 2) list:quicksort (2 2 2 3)}] + [ a r:Fact; r:gives {(2 2 2 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2940 - skolem:lemma2941 - [ a r:Fact; r:gives {(0 2 2 3) list:reverse (3 2 2 0)}] - skolem:lemma2103 - skolem:lemma2104 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 223]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1323 a r:Inference; r:gives { - 2321 :kaprekar 6174 . + 2323 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2323 math:notEqualTo 0}] + skolem:lemma2593 + [ a r:Fact; r:gives {(2 3 2 3) list:quicksort (2 2 3 3)}] + [ a r:Fact; r:gives {(2 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2942 - skolem:lemma2943 - [ a r:Fact; r:gives {(1 2 2 3) list:reverse (3 2 2 1)}] - skolem:lemma2408 - skolem:lemma2409 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1223]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1324 a r:Inference; r:gives { - 2322 :kaprekar 6174 . + 2324 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2324 math:notEqualTo 0}] + skolem:lemma2594 + [ a r:Fact; r:gives {(2 3 2 4) list:quicksort (2 2 3 4)}] + [ a r:Fact; r:gives {(2 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2944 - skolem:lemma2945 - [ a r:Fact; r:gives {(2 2 2 3) list:reverse (3 2 2 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(3222 2223) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2223]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1325 a r:Inference; r:gives { - 2323 :kaprekar 6174 . + 2325 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2325 math:notEqualTo 0}] + skolem:lemma2595 + [ a r:Fact; r:gives {(2 3 2 5) list:quicksort (2 2 3 5)}] + [ a r:Fact; r:gives {(2 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2946 - skolem:lemma2947 - [ a r:Fact; r:gives {(2 2 3 3) list:reverse (3 3 2 2)}] - skolem:lemma2713 - skolem:lemma2714 - [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2323]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2233]; - 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_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1326 a r:Inference; r:gives { - 2324 :kaprekar 6174 . + 2326 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2326 math:notEqualTo 0}] + skolem:lemma2596 + [ a r:Fact; r:gives {(2 3 2 6) list:quicksort (2 2 3 6)}] + [ a r:Fact; r:gives {(2 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(2 2 3 4) list:reverse (4 3 2 2)}] - skolem:lemma2717 - skolem:lemma2718 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2324]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2234]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1327 a r:Inference; r:gives { - 2325 :kaprekar 6174 . + 2327 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2327 math:notEqualTo 0}] + skolem:lemma2597 + [ a r:Fact; r:gives {(2 3 2 7) list:quicksort (2 2 3 7)}] + [ a r:Fact; r:gives {(2 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2950 - skolem:lemma2951 - [ a r:Fact; r:gives {(2 2 3 5) list:reverse (5 3 2 2)}] - skolem:lemma2721 - skolem:lemma2722 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2325]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2235]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1328 a r:Inference; r:gives { - 2326 :kaprekar 6174 . + 2328 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2328 math:notEqualTo 0}] + skolem:lemma2598 + [ a r:Fact; r:gives {(2 3 2 8) list:quicksort (2 2 3 8)}] + [ a r:Fact; r:gives {(2 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2952 - skolem:lemma2953 - [ a r:Fact; r:gives {(2 2 3 6) list:reverse (6 3 2 2)}] - skolem:lemma2725 - skolem:lemma2726 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2326]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2236]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1329 a r:Inference; r:gives { - 2327 :kaprekar 6174 . + 2329 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2329 math:notEqualTo 0}] + skolem:lemma2599 + [ a r:Fact; r:gives {(2 3 2 9) list:quicksort (2 2 3 9)}] + [ a r:Fact; r:gives {(2 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(2 2 3 7) list:reverse (7 3 2 2)}] - skolem:lemma2729 - skolem:lemma2730 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2327]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2237]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1330 a r:Inference; r:gives { - 2328 :kaprekar 6174 . + 2330 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2330 math:notEqualTo 0}] + skolem:lemma2600 + [ a r:Fact; r:gives {(2 3 3 0) list:quicksort (0 2 3 3)}] + [ a r:Fact; r:gives {(0 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2956 - skolem:lemma2957 - [ a r:Fact; r:gives {(2 2 3 8) list:reverse (8 3 2 2)}] - skolem:lemma2733 - skolem:lemma2734 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2328]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2238]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1331 a r:Inference; r:gives { - 2329 :kaprekar 6174 . + 2331 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2331 math:notEqualTo 0}] + skolem:lemma2601 + [ a r:Fact; r:gives {(2 3 3 1) list:quicksort (1 2 3 3)}] + [ a r:Fact; r:gives {(1 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2958 - skolem:lemma2959 - [ a r:Fact; r:gives {(2 2 3 9) list:reverse (9 3 2 2)}] - skolem:lemma2737 - skolem:lemma2738 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2329]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2239]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1332 a r:Inference; r:gives { - 2330 :kaprekar 6174 . + 2332 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2332 math:notEqualTo 0}] + skolem:lemma2602 + [ a r:Fact; r:gives {(2 3 3 2) list:quicksort (2 2 3 3)}] + [ a r:Fact; r:gives {(2 2 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2960 - skolem:lemma2961 - [ a r:Fact; r:gives {(0 2 3 3) list:reverse (3 3 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(3320 233) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2330]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 233]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1333 a r:Inference; r:gives { - 2331 :kaprekar 6174 . + 2333 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2333 math:notEqualTo 0}] + skolem:lemma2603 + [ a r:Fact; r:gives {(2 3 3 3) list:quicksort (2 3 3 3)}] + [ a r:Fact; r:gives {(2 3 3 3) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2962 - skolem:lemma2963 - [ a r:Fact; r:gives {(1 2 3 3) list:reverse (3 3 2 1)}] - skolem:lemma2442 - skolem:lemma2443 - [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2331]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1233]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1334 a r:Inference; r:gives { - 2332 :kaprekar 6174 . + 2334 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2334 math:notEqualTo 0}] + skolem:lemma2606 + [ a r:Fact; r:gives {(2 3 3 4) list:quicksort (2 3 3 4)}] + [ a r:Fact; r:gives {(2 3 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2964 - skolem:lemma2965 - [ a r:Fact; r:gives {(2 2 3 3) list:reverse (3 3 2 2)}] - skolem:lemma2713 - skolem:lemma2714 - [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2233]; - 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_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1335 a r:Inference; r:gives { - 2333 :kaprekar 6174 . + 2335 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2335 math:notEqualTo 0}] + skolem:lemma2609 + [ a r:Fact; r:gives {(2 3 3 5) list:quicksort (2 3 3 5)}] + [ a r:Fact; r:gives {(2 3 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2966 - skolem:lemma2967 - [ a r:Fact; r:gives {(2 3 3 3) list:reverse (3 3 3 2)}] - skolem:lemma2968 - skolem:lemma2969 - [ a r:Fact; r:gives {(3332 2333) math:difference 999}] - [ a r:Fact; r:gives {999 math:notEqualTo 6174}] - skolem:lemma2364 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2333]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2333]; - 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_8"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1336 a r:Inference; r:gives { - 2334 :kaprekar 6174 . + 2336 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2336 math:notEqualTo 0}] + skolem:lemma2612 + [ a r:Fact; r:gives {(2 3 3 6) list:quicksort (2 3 3 6)}] + [ a r:Fact; r:gives {(2 3 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(2 3 3 4) list:reverse (4 3 3 2)}] - skolem:lemma2972 - skolem:lemma2973 - [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2334]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2334]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1337 a r:Inference; r:gives { - 2335 :kaprekar 6174 . + 2337 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2337 math:notEqualTo 0}] + skolem:lemma2615 + [ a r:Fact; r:gives {(2 3 3 7) list:quicksort (2 3 3 7)}] + [ a r:Fact; r:gives {(2 3 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2974 - skolem:lemma2975 - [ a r:Fact; r:gives {(2 3 3 5) list:reverse (5 3 3 2)}] - skolem:lemma2976 - skolem:lemma2977 - [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2335]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2335]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1338 a r:Inference; r:gives { - 2336 :kaprekar 6174 . + 2338 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2338 math:notEqualTo 0}] + skolem:lemma2618 + [ a r:Fact; r:gives {(2 3 3 8) list:quicksort (2 3 3 8)}] + [ a r:Fact; r:gives {(2 3 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2978 - skolem:lemma2979 - [ a r:Fact; r:gives {(2 3 3 6) list:reverse (6 3 3 2)}] - skolem:lemma2980 - skolem:lemma2981 - [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2336]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2336]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1339 a r:Inference; r:gives { - 2337 :kaprekar 6174 . + 2339 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2339 math:notEqualTo 0}] + skolem:lemma2621 + [ a r:Fact; r:gives {(2 3 3 9) list:quicksort (2 3 3 9)}] + [ a r:Fact; r:gives {(2 3 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2982 - skolem:lemma2983 - [ a r:Fact; r:gives {(2 3 3 7) list:reverse (7 3 3 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2337]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2337]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1340 a r:Inference; r:gives { - 2338 :kaprekar 6174 . + 2340 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2340 math:notEqualTo 0}] + skolem:lemma2624 + [ a r:Fact; r:gives {(2 3 4 0) list:quicksort (0 2 3 4)}] + [ a r:Fact; r:gives {(0 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2986 - skolem:lemma2987 - [ a r:Fact; r:gives {(2 3 3 8) list:reverse (8 3 3 2)}] - skolem:lemma2988 - skolem:lemma2989 - [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2338]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2338]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1341 a r:Inference; r:gives { - 2339 :kaprekar 6174 . + 2341 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2341 math:notEqualTo 0}] + skolem:lemma2625 + [ a r:Fact; r:gives {(2 3 4 1) list:quicksort (1 2 3 4)}] + [ a r:Fact; r:gives {(1 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2990 - skolem:lemma2991 - [ a r:Fact; r:gives {(2 3 3 9) list:reverse (9 3 3 2)}] - skolem:lemma2992 - skolem:lemma2993 - [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2339]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2339]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1342 a r:Inference; r:gives { - 2340 :kaprekar 6174 . + 2342 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2342 math:notEqualTo 0}] + skolem:lemma2626 + [ a r:Fact; r:gives {(2 3 4 2) list:quicksort (2 2 3 4)}] + [ a r:Fact; r:gives {(2 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2994 - skolem:lemma2995 - [ a r:Fact; r:gives {(0 2 3 4) list:reverse (4 3 2 0)}] - skolem:lemma2147 - skolem:lemma2148 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2340]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 234]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1343 a r:Inference; r:gives { - 2341 :kaprekar 6174 . + 2343 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2343 math:notEqualTo 0}] + skolem:lemma2627 + [ a r:Fact; r:gives {(2 3 4 3) list:quicksort (2 3 3 4)}] + [ a r:Fact; r:gives {(2 3 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2996 - skolem:lemma2997 - [ a r:Fact; r:gives {(1 2 3 4) list:reverse (4 3 2 1)}] - skolem:lemma2446 - skolem:lemma2447 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2341]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1234]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1344 a r:Inference; r:gives { - 2342 :kaprekar 6174 . + 2344 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2344 math:notEqualTo 0}] + skolem:lemma2628 + [ a r:Fact; r:gives {(2 3 4 4) list:quicksort (2 3 4 4)}] + [ a r:Fact; r:gives {(2 3 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma2998 - skolem:lemma2999 - [ a r:Fact; r:gives {(2 2 3 4) list:reverse (4 3 2 2)}] - skolem:lemma2717 - skolem:lemma2718 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2342]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2234]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1345 a r:Inference; r:gives { - 2343 :kaprekar 6174 . + 2345 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2345 math:notEqualTo 0}] + skolem:lemma2631 + [ a r:Fact; r:gives {(2 3 4 5) list:quicksort (2 3 4 5)}] + [ a r:Fact; r:gives {(2 3 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3000 - skolem:lemma3001 - [ a r:Fact; r:gives {(2 3 3 4) list:reverse (4 3 3 2)}] - skolem:lemma2972 - skolem:lemma2973 - [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2343]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2334]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1346 a r:Inference; r:gives { - 2344 :kaprekar 6174 . + 2346 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2346 math:notEqualTo 0}] + skolem:lemma2634 + [ a r:Fact; r:gives {(2 3 4 6) list:quicksort (2 3 4 6)}] + [ a r:Fact; r:gives {(2 3 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3002 - skolem:lemma3003 - [ a r:Fact; r:gives {(2 3 4 4) list:reverse (4 4 3 2)}] - skolem:lemma3004 - skolem:lemma3005 - [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2344]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2344]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1347 a r:Inference; r:gives { - 2345 :kaprekar 6174 . + 2347 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2347 math:notEqualTo 0}] + skolem:lemma2637 + [ a r:Fact; r:gives {(2 3 4 7) list:quicksort (2 3 4 7)}] + [ a r:Fact; r:gives {(2 3 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3006 - skolem:lemma3007 - [ a r:Fact; r:gives {(2 3 4 5) list:reverse (5 4 3 2)}] - skolem:lemma3008 - skolem:lemma3009 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2345]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1348 a r:Inference; r:gives { - 2346 :kaprekar 6174 . + 2348 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2348 math:notEqualTo 0}] + skolem:lemma2640 + [ a r:Fact; r:gives {(2 3 4 8) list:quicksort (2 3 4 8)}] + [ a r:Fact; r:gives {(2 3 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3010 - skolem:lemma3011 - [ a r:Fact; r:gives {(2 3 4 6) list:reverse (6 4 3 2)}] - skolem:lemma3012 - skolem:lemma3013 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2346]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1349 a r:Inference; r:gives { - 2347 :kaprekar 6174 . + 2349 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2349 math:notEqualTo 0}] + skolem:lemma2643 + [ a r:Fact; r:gives {(2 3 4 9) list:quicksort (2 3 4 9)}] + [ a r:Fact; r:gives {(2 3 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3014 - skolem:lemma3015 - [ a r:Fact; r:gives {(2 3 4 7) list:reverse (7 4 3 2)}] - skolem:lemma3016 - skolem:lemma3017 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2347]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1350 a r:Inference; r:gives { - 2348 :kaprekar 6174 . + 2350 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2350 math:notEqualTo 0}] + skolem:lemma2646 + [ a r:Fact; r:gives {(2 3 5 0) list:quicksort (0 2 3 5)}] + [ a r:Fact; r:gives {(0 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3018 - skolem:lemma3019 - [ a r:Fact; r:gives {(2 3 4 8) list:reverse (8 4 3 2)}] - skolem:lemma3020 - skolem:lemma3021 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2348]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1351 a r:Inference; r:gives { - 2349 :kaprekar 6174 . + 2351 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2351 math:notEqualTo 0}] + skolem:lemma2647 + [ a r:Fact; r:gives {(2 3 5 1) list:quicksort (1 2 3 5)}] + [ a r:Fact; r:gives {(1 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3022 - skolem:lemma3023 - [ a r:Fact; r:gives {(2 3 4 9) list:reverse (9 4 3 2)}] - skolem:lemma3024 - skolem:lemma3025 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2349]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1352 a r:Inference; r:gives { - 2350 :kaprekar 6174 . + 2352 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2352 math:notEqualTo 0}] + skolem:lemma2648 + [ a r:Fact; r:gives {(2 3 5 2) list:quicksort (2 2 3 5)}] + [ a r:Fact; r:gives {(2 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3026 - skolem:lemma3027 - [ a r:Fact; r:gives {(0 2 3 5) list:reverse (5 3 2 0)}] - skolem:lemma2151 - skolem:lemma2152 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2350]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 235]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1353 a r:Inference; r:gives { - 2351 :kaprekar 6174 . + 2353 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2353 math:notEqualTo 0}] + skolem:lemma2649 + [ a r:Fact; r:gives {(2 3 5 3) list:quicksort (2 3 3 5)}] + [ a r:Fact; r:gives {(2 3 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3028 - skolem:lemma3029 - [ a r:Fact; r:gives {(1 2 3 5) list:reverse (5 3 2 1)}] - skolem:lemma2450 - skolem:lemma2451 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1235]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1354 a r:Inference; r:gives { - 2352 :kaprekar 6174 . + 2354 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2354 math:notEqualTo 0}] + skolem:lemma2650 + [ a r:Fact; r:gives {(2 3 5 4) list:quicksort (2 3 4 5)}] + [ a r:Fact; r:gives {(2 3 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3030 - skolem:lemma3031 - [ a r:Fact; r:gives {(2 2 3 5) list:reverse (5 3 2 2)}] - skolem:lemma2721 - skolem:lemma2722 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2235]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1355 a r:Inference; r:gives { - 2353 :kaprekar 6174 . + 2355 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2355 math:notEqualTo 0}] + skolem:lemma2651 + [ a r:Fact; r:gives {(2 3 5 5) list:quicksort (2 3 5 5)}] + [ a r:Fact; r:gives {(2 3 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3032 - skolem:lemma3033 - [ a r:Fact; r:gives {(2 3 3 5) list:reverse (5 3 3 2)}] - skolem:lemma2976 - skolem:lemma2977 - [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2335]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1356 a r:Inference; r:gives { - 2354 :kaprekar 6174 . + 2356 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2356 math:notEqualTo 0}] + skolem:lemma2654 + [ a r:Fact; r:gives {(2 3 5 6) list:quicksort (2 3 5 6)}] + [ a r:Fact; r:gives {(2 3 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3034 - skolem:lemma3035 - [ a r:Fact; r:gives {(2 3 4 5) list:reverse (5 4 3 2)}] - skolem:lemma3008 - skolem:lemma3009 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2345]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1357 a r:Inference; r:gives { - 2355 :kaprekar 6174 . + 2357 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2357 math:notEqualTo 0}] + skolem:lemma2657 + [ a r:Fact; r:gives {(2 3 5 7) list:quicksort (2 3 5 7)}] + [ a r:Fact; r:gives {(2 3 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3036 - skolem:lemma3037 - [ a r:Fact; r:gives {(2 3 5 5) list:reverse (5 5 3 2)}] - skolem:lemma3038 - skolem:lemma3039 - [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2355]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1358 a r:Inference; r:gives { - 2356 :kaprekar 6174 . + 2358 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2358 math:notEqualTo 0}] + skolem:lemma2660 + [ a r:Fact; r:gives {(2 3 5 8) list:quicksort (2 3 5 8)}] + [ a r:Fact; r:gives {(2 3 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3040 - skolem:lemma3041 - [ a r:Fact; r:gives {(2 3 5 6) list:reverse (6 5 3 2)}] - skolem:lemma3042 - skolem:lemma3043 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2356]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1359 a r:Inference; r:gives { - 2357 :kaprekar 6174 . + 2359 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2359 math:notEqualTo 0}] + skolem:lemma2663 + [ a r:Fact; r:gives {(2 3 5 9) list:quicksort (2 3 5 9)}] + [ a r:Fact; r:gives {(2 3 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3044 - skolem:lemma3045 - [ a r:Fact; r:gives {(2 3 5 7) list:reverse (7 5 3 2)}] - skolem:lemma3046 - skolem:lemma3047 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2357]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1360 a r:Inference; r:gives { - 2358 :kaprekar 6174 . + 2360 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2360 math:notEqualTo 0}] + skolem:lemma2666 + [ a r:Fact; r:gives {(2 3 6 0) list:quicksort (0 2 3 6)}] + [ a r:Fact; r:gives {(0 2 3 6) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2358]; - r:rule skolem:lemma2032. + 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. skolem:lemma1361 a r:Inference; r:gives { - 2359 :kaprekar 6174 . + 2361 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2361 math:notEqualTo 0}] + skolem:lemma2667 + [ a r:Fact; r:gives {(2 3 6 1) list:quicksort (1 2 3 6)}] + [ a r:Fact; r:gives {(1 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3048 - skolem:lemma3049 - [ a r:Fact; r:gives {(2 3 5 9) list:reverse (9 5 3 2)}] - skolem:lemma3050 - skolem:lemma3051 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2359]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1362 a r:Inference; r:gives { - 2360 :kaprekar 6174 . + 2362 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2362 math:notEqualTo 0}] + skolem:lemma2668 + [ a r:Fact; r:gives {(2 3 6 2) list:quicksort (2 2 3 6)}] + [ a r:Fact; r:gives {(2 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3052 - skolem:lemma3053 - [ a r:Fact; r:gives {(0 2 3 6) list:reverse (6 3 2 0)}] - skolem:lemma2155 - skolem:lemma2156 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2360]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 236]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1363 a r:Inference; r:gives { - 2361 :kaprekar 6174 . + 2363 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2363 math:notEqualTo 0}] + skolem:lemma2669 + [ a r:Fact; r:gives {(2 3 6 3) list:quicksort (2 3 3 6)}] + [ a r:Fact; r:gives {(2 3 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3054 - skolem:lemma3055 - [ a r:Fact; r:gives {(1 2 3 6) list:reverse (6 3 2 1)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2361]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1236]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1364 a r:Inference; r:gives { - 2362 :kaprekar 6174 . + 2364 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2364 math:notEqualTo 0}] + skolem:lemma2670 + [ a r:Fact; r:gives {(2 3 6 4) list:quicksort (2 3 4 6)}] + [ a r:Fact; r:gives {(2 3 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3056 - skolem:lemma3057 - [ a r:Fact; r:gives {(2 2 3 6) list:reverse (6 3 2 2)}] - skolem:lemma2725 - skolem:lemma2726 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2362]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2236]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1365 a r:Inference; r:gives { - 2363 :kaprekar 6174 . + 2365 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2365 math:notEqualTo 0}] + skolem:lemma2671 + [ a r:Fact; r:gives {(2 3 6 5) list:quicksort (2 3 5 6)}] + [ a r:Fact; r:gives {(2 3 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3058 - skolem:lemma3059 - [ a r:Fact; r:gives {(2 3 3 6) list:reverse (6 3 3 2)}] - skolem:lemma2980 - skolem:lemma2981 - [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2363]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2336]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1366 a r:Inference; r:gives { - 2364 :kaprekar 6174 . + 2366 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2366 math:notEqualTo 0}] + skolem:lemma2672 + [ a r:Fact; r:gives {(2 3 6 6) list:quicksort (2 3 6 6)}] + [ a r:Fact; r:gives {(2 3 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3060 - skolem:lemma3061 - [ a r:Fact; r:gives {(2 3 4 6) list:reverse (6 4 3 2)}] - skolem:lemma3012 - skolem:lemma3013 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2364]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2346]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1367 a r:Inference; r:gives { - 2365 :kaprekar 6174 . + 2367 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2367 math:notEqualTo 0}] + skolem:lemma2675 + [ a r:Fact; r:gives {(2 3 6 7) list:quicksort (2 3 6 7)}] + [ a r:Fact; r:gives {(2 3 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3062 - skolem:lemma3063 - [ a r:Fact; r:gives {(2 3 5 6) list:reverse (6 5 3 2)}] - skolem:lemma3042 - skolem:lemma3043 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2365]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2356]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1368 a r:Inference; r:gives { - 2366 :kaprekar 6174 . + 2368 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2368 math:notEqualTo 0}] + skolem:lemma2678 + [ a r:Fact; r:gives {(2 3 6 8) list:quicksort (2 3 6 8)}] + [ a r:Fact; r:gives {(2 3 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3064 - skolem:lemma3065 - [ a r:Fact; r:gives {(2 3 6 6) list:reverse (6 6 3 2)}] - skolem:lemma3066 - skolem:lemma3067 - [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2366]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2366]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1369 a r:Inference; r:gives { - 2367 :kaprekar 6174 . + 2369 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2369 math:notEqualTo 0}] + skolem:lemma2681 + [ a r:Fact; r:gives {(2 3 6 9) list:quicksort (2 3 6 9)}] + [ a r:Fact; r:gives {(2 3 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3068 - skolem:lemma3069 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1370 a r:Inference; r:gives { - 2368 :kaprekar 6174 . + 2370 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2370 math:notEqualTo 0}] + skolem:lemma2684 + [ a r:Fact; r:gives {(2 3 7 0) list:quicksort (0 2 3 7)}] + [ a r:Fact; r:gives {(0 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3072 - skolem:lemma3073 - [ a r:Fact; r:gives {(2 3 6 8) list:reverse (8 6 3 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2368]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1371 a r:Inference; r:gives { - 2369 :kaprekar 6174 . + 2371 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2371 math:notEqualTo 0}] + skolem:lemma2685 + [ a r:Fact; r:gives {(2 3 7 1) list:quicksort (1 2 3 7)}] + [ a r:Fact; r:gives {(1 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3076 - skolem:lemma3077 - [ a r:Fact; r:gives {(2 3 6 9) list:reverse (9 6 3 2)}] - skolem:lemma3078 - skolem:lemma3079 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2369]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1372 a r:Inference; r:gives { - 2370 :kaprekar 6174 . + 2372 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2372 math:notEqualTo 0}] + skolem:lemma2686 + [ a r:Fact; r:gives {(2 3 7 2) list:quicksort (2 2 3 7)}] + [ a r:Fact; r:gives {(2 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3080 - skolem:lemma3081 - [ a r:Fact; r:gives {(0 2 3 7) list:reverse (7 3 2 0)}] - skolem:lemma2159 - skolem:lemma2160 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2370]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 237]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1373 a r:Inference; r:gives { - 2371 :kaprekar 6174 . + 2373 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2373 math:notEqualTo 0}] + skolem:lemma2687 + [ a r:Fact; r:gives {(2 3 7 3) list:quicksort (2 3 3 7)}] + [ a r:Fact; r:gives {(2 3 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3082 - skolem:lemma3083 - [ a r:Fact; r:gives {(1 2 3 7) list:reverse (7 3 2 1)}] - skolem:lemma2458 - skolem:lemma2459 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2371]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1237]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1374 a r:Inference; r:gives { - 2372 :kaprekar 6174 . + 2374 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2374 math:notEqualTo 0}] + skolem:lemma2688 + [ a r:Fact; r:gives {(2 3 7 4) list:quicksort (2 3 4 7)}] + [ a r:Fact; r:gives {(2 3 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3084 - skolem:lemma3085 - [ a r:Fact; r:gives {(2 2 3 7) list:reverse (7 3 2 2)}] - skolem:lemma2729 - skolem:lemma2730 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2372]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2237]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1375 a r:Inference; r:gives { - 2373 :kaprekar 6174 . + 2375 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2375 math:notEqualTo 0}] + skolem:lemma2689 + [ a r:Fact; r:gives {(2 3 7 5) list:quicksort (2 3 5 7)}] + [ a r:Fact; r:gives {(2 3 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3086 - skolem:lemma3087 - [ a r:Fact; r:gives {(2 3 3 7) list:reverse (7 3 3 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2373]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2337]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1376 a r:Inference; r:gives { - 2374 :kaprekar 6174 . + 2376 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2376 math:notEqualTo 0}] + skolem:lemma2690 + [ a r:Fact; r:gives {(2 3 7 6) list:quicksort (2 3 6 7)}] + [ a r:Fact; r:gives {(2 3 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3088 - skolem:lemma3089 - [ a r:Fact; r:gives {(2 3 4 7) list:reverse (7 4 3 2)}] - skolem:lemma3016 - skolem:lemma3017 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2374]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2347]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1377 a r:Inference; r:gives { - 2375 :kaprekar 6174 . + 2377 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2377 math:notEqualTo 0}] + skolem:lemma2691 + [ a r:Fact; r:gives {(2 3 7 7) list:quicksort (2 3 7 7)}] + [ a r:Fact; r:gives {(2 3 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(2 3 5 7) list:reverse (7 5 3 2)}] - skolem:lemma3046 - skolem:lemma3047 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2375]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2357]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1378 a r:Inference; r:gives { - 2376 :kaprekar 6174 . + 2378 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2378 math:notEqualTo 0}] + skolem:lemma2694 + [ a r:Fact; r:gives {(2 3 7 8) list:quicksort (2 3 7 8)}] + [ a r:Fact; r:gives {(2 3 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3092 - skolem:lemma3093 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2376]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1379 a r:Inference; r:gives { - 2377 :kaprekar 6174 . + 2379 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2379 math:notEqualTo 0}] + skolem:lemma2697 + [ a r:Fact; r:gives {(2 3 7 9) list:quicksort (2 3 7 9)}] + [ a r:Fact; r:gives {(2 3 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3094 - skolem:lemma3095 - [ a r:Fact; r:gives {(2 3 7 7) list:reverse (7 7 3 2)}] - skolem:lemma3096 - skolem:lemma3097 - [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2377]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2377]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1380 a r:Inference; r:gives { - 2378 :kaprekar 6174 . + 2380 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2380 math:notEqualTo 0}] + skolem:lemma2700 + [ a r:Fact; r:gives {(2 3 8 0) list:quicksort (0 2 3 8)}] + [ a r:Fact; r:gives {(0 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3098 - skolem:lemma3099 - [ a r:Fact; r:gives {(2 3 7 8) list:reverse (8 7 3 2)}] - skolem:lemma3100 - skolem:lemma3101 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2378]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1381 a r:Inference; r:gives { - 2379 :kaprekar 6174 . + 2381 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2381 math:notEqualTo 0}] + skolem:lemma2701 + [ a r:Fact; r:gives {(2 3 8 1) list:quicksort (1 2 3 8)}] + [ a r:Fact; r:gives {(1 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3102 - skolem:lemma3103 - [ a r:Fact; r:gives {(2 3 7 9) list:reverse (9 7 3 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2379]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1382 a r:Inference; r:gives { - 2380 :kaprekar 6174 . + 2382 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2382 math:notEqualTo 0}] + skolem:lemma2702 + [ a r:Fact; r:gives {(2 3 8 2) list:quicksort (2 2 3 8)}] + [ a r:Fact; r:gives {(2 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3106 - skolem:lemma3107 - [ a r:Fact; r:gives {(0 2 3 8) list:reverse (8 3 2 0)}] - skolem:lemma2163 - skolem:lemma2164 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2380]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 238]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1383 a r:Inference; r:gives { - 2381 :kaprekar 6174 . + 2383 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2383 math:notEqualTo 0}] + skolem:lemma2703 + [ a r:Fact; r:gives {(2 3 8 3) list:quicksort (2 3 3 8)}] + [ a r:Fact; r:gives {(2 3 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3108 - skolem:lemma3109 - [ a r:Fact; r:gives {(1 2 3 8) list:reverse (8 3 2 1)}] - skolem:lemma2462 - skolem:lemma2463 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2381]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1238]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1384 a r:Inference; r:gives { - 2382 :kaprekar 6174 . + 2384 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2384 math:notEqualTo 0}] + skolem:lemma2704 + [ a r:Fact; r:gives {(2 3 8 4) list:quicksort (2 3 4 8)}] + [ a r:Fact; r:gives {(2 3 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3110 - skolem:lemma3111 - [ a r:Fact; r:gives {(2 2 3 8) list:reverse (8 3 2 2)}] - skolem:lemma2733 - skolem:lemma2734 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2382]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2238]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1385 a r:Inference; r:gives { - 2383 :kaprekar 6174 . + 2385 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2385 math:notEqualTo 0}] + skolem:lemma2705 + [ a r:Fact; r:gives {(2 3 8 5) list:quicksort (2 3 5 8)}] + [ a r:Fact; r:gives {(2 3 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3112 - skolem:lemma3113 - [ a r:Fact; r:gives {(2 3 3 8) list:reverse (8 3 3 2)}] - skolem:lemma2988 - skolem:lemma2989 - [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2383]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2338]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1386 a r:Inference; r:gives { - 2384 :kaprekar 6174 . + 2386 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2386 math:notEqualTo 0}] + skolem:lemma2706 + [ a r:Fact; r:gives {(2 3 8 6) list:quicksort (2 3 6 8)}] + [ a r:Fact; r:gives {(2 3 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3114 - skolem:lemma3115 - [ a r:Fact; r:gives {(2 3 4 8) list:reverse (8 4 3 2)}] - skolem:lemma3020 - skolem:lemma3021 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2384]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2348]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1387 a r:Inference; r:gives { - 2385 :kaprekar 6174 . + 2387 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2387 math:notEqualTo 0}] + skolem:lemma2707 + [ a r:Fact; r:gives {(2 3 8 7) list:quicksort (2 3 7 8)}] + [ a r:Fact; r:gives {(2 3 7 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2385]; - r:rule skolem:lemma2032. + 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. skolem:lemma1388 a r:Inference; r:gives { - 2386 :kaprekar 6174 . + 2388 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2388 math:notEqualTo 0}] + skolem:lemma2708 + [ a r:Fact; r:gives {(2 3 8 8) list:quicksort (2 3 8 8)}] + [ a r:Fact; r:gives {(2 3 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3116 - skolem:lemma3117 - [ a r:Fact; r:gives {(2 3 6 8) list:reverse (8 6 3 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2386]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2368]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1389 a r:Inference; r:gives { - 2387 :kaprekar 6174 . + 2389 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2389 math:notEqualTo 0}] + skolem:lemma2711 + [ a r:Fact; r:gives {(2 3 8 9) list:quicksort (2 3 8 9)}] + [ a r:Fact; r:gives {(2 3 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3118 - skolem:lemma3119 - [ a r:Fact; r:gives {(2 3 7 8) list:reverse (8 7 3 2)}] - skolem:lemma3100 - skolem:lemma3101 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2387]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2378]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1390 a r:Inference; r:gives { - 2388 :kaprekar 6174 . + 2390 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2390 math:notEqualTo 0}] + skolem:lemma2714 + [ a r:Fact; r:gives {(2 3 9 0) list:quicksort (0 2 3 9)}] + [ a r:Fact; r:gives {(0 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3120 - skolem:lemma3121 - [ a r:Fact; r:gives {(2 3 8 8) list:reverse (8 8 3 2)}] - skolem:lemma3122 - skolem:lemma3123 - [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2388]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2388]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1391 a r:Inference; r:gives { - 2389 :kaprekar 6174 . + 2391 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2391 math:notEqualTo 0}] + skolem:lemma2715 + [ a r:Fact; r:gives {(2 3 9 1) list:quicksort (1 2 3 9)}] + [ a r:Fact; r:gives {(1 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3124 - skolem:lemma3125 - [ a r:Fact; r:gives {(2 3 8 9) list:reverse (9 8 3 2)}] - skolem:lemma3126 - skolem:lemma3127 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2389]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1392 a r:Inference; r:gives { - 2390 :kaprekar 6174 . + 2392 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2392 math:notEqualTo 0}] + skolem:lemma2716 + [ a r:Fact; r:gives {(2 3 9 2) list:quicksort (2 2 3 9)}] + [ a r:Fact; r:gives {(2 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3128 - skolem:lemma3129 - [ a r:Fact; r:gives {(0 2 3 9) list:reverse (9 3 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2390]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 239]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1393 a r:Inference; r:gives { - 2391 :kaprekar 6174 . + 2393 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2393 math:notEqualTo 0}] + skolem:lemma2717 + [ a r:Fact; r:gives {(2 3 9 3) list:quicksort (2 3 3 9)}] + [ a r:Fact; r:gives {(2 3 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3130 - skolem:lemma3131 - [ a r:Fact; r:gives {(1 2 3 9) list:reverse (9 3 2 1)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2391]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1239]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1394 a r:Inference; r:gives { - 2392 :kaprekar 6174 . + 2394 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2394 math:notEqualTo 0}] + skolem:lemma2718 + [ a r:Fact; r:gives {(2 3 9 4) list:quicksort (2 3 4 9)}] + [ a r:Fact; r:gives {(2 3 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3132 - skolem:lemma3133 - [ a r:Fact; r:gives {(2 2 3 9) list:reverse (9 3 2 2)}] - skolem:lemma2737 - skolem:lemma2738 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2392]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2239]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1395 a r:Inference; r:gives { - 2393 :kaprekar 6174 . + 2395 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2395 math:notEqualTo 0}] + skolem:lemma2719 + [ a r:Fact; r:gives {(2 3 9 5) list:quicksort (2 3 5 9)}] + [ a r:Fact; r:gives {(2 3 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3134 - skolem:lemma3135 - [ a r:Fact; r:gives {(2 3 3 9) list:reverse (9 3 3 2)}] - skolem:lemma2992 - skolem:lemma2993 - [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2393]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2339]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1396 a r:Inference; r:gives { - 2394 :kaprekar 6174 . + 2396 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2396 math:notEqualTo 0}] + skolem:lemma2720 + [ a r:Fact; r:gives {(2 3 9 6) list:quicksort (2 3 6 9)}] + [ a r:Fact; r:gives {(2 3 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3136 - skolem:lemma3137 - [ a r:Fact; r:gives {(2 3 4 9) list:reverse (9 4 3 2)}] - skolem:lemma3024 - skolem:lemma3025 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2394]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2349]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1397 a r:Inference; r:gives { - 2395 :kaprekar 6174 . + 2397 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2397 math:notEqualTo 0}] + skolem:lemma2721 + [ a r:Fact; r:gives {(2 3 9 7) list:quicksort (2 3 7 9)}] + [ a r:Fact; r:gives {(2 3 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3138 - skolem:lemma3139 - [ a r:Fact; r:gives {(2 3 5 9) list:reverse (9 5 3 2)}] - skolem:lemma3050 - skolem:lemma3051 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2395]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2359]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1398 a r:Inference; r:gives { - 2396 :kaprekar 6174 . + 2398 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2398 math:notEqualTo 0}] + skolem:lemma2722 + [ a r:Fact; r:gives {(2 3 9 8) list:quicksort (2 3 8 9)}] + [ a r:Fact; r:gives {(2 3 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3140 - skolem:lemma3141 - [ a r:Fact; r:gives {(2 3 6 9) list:reverse (9 6 3 2)}] - skolem:lemma3078 - skolem:lemma3079 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2396]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2369]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1399 a r:Inference; r:gives { - 2397 :kaprekar 6174 . + 2399 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2399 math:notEqualTo 0}] + skolem:lemma2723 + [ a r:Fact; r:gives {(2 3 9 9) list:quicksort (2 3 9 9)}] + [ a r:Fact; r:gives {(2 3 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3142 - skolem:lemma3143 - [ a r:Fact; r:gives {(2 3 7 9) list:reverse (9 7 3 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2397]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2379]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1400 a r:Inference; r:gives { - 2398 :kaprekar 6174 . + 2400 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2400 math:notEqualTo 0}] + skolem:lemma2726 + [ a r:Fact; r:gives {(2 4 0 0) list:quicksort (0 0 2 4)}] + [ a r:Fact; r:gives {(0 0 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3144 - skolem:lemma3145 - [ a r:Fact; r:gives {(2 3 8 9) list:reverse (9 8 3 2)}] - skolem:lemma3126 - skolem:lemma3127 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2398]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2389]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1401 a r:Inference; r:gives { - 2399 :kaprekar 6174 . + 2401 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2401 math:notEqualTo 0}] + skolem:lemma2727 + [ a r:Fact; r:gives {(2 4 0 1) list:quicksort (0 1 2 4)}] + [ a r:Fact; r:gives {(0 1 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3146 - skolem:lemma3147 - [ a r:Fact; r:gives {(2 3 9 9) list:reverse (9 9 3 2)}] - skolem:lemma3148 - skolem:lemma3149 - [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2399]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2399]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1402 a r:Inference; r:gives { - 2400 :kaprekar 6174 . + 2402 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2402 math:notEqualTo 0}] + skolem:lemma2728 + [ a r:Fact; r:gives {(2 4 0 2) list:quicksort (0 2 2 4)}] + [ a r:Fact; r:gives {(0 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3150 - skolem:lemma3151 - [ a r:Fact; r:gives {(0 0 2 4) list:reverse (4 2 0 0)}] - skolem:lemma2024 - skolem:lemma2025 - [ a r:Fact; r:gives {(4200 24) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 24]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1403 a r:Inference; r:gives { - 2401 :kaprekar 6174 . + 2403 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2403 math:notEqualTo 0}] + skolem:lemma2729 + [ a r:Fact; r:gives {(2 4 0 3) list:quicksort (0 2 3 4)}] + [ a r:Fact; r:gives {(0 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3152 - skolem:lemma3153 - [ a r:Fact; r:gives {(0 1 2 4) list:reverse (4 2 1 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2401]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 124]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1404 a r:Inference; r:gives { - 2402 :kaprekar 6174 . + 2404 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2404 math:notEqualTo 0}] + skolem:lemma2730 + [ a r:Fact; r:gives {(2 4 0 4) list:quicksort (0 2 4 4)}] + [ a r:Fact; r:gives {(0 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3154 - skolem:lemma3155 - [ a r:Fact; r:gives {(0 2 2 4) list:reverse (4 2 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2402]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 224]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1405 a r:Inference; r:gives { - 2403 :kaprekar 6174 . + 2405 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2405 math:notEqualTo 0}] + skolem:lemma2731 + [ a r:Fact; r:gives {(2 4 0 5) list:quicksort (0 2 4 5)}] + [ a r:Fact; r:gives {(0 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3156 - skolem:lemma3157 - [ a r:Fact; r:gives {(0 2 3 4) list:reverse (4 3 2 0)}] - skolem:lemma2147 - skolem:lemma2148 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2403]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 234]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1406 a r:Inference; r:gives { - 2404 :kaprekar 6174 . + 2406 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2406 math:notEqualTo 0}] + skolem:lemma2732 + [ a r:Fact; r:gives {(2 4 0 6) list:quicksort (0 2 4 6)}] + [ a r:Fact; r:gives {(0 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3158 - skolem:lemma3159 - [ a r:Fact; r:gives {(0 2 4 4) list:reverse (4 4 2 0)}] - skolem:lemma2179 - skolem:lemma2180 - [ a r:Fact; r:gives {(4420 244) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2404]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 244]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1407 a r:Inference; r:gives { - 2405 :kaprekar 6174 . + 2407 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2407 math:notEqualTo 0}] + skolem:lemma2733 + [ a r:Fact; r:gives {(2 4 0 7) list:quicksort (0 2 4 7)}] + [ a r:Fact; r:gives {(0 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3160 - skolem:lemma3161 - [ a r:Fact; r:gives {(0 2 4 5) list:reverse (5 4 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2405]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 245]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1408 a r:Inference; r:gives { - 2406 :kaprekar 6174 . + 2408 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2408 math:notEqualTo 0}] + skolem:lemma2734 + [ a r:Fact; r:gives {(2 4 0 8) list:quicksort (0 2 4 8)}] + [ a r:Fact; r:gives {(0 2 4 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2406]; - r:rule skolem:lemma2032. + 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. skolem:lemma1409 a r:Inference; r:gives { - 2407 :kaprekar 6174 . + 2409 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2409 math:notEqualTo 0}] + skolem:lemma2735 + [ a r:Fact; r:gives {(2 4 0 9) list:quicksort (0 2 4 9)}] + [ a r:Fact; r:gives {(0 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3162 - skolem:lemma3163 - [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] - skolem:lemma2187 - skolem:lemma2188 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2407]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 247]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1410 a r:Inference; r:gives { - 2408 :kaprekar 6174 . + 2410 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3164 - skolem:lemma3165 - [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] - skolem:lemma2191 - skolem:lemma2192 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] + [ a r:Fact; r:gives {2410 math:notEqualTo 0}] + skolem:lemma2736 + [ a r:Fact; r:gives {(2 4 1 0) list:quicksort (0 1 2 4)}] + [ a r:Fact; r:gives {(0 1 2 4) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2408]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 248]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1411 a r:Inference; r:gives { - 2409 :kaprekar 6174 . + 2411 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2411 math:notEqualTo 0}] + skolem:lemma2737 + [ a r:Fact; r:gives {(2 4 1 1) list:quicksort (1 1 2 4)}] + [ a r:Fact; r:gives {(1 1 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3166 - skolem:lemma3167 - [ a r:Fact; r:gives {(0 2 4 9) list:reverse (9 4 2 0)}] - skolem:lemma2195 - skolem:lemma2196 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2409]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 249]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1412 a r:Inference; r:gives { - 2410 :kaprekar 6174 . + 2412 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2412 math:notEqualTo 0}] + skolem:lemma2738 + [ a r:Fact; r:gives {(2 4 1 2) list:quicksort (1 2 2 4)}] + [ a r:Fact; r:gives {(1 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3168 - skolem:lemma3169 - [ a r:Fact; r:gives {(0 1 2 4) list:reverse (4 2 1 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2410]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 124]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1413 a r:Inference; r:gives { - 2411 :kaprekar 6174 . + 2413 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2413 math:notEqualTo 0}] + skolem:lemma2739 + [ a r:Fact; r:gives {(2 4 1 3) list:quicksort (1 2 3 4)}] + [ a r:Fact; r:gives {(1 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3170 - skolem:lemma3171 - [ a r:Fact; r:gives {(1 1 2 4) list:reverse (4 2 1 1)}] - skolem:lemma2376 - skolem:lemma2377 - [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2411]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1124]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1414 a r:Inference; r:gives { - 2412 :kaprekar 6174 . + 2414 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2414 math:notEqualTo 0}] + skolem:lemma2740 + [ a r:Fact; r:gives {(2 4 1 4) list:quicksort (1 2 4 4)}] + [ a r:Fact; r:gives {(1 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3172 - skolem:lemma3173 - [ a r:Fact; r:gives {(1 2 2 4) list:reverse (4 2 2 1)}] - skolem:lemma2412 - skolem:lemma2413 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2412]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1224]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1415 a r:Inference; r:gives { - 2413 :kaprekar 6174 . + 2415 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2415 math:notEqualTo 0}] + skolem:lemma2741 + [ a r:Fact; r:gives {(2 4 1 5) list:quicksort (1 2 4 5)}] + [ a r:Fact; r:gives {(1 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3174 - skolem:lemma3175 - [ a r:Fact; r:gives {(1 2 3 4) list:reverse (4 3 2 1)}] - skolem:lemma2446 - skolem:lemma2447 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2413]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1234]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1416 a r:Inference; r:gives { - 2414 :kaprekar 6174 . + 2416 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2416 math:notEqualTo 0}] + skolem:lemma2742 + [ a r:Fact; r:gives {(2 4 1 6) list:quicksort (1 2 4 6)}] + [ a r:Fact; r:gives {(1 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3176 - skolem:lemma3177 - [ a r:Fact; r:gives {(1 2 4 4) list:reverse (4 4 2 1)}] - skolem:lemma2478 - skolem:lemma2479 - [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2414]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1244]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1417 a r:Inference; r:gives { - 2415 :kaprekar 6174 . + 2417 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2417 math:notEqualTo 0}] + skolem:lemma2743 + [ a r:Fact; r:gives {(2 4 1 7) list:quicksort (1 2 4 7)}] + [ a r:Fact; r:gives {(1 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3178 - skolem:lemma3179 - [ a r:Fact; r:gives {(1 2 4 5) list:reverse (5 4 2 1)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2415]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1245]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1418 a r:Inference; r:gives { - 2416 :kaprekar 6174 . + 2418 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2418 math:notEqualTo 0}] + skolem:lemma2744 + [ a r:Fact; r:gives {(2 4 1 8) list:quicksort (1 2 4 8)}] + [ a r:Fact; r:gives {(1 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3180 - skolem:lemma3181 - [ a r:Fact; r:gives {(1 2 4 6) list:reverse (6 4 2 1)}] - skolem:lemma2486 - skolem:lemma2487 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2416]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1246]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1419 a r:Inference; r:gives { - 2417 :kaprekar 6174 . + 2419 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2419 math:notEqualTo 0}] + skolem:lemma2745 + [ a r:Fact; r:gives {(2 4 1 9) list:quicksort (1 2 4 9)}] + [ a r:Fact; r:gives {(1 2 4 9) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2417]; - r:rule skolem:lemma2032. + 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. skolem:lemma1420 a r:Inference; r:gives { - 2418 :kaprekar 6174 . + 2420 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2420 math:notEqualTo 0}] + skolem:lemma2746 + [ a r:Fact; r:gives {(2 4 2 0) list:quicksort (0 2 2 4)}] + [ a r:Fact; r:gives {(0 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3182 - skolem:lemma3183 - [ a r:Fact; r:gives {(1 2 4 8) list:reverse (8 4 2 1)}] - skolem:lemma2490 - skolem:lemma2491 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2418]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1248]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1421 a r:Inference; r:gives { - 2419 :kaprekar 6174 . + 2421 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2421 math:notEqualTo 0}] + skolem:lemma2747 + [ a r:Fact; r:gives {(2 4 2 1) list:quicksort (1 2 2 4)}] + [ a r:Fact; r:gives {(1 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3184 - skolem:lemma3185 - [ a r:Fact; r:gives {(1 2 4 9) list:reverse (9 4 2 1)}] - skolem:lemma2494 - skolem:lemma2495 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2419]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1249]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1422 a r:Inference; r:gives { - 2420 :kaprekar 6174 . + 2422 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2422 math:notEqualTo 0}] + skolem:lemma2748 + [ a r:Fact; r:gives {(2 4 2 2) list:quicksort (2 2 2 4)}] + [ a r:Fact; r:gives {(2 2 2 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3186 - skolem:lemma3187 - [ a r:Fact; r:gives {(0 2 2 4) list:reverse (4 2 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 224]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1423 a r:Inference; r:gives { - 2421 :kaprekar 6174 . + 2423 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2423 math:notEqualTo 0}] + skolem:lemma2749 + [ a r:Fact; r:gives {(2 4 2 3) list:quicksort (2 2 3 4)}] + [ a r:Fact; r:gives {(2 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3188 - skolem:lemma3189 - [ a r:Fact; r:gives {(1 2 2 4) list:reverse (4 2 2 1)}] - skolem:lemma2412 - skolem:lemma2413 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1224]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1424 a r:Inference; r:gives { - 2422 :kaprekar 6174 . + 2424 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2424 math:notEqualTo 0}] + skolem:lemma2750 + [ a r:Fact; r:gives {(2 4 2 4) list:quicksort (2 2 4 4)}] + [ a r:Fact; r:gives {(2 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3190 - skolem:lemma3191 - [ a r:Fact; r:gives {(2 2 2 4) list:reverse (4 2 2 2)}] - skolem:lemma2683 - skolem:lemma2684 - [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2224]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1425 a r:Inference; r:gives { - 2423 :kaprekar 6174 . + 2425 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2425 math:notEqualTo 0}] + skolem:lemma2751 + [ a r:Fact; r:gives {(2 4 2 5) list:quicksort (2 2 4 5)}] + [ a r:Fact; r:gives {(2 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3192 - skolem:lemma3193 - [ a r:Fact; r:gives {(2 2 3 4) list:reverse (4 3 2 2)}] - skolem:lemma2717 - skolem:lemma2718 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2423]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2234]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1426 a r:Inference; r:gives { - 2424 :kaprekar 6174 . + 2426 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2426 math:notEqualTo 0}] + skolem:lemma2752 + [ a r:Fact; r:gives {(2 4 2 6) list:quicksort (2 2 4 6)}] + [ a r:Fact; r:gives {(2 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3194 - skolem:lemma3195 - [ a r:Fact; r:gives {(2 2 4 4) list:reverse (4 4 2 2)}] - skolem:lemma2749 - skolem:lemma2750 - [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] - [ a r:Fact; r:gives {2178 math:notEqualTo 6174}] - skolem:lemma1180 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2424]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2244]; - 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_8"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1427 a r:Inference; r:gives { - 2425 :kaprekar 6174 . + 2427 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3196 - skolem:lemma3197 - [ a r:Fact; r:gives {(2 2 4 5) list:reverse (5 4 2 2)}] + [ a r:Fact; r:gives {2427 math:notEqualTo 0}] skolem:lemma2753 - skolem:lemma2754 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ a r:Fact; r:gives {(2 4 2 7) list:quicksort (2 2 4 7)}] + [ a r:Fact; r:gives {(2 2 4 7) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2425]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2245]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1428 a r:Inference; r:gives { - 2426 :kaprekar 6174 . + 2428 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2428 math:notEqualTo 0}] + skolem:lemma2754 + [ a r:Fact; r:gives {(2 4 2 8) list:quicksort (2 2 4 8)}] + [ a r:Fact; r:gives {(2 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3198 - skolem:lemma3199 - [ a r:Fact; r:gives {(2 2 4 6) list:reverse (6 4 2 2)}] - skolem:lemma2757 - skolem:lemma2758 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2426]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2246]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1429 a r:Inference; r:gives { - 2427 :kaprekar 6174 . + 2429 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2429 math:notEqualTo 0}] + skolem:lemma2755 + [ a r:Fact; r:gives {(2 4 2 9) list:quicksort (2 2 4 9)}] + [ a r:Fact; r:gives {(2 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3200 - skolem:lemma3201 - [ a r:Fact; r:gives {(2 2 4 7) list:reverse (7 4 2 2)}] - skolem:lemma2761 - skolem:lemma2762 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2427]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2247]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1430 a r:Inference; r:gives { - 2428 :kaprekar 6174 . + 2430 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2430 math:notEqualTo 0}] + skolem:lemma2756 + [ a r:Fact; r:gives {(2 4 3 0) list:quicksort (0 2 3 4)}] + [ a r:Fact; r:gives {(0 2 3 4) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2428]; - r:rule skolem:lemma2032. + 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. skolem:lemma1431 a r:Inference; r:gives { - 2429 :kaprekar 6174 . + 2431 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2431 math:notEqualTo 0}] + skolem:lemma2757 + [ a r:Fact; r:gives {(2 4 3 1) list:quicksort (1 2 3 4)}] + [ a r:Fact; r:gives {(1 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3202 - skolem:lemma3203 - [ a r:Fact; r:gives {(2 2 4 9) list:reverse (9 4 2 2)}] - skolem:lemma2765 - skolem:lemma2766 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2429]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2249]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1432 a r:Inference; r:gives { - 2430 :kaprekar 6174 . + 2432 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2432 math:notEqualTo 0}] + skolem:lemma2758 + [ a r:Fact; r:gives {(2 4 3 2) list:quicksort (2 2 3 4)}] + [ a r:Fact; r:gives {(2 2 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3204 - skolem:lemma3205 - [ a r:Fact; r:gives {(0 2 3 4) list:reverse (4 3 2 0)}] - skolem:lemma2147 - skolem:lemma2148 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2430]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 234]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1433 a r:Inference; r:gives { - 2431 :kaprekar 6174 . + 2433 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2433 math:notEqualTo 0}] + skolem:lemma2759 + [ a r:Fact; r:gives {(2 4 3 3) list:quicksort (2 3 3 4)}] + [ a r:Fact; r:gives {(2 3 3 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3206 - skolem:lemma3207 - [ a r:Fact; r:gives {(1 2 3 4) list:reverse (4 3 2 1)}] - skolem:lemma2446 - skolem:lemma2447 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2431]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1234]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1434 a r:Inference; r:gives { - 2432 :kaprekar 6174 . + 2434 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2434 math:notEqualTo 0}] + skolem:lemma2760 + [ a r:Fact; r:gives {(2 4 3 4) list:quicksort (2 3 4 4)}] + [ a r:Fact; r:gives {(2 3 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3208 - skolem:lemma3209 - [ a r:Fact; r:gives {(2 2 3 4) list:reverse (4 3 2 2)}] - skolem:lemma2717 - skolem:lemma2718 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2234]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1435 a r:Inference; r:gives { - 2433 :kaprekar 6174 . + 2435 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2435 math:notEqualTo 0}] + skolem:lemma2761 + [ a r:Fact; r:gives {(2 4 3 5) list:quicksort (2 3 4 5)}] + [ a r:Fact; r:gives {(2 3 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3210 - skolem:lemma3211 - [ a r:Fact; r:gives {(2 3 3 4) list:reverse (4 3 3 2)}] - skolem:lemma2972 - skolem:lemma2973 - [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2433]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2334]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1436 a r:Inference; r:gives { - 2434 :kaprekar 6174 . + 2436 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2436 math:notEqualTo 0}] + skolem:lemma2762 + [ a r:Fact; r:gives {(2 4 3 6) list:quicksort (2 3 4 6)}] + [ a r:Fact; r:gives {(2 3 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3212 - skolem:lemma3213 - [ a r:Fact; r:gives {(2 3 4 4) list:reverse (4 4 3 2)}] - skolem:lemma3004 - skolem:lemma3005 - [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2434]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2344]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1437 a r:Inference; r:gives { - 2435 :kaprekar 6174 . + 2437 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2437 math:notEqualTo 0}] + skolem:lemma2763 + [ a r:Fact; r:gives {(2 4 3 7) list:quicksort (2 3 4 7)}] + [ a r:Fact; r:gives {(2 3 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3214 - skolem:lemma3215 - [ a r:Fact; r:gives {(2 3 4 5) list:reverse (5 4 3 2)}] - skolem:lemma3008 - skolem:lemma3009 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2435]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2345]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1438 a r:Inference; r:gives { - 2436 :kaprekar 6174 . + 2438 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2438 math:notEqualTo 0}] + skolem:lemma2764 + [ a r:Fact; r:gives {(2 4 3 8) list:quicksort (2 3 4 8)}] + [ a r:Fact; r:gives {(2 3 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(2 3 4 6) list:reverse (6 4 3 2)}] - skolem:lemma3012 - skolem:lemma3013 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2436]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2346]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1439 a r:Inference; r:gives { - 2437 :kaprekar 6174 . + 2439 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2439 math:notEqualTo 0}] + skolem:lemma2765 + [ a r:Fact; r:gives {(2 4 3 9) list:quicksort (2 3 4 9)}] + [ a r:Fact; r:gives {(2 3 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3218 - skolem:lemma3219 - [ a r:Fact; r:gives {(2 3 4 7) list:reverse (7 4 3 2)}] - skolem:lemma3016 - skolem:lemma3017 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2437]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2347]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1440 a r:Inference; r:gives { - 2438 :kaprekar 6174 . + 2440 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2440 math:notEqualTo 0}] + skolem:lemma2766 + [ a r:Fact; r:gives {(2 4 4 0) list:quicksort (0 2 4 4)}] + [ a r:Fact; r:gives {(0 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3220 - skolem:lemma3221 - [ a r:Fact; r:gives {(2 3 4 8) list:reverse (8 4 3 2)}] - skolem:lemma3020 - skolem:lemma3021 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2438]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2348]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1441 a r:Inference; r:gives { - 2439 :kaprekar 6174 . + 2441 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2441 math:notEqualTo 0}] + skolem:lemma2767 + [ a r:Fact; r:gives {(2 4 4 1) list:quicksort (1 2 4 4)}] + [ a r:Fact; r:gives {(1 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3222 - skolem:lemma3223 - [ a r:Fact; r:gives {(2 3 4 9) list:reverse (9 4 3 2)}] - skolem:lemma3024 - skolem:lemma3025 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2439]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2349]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1442 a r:Inference; r:gives { - 2440 :kaprekar 6174 . + 2442 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2442 math:notEqualTo 0}] + skolem:lemma2768 + [ a r:Fact; r:gives {(2 4 4 2) list:quicksort (2 2 4 4)}] + [ a r:Fact; r:gives {(2 2 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3224 - skolem:lemma3225 - [ a r:Fact; r:gives {(0 2 4 4) list:reverse (4 4 2 0)}] - skolem:lemma2179 - skolem:lemma2180 - [ a r:Fact; r:gives {(4420 244) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2440]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 244]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1443 a r:Inference; r:gives { - 2441 :kaprekar 6174 . + 2443 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2443 math:notEqualTo 0}] + skolem:lemma2769 + [ a r:Fact; r:gives {(2 4 4 3) list:quicksort (2 3 4 4)}] + [ a r:Fact; r:gives {(2 3 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3226 - skolem:lemma3227 - [ a r:Fact; r:gives {(1 2 4 4) list:reverse (4 4 2 1)}] - skolem:lemma2478 - skolem:lemma2479 - [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1244]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1444 a r:Inference; r:gives { - 2442 :kaprekar 6174 . + 2444 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2444 math:notEqualTo 0}] + skolem:lemma2770 + [ a r:Fact; r:gives {(2 4 4 4) list:quicksort (2 4 4 4)}] + [ a r:Fact; r:gives {(2 4 4 4) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3228 - skolem:lemma3229 - [ a r:Fact; r:gives {(2 2 4 4) list:reverse (4 4 2 2)}] - skolem:lemma2749 - skolem:lemma2750 - [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] - [ a r:Fact; r:gives {2178 math:notEqualTo 6174}] - skolem:lemma1180 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2244]; - 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_8"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1445 a r:Inference; r:gives { - 2443 :kaprekar 6174 . + 2445 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2445 math:notEqualTo 0}] + skolem:lemma2773 + [ a r:Fact; r:gives {(2 4 4 5) list:quicksort (2 4 4 5)}] + [ a r:Fact; r:gives {(2 4 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3230 - skolem:lemma3231 - [ a r:Fact; r:gives {(2 3 4 4) list:reverse (4 4 3 2)}] - skolem:lemma3004 - skolem:lemma3005 - [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] - [ a r:Fact; r:gives {2088 math:notEqualTo 6174}] - skolem:lemma1090 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2344]; - 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_8"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1446 a r:Inference; r:gives { - 2444 :kaprekar 6174 . + 2446 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2446 math:notEqualTo 0}] + skolem:lemma2776 + [ a r:Fact; r:gives {(2 4 4 6) list:quicksort (2 4 4 6)}] + [ a r:Fact; r:gives {(2 4 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3232 - skolem:lemma3233 - [ a r:Fact; r:gives {(2 4 4 4) list:reverse (4 4 4 2)}] - skolem:lemma3234 - skolem:lemma3235 - [ a r:Fact; r:gives {(4442 2444) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2444]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1447 a r:Inference; r:gives { - 2445 :kaprekar 6174 . + 2447 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2447 math:notEqualTo 0}] + skolem:lemma2779 + [ a r:Fact; r:gives {(2 4 4 7) list:quicksort (2 4 4 7)}] + [ a r:Fact; r:gives {(2 4 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3236 - skolem:lemma3237 - [ a r:Fact; r:gives {(2 4 4 5) list:reverse (5 4 4 2)}] - skolem:lemma3238 - skolem:lemma3239 - [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2445]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1448 a r:Inference; r:gives { - 2446 :kaprekar 6174 . + 2448 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2448 math:notEqualTo 0}] + skolem:lemma2782 + [ a r:Fact; r:gives {(2 4 4 8) list:quicksort (2 4 4 8)}] + [ a r:Fact; r:gives {(2 4 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3240 - skolem:lemma3241 - [ a r:Fact; r:gives {(2 4 4 6) list:reverse (6 4 4 2)}] - skolem:lemma3242 - skolem:lemma3243 - [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2446]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1449 a r:Inference; r:gives { - 2447 :kaprekar 6174 . + 2449 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2449 math:notEqualTo 0}] + skolem:lemma2785 + [ a r:Fact; r:gives {(2 4 4 9) list:quicksort (2 4 4 9)}] + [ a r:Fact; r:gives {(2 4 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3244 - skolem:lemma3245 - [ a r:Fact; r:gives {(2 4 4 7) list:reverse (7 4 4 2)}] - skolem:lemma3246 - skolem:lemma3247 - [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2447]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2447]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1450 a r:Inference; r:gives { - 2448 :kaprekar 6174 . + 2450 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2450 math:notEqualTo 0}] + skolem:lemma2788 + [ a r:Fact; r:gives {(2 4 5 0) list:quicksort (0 2 4 5)}] + [ a r:Fact; r:gives {(0 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3248 - skolem:lemma3249 - [ a r:Fact; r:gives {(2 4 4 8) list:reverse (8 4 4 2)}] - skolem:lemma3250 - skolem:lemma3251 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2448]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2448]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1451 a r:Inference; r:gives { - 2449 :kaprekar 6174 . + 2451 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2451 math:notEqualTo 0}] + skolem:lemma2789 + [ a r:Fact; r:gives {(2 4 5 1) list:quicksort (1 2 4 5)}] + [ a r:Fact; r:gives {(1 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3252 - skolem:lemma3253 - [ a r:Fact; r:gives {(2 4 4 9) list:reverse (9 4 4 2)}] - skolem:lemma3254 - skolem:lemma3255 - [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2449]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1452 a r:Inference; r:gives { - 2450 :kaprekar 6174 . + 2452 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2452 math:notEqualTo 0}] + skolem:lemma2790 + [ a r:Fact; r:gives {(2 4 5 2) list:quicksort (2 2 4 5)}] + [ a r:Fact; r:gives {(2 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3256 - skolem:lemma3257 - [ a r:Fact; r:gives {(0 2 4 5) list:reverse (5 4 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2450]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 245]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1453 a r:Inference; r:gives { - 2451 :kaprekar 6174 . + 2453 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2453 math:notEqualTo 0}] + skolem:lemma2791 + [ a r:Fact; r:gives {(2 4 5 3) list:quicksort (2 3 4 5)}] + [ a r:Fact; r:gives {(2 3 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3258 - skolem:lemma3259 - [ a r:Fact; r:gives {(1 2 4 5) list:reverse (5 4 2 1)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2451]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1245]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1454 a r:Inference; r:gives { - 2452 :kaprekar 6174 . + 2454 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2454 math:notEqualTo 0}] + skolem:lemma2792 + [ a r:Fact; r:gives {(2 4 5 4) list:quicksort (2 4 4 5)}] + [ a r:Fact; r:gives {(2 4 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3260 - skolem:lemma3261 - [ a r:Fact; r:gives {(2 2 4 5) list:reverse (5 4 2 2)}] - skolem:lemma2753 - skolem:lemma2754 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2452]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2245]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1455 a r:Inference; r:gives { - 2453 :kaprekar 6174 . + 2455 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2455 math:notEqualTo 0}] + skolem:lemma2793 + [ a r:Fact; r:gives {(2 4 5 5) list:quicksort (2 4 5 5)}] + [ a r:Fact; r:gives {(2 4 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3262 - skolem:lemma3263 - [ a r:Fact; r:gives {(2 3 4 5) list:reverse (5 4 3 2)}] - skolem:lemma3008 - skolem:lemma3009 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2453]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2345]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1456 a r:Inference; r:gives { - 2454 :kaprekar 6174 . + 2456 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2456 math:notEqualTo 0}] + skolem:lemma2796 + [ a r:Fact; r:gives {(2 4 5 6) list:quicksort (2 4 5 6)}] + [ a r:Fact; r:gives {(2 4 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3264 - skolem:lemma3265 - [ a r:Fact; r:gives {(2 4 4 5) list:reverse (5 4 4 2)}] - skolem:lemma3238 - skolem:lemma3239 - [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2454]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2445]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1457 a r:Inference; r:gives { - 2455 :kaprekar 6174 . + 2457 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2457 math:notEqualTo 0}] + skolem:lemma2799 + [ a r:Fact; r:gives {(2 4 5 7) list:quicksort (2 4 5 7)}] + [ a r:Fact; r:gives {(2 4 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3266 - skolem:lemma3267 - [ a r:Fact; r:gives {(2 4 5 5) list:reverse (5 5 4 2)}] - skolem:lemma3268 - skolem:lemma3269 - [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2455]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1458 a r:Inference; r:gives { - 2456 :kaprekar 6174 . + 2458 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2458 math:notEqualTo 0}] + skolem:lemma2802 + [ a r:Fact; r:gives {(2 4 5 8) list:quicksort (2 4 5 8)}] + [ a r:Fact; r:gives {(2 4 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3270 - skolem:lemma3271 - [ a r:Fact; r:gives {(2 4 5 6) list:reverse (6 5 4 2)}] - skolem:lemma3272 - skolem:lemma3273 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2456]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1459 a r:Inference; r:gives { - 2457 :kaprekar 6174 . + 2459 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3274 - skolem:lemma3275 - [ a r:Fact; r:gives {(2 4 5 7) list:reverse (7 5 4 2)}] - skolem:lemma3276 - skolem:lemma3277 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ a r:Fact; r:gives {2459 math:notEqualTo 0}] + skolem:lemma2805 + [ a r:Fact; r:gives {(2 4 5 9) list:quicksort (2 4 5 9)}] + [ a r:Fact; r:gives {(2 4 5 9) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2457]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1460 a r:Inference; r:gives { - 2458 :kaprekar 6174 . + 2460 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2460 math:notEqualTo 0}] + skolem:lemma2808 + [ a r:Fact; r:gives {(2 4 6 0) list:quicksort (0 2 4 6)}] + [ a r:Fact; r:gives {(0 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3278 - skolem:lemma3279 - [ a r:Fact; r:gives {(2 4 5 8) list:reverse (8 5 4 2)}] - skolem:lemma3280 - skolem:lemma3281 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2458]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1461 a r:Inference; r:gives { - 2459 :kaprekar 6174 . + 2461 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2461 math:notEqualTo 0}] + skolem:lemma2809 + [ a r:Fact; r:gives {(2 4 6 1) list:quicksort (1 2 4 6)}] + [ a r:Fact; r:gives {(1 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3282 - skolem:lemma3283 - [ a r:Fact; r:gives {(2 4 5 9) list:reverse (9 5 4 2)}] - skolem:lemma3284 - skolem:lemma3285 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2459]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1462 a r:Inference; r:gives { - 2460 :kaprekar 6174 . + 2462 :kaprekar (0 2). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2462 math:notEqualTo 0}] + skolem:lemma2810 + [ a r:Fact; r:gives {(2 4 6 2) list:quicksort (2 2 4 6)}] + [ a r:Fact; r:gives {(2 2 4 6) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2460]; - r:rule skolem:lemma2032. + 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. skolem:lemma1463 a r:Inference; r:gives { - 2461 :kaprekar 6174 . + 2463 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2463 math:notEqualTo 0}] + skolem:lemma2811 + [ a r:Fact; r:gives {(2 4 6 3) list:quicksort (2 3 4 6)}] + [ a r:Fact; r:gives {(2 3 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3286 - skolem:lemma3287 - [ a r:Fact; r:gives {(1 2 4 6) list:reverse (6 4 2 1)}] - skolem:lemma2486 - skolem:lemma2487 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2461]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1246]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1464 a r:Inference; r:gives { - 2462 :kaprekar 6174 . + 2464 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2464 math:notEqualTo 0}] + skolem:lemma2812 + [ a r:Fact; r:gives {(2 4 6 4) list:quicksort (2 4 4 6)}] + [ a r:Fact; r:gives {(2 4 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3288 - skolem:lemma3289 - [ a r:Fact; r:gives {(2 2 4 6) list:reverse (6 4 2 2)}] - skolem:lemma2757 - skolem:lemma2758 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2462]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2246]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1465 a r:Inference; r:gives { - 2463 :kaprekar 6174 . + 2465 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2465 math:notEqualTo 0}] + skolem:lemma2813 + [ a r:Fact; r:gives {(2 4 6 5) list:quicksort (2 4 5 6)}] + [ a r:Fact; r:gives {(2 4 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3290 - skolem:lemma3291 - [ a r:Fact; r:gives {(2 3 4 6) list:reverse (6 4 3 2)}] - skolem:lemma3012 - skolem:lemma3013 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2463]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2346]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1466 a r:Inference; r:gives { - 2464 :kaprekar 6174 . + 2466 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2466 math:notEqualTo 0}] + skolem:lemma2814 + [ a r:Fact; r:gives {(2 4 6 6) list:quicksort (2 4 6 6)}] + [ a r:Fact; r:gives {(2 4 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3292 - skolem:lemma3293 - [ a r:Fact; r:gives {(2 4 4 6) list:reverse (6 4 4 2)}] - skolem:lemma3242 - skolem:lemma3243 - [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2464]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2446]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1467 a r:Inference; r:gives { - 2465 :kaprekar 6174 . + 2467 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2467 math:notEqualTo 0}] + skolem:lemma2817 + [ a r:Fact; r:gives {(2 4 6 7) list:quicksort (2 4 6 7)}] + [ a r:Fact; r:gives {(2 4 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3294 - skolem:lemma3295 - [ a r:Fact; r:gives {(2 4 5 6) list:reverse (6 5 4 2)}] - skolem:lemma3272 - skolem:lemma3273 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2465]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2456]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1468 a r:Inference; r:gives { - 2466 :kaprekar 6174 . + 2468 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2468 math:notEqualTo 0}] + skolem:lemma2820 + [ a r:Fact; r:gives {(2 4 6 8) list:quicksort (2 4 6 8)}] + [ a r:Fact; r:gives {(2 4 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3296 - skolem:lemma3297 - [ a r:Fact; r:gives {(2 4 6 6) list:reverse (6 6 4 2)}] - skolem:lemma3298 - skolem:lemma3299 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2466]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2466]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1469 a r:Inference; r:gives { - 2467 :kaprekar 6174 . + 2469 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2469 math:notEqualTo 0}] + skolem:lemma2823 + [ a r:Fact; r:gives {(2 4 6 9) list:quicksort (2 4 6 9)}] + [ a r:Fact; r:gives {(2 4 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3300 - skolem:lemma3301 - [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] - skolem:lemma3302 - skolem:lemma3303 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2467]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1470 a r:Inference; r:gives { - 2468 :kaprekar 6174 . + 2470 :kaprekar (0 5). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2470 math:notEqualTo 0}] + skolem:lemma2826 + [ a r:Fact; r:gives {(2 4 7 0) list:quicksort (0 2 4 7)}] + [ a r:Fact; r:gives {(0 2 4 7) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2468]; - r:rule skolem:lemma2032. + 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. skolem:lemma1471 a r:Inference; r:gives { - 2469 :kaprekar 6174 . + 2471 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2471 math:notEqualTo 0}] + skolem:lemma2827 + [ a r:Fact; r:gives {(2 4 7 1) list:quicksort (1 2 4 7)}] + [ a r:Fact; r:gives {(1 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3304 - skolem:lemma3305 - [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] - skolem:lemma3306 - skolem:lemma3307 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2469]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1472 a r:Inference; r:gives { - 2470 :kaprekar 6174 . + 2472 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2472 math:notEqualTo 0}] + skolem:lemma2828 + [ a r:Fact; r:gives {(2 4 7 2) list:quicksort (2 2 4 7)}] + [ a r:Fact; r:gives {(2 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3308 - skolem:lemma3309 - [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] - skolem:lemma2187 - skolem:lemma2188 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2470]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 247]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1473 a r:Inference; r:gives { - 2471 :kaprekar 6174 . + 2473 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2473 math:notEqualTo 0}] + skolem:lemma2829 + [ a r:Fact; r:gives {(2 4 7 3) list:quicksort (2 3 4 7)}] + [ a r:Fact; r:gives {(2 3 4 7) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2471]; - r:rule skolem:lemma2032. + 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. skolem:lemma1474 a r:Inference; r:gives { - 2472 :kaprekar 6174 . + 2474 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2474 math:notEqualTo 0}] + skolem:lemma2830 + [ a r:Fact; r:gives {(2 4 7 4) list:quicksort (2 4 4 7)}] + [ a r:Fact; r:gives {(2 4 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3310 - skolem:lemma3311 - [ a r:Fact; r:gives {(2 2 4 7) list:reverse (7 4 2 2)}] - skolem:lemma2761 - skolem:lemma2762 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2472]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2247]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1475 a r:Inference; r:gives { - 2473 :kaprekar 6174 . + 2475 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2475 math:notEqualTo 0}] + skolem:lemma2831 + [ a r:Fact; r:gives {(2 4 7 5) list:quicksort (2 4 5 7)}] + [ a r:Fact; r:gives {(2 4 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3312 - skolem:lemma3313 - [ a r:Fact; r:gives {(2 3 4 7) list:reverse (7 4 3 2)}] - skolem:lemma3016 - skolem:lemma3017 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2473]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2347]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1476 a r:Inference; r:gives { - 2474 :kaprekar 6174 . + 2476 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2476 math:notEqualTo 0}] + skolem:lemma2832 + [ a r:Fact; r:gives {(2 4 7 6) list:quicksort (2 4 6 7)}] + [ a r:Fact; r:gives {(2 4 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3314 - skolem:lemma3315 - [ a r:Fact; r:gives {(2 4 4 7) list:reverse (7 4 4 2)}] - skolem:lemma3246 - skolem:lemma3247 - [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2474]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2447]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1477 a r:Inference; r:gives { - 2475 :kaprekar 6174 . + 2477 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2477 math:notEqualTo 0}] + skolem:lemma2833 + [ a r:Fact; r:gives {(2 4 7 7) list:quicksort (2 4 7 7)}] + [ a r:Fact; r:gives {(2 4 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3316 - skolem:lemma3317 - [ a r:Fact; r:gives {(2 4 5 7) list:reverse (7 5 4 2)}] - skolem:lemma3276 - skolem:lemma3277 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2475]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2457]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1478 a r:Inference; r:gives { - 2476 :kaprekar 6174 . + 2478 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2478 math:notEqualTo 0}] + skolem:lemma2836 + [ a r:Fact; r:gives {(2 4 7 8) list:quicksort (2 4 7 8)}] + [ a r:Fact; r:gives {(2 4 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3318 - skolem:lemma3319 - [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] - skolem:lemma3302 - skolem:lemma3303 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2476]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2467]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1479 a r:Inference; r:gives { - 2477 :kaprekar 6174 . + 2479 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2479 math:notEqualTo 0}] + skolem:lemma2839 + [ a r:Fact; r:gives {(2 4 7 9) list:quicksort (2 4 7 9)}] + [ a r:Fact; r:gives {(2 4 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3320 - skolem:lemma3321 - [ a r:Fact; r:gives {(2 4 7 7) list:reverse (7 7 4 2)}] - skolem:lemma3322 - skolem:lemma3323 - [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2477]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2477]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1480 a r:Inference; r:gives { - 2478 :kaprekar 6174 . + 2480 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2480 math:notEqualTo 0}] + skolem:lemma2842 + [ a r:Fact; r:gives {(2 4 8 0) list:quicksort (0 2 4 8)}] + [ a r:Fact; r:gives {(0 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3324 - skolem:lemma3325 - [ a r:Fact; r:gives {(2 4 7 8) list:reverse (8 7 4 2)}] - skolem:lemma3326 - skolem:lemma3327 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2478]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1481 a r:Inference; r:gives { - 2479 :kaprekar 6174 . + 2481 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2481 math:notEqualTo 0}] + skolem:lemma2843 + [ a r:Fact; r:gives {(2 4 8 1) list:quicksort (1 2 4 8)}] + [ a r:Fact; r:gives {(1 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3328 - skolem:lemma3329 - [ a r:Fact; r:gives {(2 4 7 9) list:reverse (9 7 4 2)}] - skolem:lemma3330 - skolem:lemma3331 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2479]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1482 a r:Inference; r:gives { - 2480 :kaprekar 6174 . + 2482 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2482 math:notEqualTo 0}] + skolem:lemma2844 + [ a r:Fact; r:gives {(2 4 8 2) list:quicksort (2 2 4 8)}] + [ a r:Fact; r:gives {(2 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3332 - skolem:lemma3333 - [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] - skolem:lemma2191 - skolem:lemma2192 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2480]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 248]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1483 a r:Inference; r:gives { - 2481 :kaprekar 6174 . + 2483 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2483 math:notEqualTo 0}] + skolem:lemma2845 + [ a r:Fact; r:gives {(2 4 8 3) list:quicksort (2 3 4 8)}] + [ a r:Fact; r:gives {(2 3 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3334 - skolem:lemma3335 - [ a r:Fact; r:gives {(1 2 4 8) list:reverse (8 4 2 1)}] - skolem:lemma2490 - skolem:lemma2491 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2481]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1248]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1484 a r:Inference; r:gives { - 2482 :kaprekar 6174 . + 2484 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2484 math:notEqualTo 0}] + skolem:lemma2846 + [ a r:Fact; r:gives {(2 4 8 4) list:quicksort (2 4 4 8)}] + [ a r:Fact; r:gives {(2 4 4 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2482]; - r:rule skolem:lemma2032. + 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. skolem:lemma1485 a r:Inference; r:gives { - 2483 :kaprekar 6174 . + 2485 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2485 math:notEqualTo 0}] + skolem:lemma2847 + [ a r:Fact; r:gives {(2 4 8 5) list:quicksort (2 4 5 8)}] + [ a r:Fact; r:gives {(2 4 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3336 - skolem:lemma3337 - [ a r:Fact; r:gives {(2 3 4 8) list:reverse (8 4 3 2)}] - skolem:lemma3020 - skolem:lemma3021 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2483]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2348]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1486 a r:Inference; r:gives { - 2484 :kaprekar 6174 . + 2486 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2486 math:notEqualTo 0}] + skolem:lemma2848 + [ a r:Fact; r:gives {(2 4 8 6) list:quicksort (2 4 6 8)}] + [ a r:Fact; r:gives {(2 4 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3338 - skolem:lemma3339 - [ a r:Fact; r:gives {(2 4 4 8) list:reverse (8 4 4 2)}] - skolem:lemma3250 - skolem:lemma3251 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2484]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2448]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1487 a r:Inference; r:gives { - 2485 :kaprekar 6174 . + 2487 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2487 math:notEqualTo 0}] + skolem:lemma2849 + [ a r:Fact; r:gives {(2 4 8 7) list:quicksort (2 4 7 8)}] + [ a r:Fact; r:gives {(2 4 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3340 - skolem:lemma3341 - [ a r:Fact; r:gives {(2 4 5 8) list:reverse (8 5 4 2)}] - skolem:lemma3280 - skolem:lemma3281 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2485]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2458]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1488 a r:Inference; r:gives { - 2486 :kaprekar 6174 . + 2488 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2488 math:notEqualTo 0}] + skolem:lemma2850 + [ a r:Fact; r:gives {(2 4 8 8) list:quicksort (2 4 8 8)}] + [ a r:Fact; r:gives {(2 4 8 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2486]; - r:rule skolem:lemma2032. + 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. skolem:lemma1489 a r:Inference; r:gives { - 2487 :kaprekar 6174 . + 2489 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2489 math:notEqualTo 0}] + skolem:lemma2853 + [ a r:Fact; r:gives {(2 4 8 9) list:quicksort (2 4 8 9)}] + [ a r:Fact; r:gives {(2 4 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3342 - skolem:lemma3343 - [ a r:Fact; r:gives {(2 4 7 8) list:reverse (8 7 4 2)}] - skolem:lemma3326 - skolem:lemma3327 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2487]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2478]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1490 a r:Inference; r:gives { - 2488 :kaprekar 6174 . + 2490 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2490 math:notEqualTo 0}] + skolem:lemma2856 + [ a r:Fact; r:gives {(2 4 9 0) list:quicksort (0 2 4 9)}] + [ a r:Fact; r:gives {(0 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3344 - skolem:lemma3345 - [ a r:Fact; r:gives {(2 4 8 8) list:reverse (8 8 4 2)}] - skolem:lemma3346 - skolem:lemma3347 - [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2488]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2488]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1491 a r:Inference; r:gives { - 2489 :kaprekar 6174 . + 2491 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2491 math:notEqualTo 0}] + skolem:lemma2857 + [ a r:Fact; r:gives {(2 4 9 1) list:quicksort (1 2 4 9)}] + [ a r:Fact; r:gives {(1 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3348 - skolem:lemma3349 - [ a r:Fact; r:gives {(2 4 8 9) list:reverse (9 8 4 2)}] - skolem:lemma3350 - skolem:lemma3351 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2489]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1492 a r:Inference; r:gives { - 2490 :kaprekar 6174 . + 2492 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2492 math:notEqualTo 0}] + skolem:lemma2858 + [ a r:Fact; r:gives {(2 4 9 2) list:quicksort (2 2 4 9)}] + [ a r:Fact; r:gives {(2 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3352 - skolem:lemma3353 - [ a r:Fact; r:gives {(0 2 4 9) list:reverse (9 4 2 0)}] - skolem:lemma2195 - skolem:lemma2196 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2490]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 249]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1493 a r:Inference; r:gives { - 2491 :kaprekar 6174 . + 2493 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2493 math:notEqualTo 0}] + skolem:lemma2859 + [ a r:Fact; r:gives {(2 4 9 3) list:quicksort (2 3 4 9)}] + [ a r:Fact; r:gives {(2 3 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3354 - skolem:lemma3355 - [ a r:Fact; r:gives {(1 2 4 9) list:reverse (9 4 2 1)}] - skolem:lemma2494 - skolem:lemma2495 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2491]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1249]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1494 a r:Inference; r:gives { - 2492 :kaprekar 6174 . + 2494 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3356 - skolem:lemma3357 - [ a r:Fact; r:gives {(2 2 4 9) list:reverse (9 4 2 2)}] - skolem:lemma2765 - skolem:lemma2766 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ a r:Fact; r:gives {2494 math:notEqualTo 0}] + skolem:lemma2860 + [ a r:Fact; r:gives {(2 4 9 4) list:quicksort (2 4 4 9)}] + [ a r:Fact; r:gives {(2 4 4 9) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2492]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2249]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1495 a r:Inference; r:gives { - 2493 :kaprekar 6174 . + 2495 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2495 math:notEqualTo 0}] + skolem:lemma2861 + [ a r:Fact; r:gives {(2 4 9 5) list:quicksort (2 4 5 9)}] + [ a r:Fact; r:gives {(2 4 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3358 - skolem:lemma3359 - [ a r:Fact; r:gives {(2 3 4 9) list:reverse (9 4 3 2)}] - skolem:lemma3024 - skolem:lemma3025 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2493]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2349]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1496 a r:Inference; r:gives { - 2494 :kaprekar 6174 . + 2496 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2496 math:notEqualTo 0}] + skolem:lemma2862 + [ a r:Fact; r:gives {(2 4 9 6) list:quicksort (2 4 6 9)}] + [ a r:Fact; r:gives {(2 4 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3360 - skolem:lemma3361 - [ a r:Fact; r:gives {(2 4 4 9) list:reverse (9 4 4 2)}] - skolem:lemma3254 - skolem:lemma3255 - [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2494]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2449]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1497 a r:Inference; r:gives { - 2495 :kaprekar 6174 . + 2497 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2497 math:notEqualTo 0}] + skolem:lemma2863 + [ a r:Fact; r:gives {(2 4 9 7) list:quicksort (2 4 7 9)}] + [ a r:Fact; r:gives {(2 4 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3362 - skolem:lemma3363 - [ a r:Fact; r:gives {(2 4 5 9) list:reverse (9 5 4 2)}] - skolem:lemma3284 - skolem:lemma3285 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2495]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2459]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1498 a r:Inference; r:gives { - 2496 :kaprekar 6174 . + 2498 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2498 math:notEqualTo 0}] + skolem:lemma2864 + [ a r:Fact; r:gives {(2 4 9 8) list:quicksort (2 4 8 9)}] + [ a r:Fact; r:gives {(2 4 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3364 - skolem:lemma3365 - [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] - skolem:lemma3306 - skolem:lemma3307 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2496]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2469]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1499 a r:Inference; r:gives { - 2497 :kaprekar 6174 . + 2499 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2499 math:notEqualTo 0}] + skolem:lemma2865 + [ a r:Fact; r:gives {(2 4 9 9) list:quicksort (2 4 9 9)}] + [ a r:Fact; r:gives {(2 4 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3366 - skolem:lemma3367 - [ a r:Fact; r:gives {(2 4 7 9) list:reverse (9 7 4 2)}] - skolem:lemma3330 - skolem:lemma3331 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2497]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2479]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1500 a r:Inference; r:gives { - 2498 :kaprekar 6174 . + 2500 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2500 math:notEqualTo 0}] + skolem:lemma2868 + [ a r:Fact; r:gives {(2 5 0 0) list:quicksort (0 0 2 5)}] + [ a r:Fact; r:gives {(0 0 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3368 - skolem:lemma3369 - [ a r:Fact; r:gives {(2 4 8 9) list:reverse (9 8 4 2)}] - skolem:lemma3350 - skolem:lemma3351 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2498]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2489]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1501 a r:Inference; r:gives { - 2499 :kaprekar 6174 . + 2501 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2501 math:notEqualTo 0}] + skolem:lemma2869 + [ a r:Fact; r:gives {(2 5 0 1) list:quicksort (0 1 2 5)}] + [ a r:Fact; r:gives {(0 1 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3370 - skolem:lemma3371 - [ a r:Fact; r:gives {(2 4 9 9) list:reverse (9 9 4 2)}] - skolem:lemma3372 - skolem:lemma3373 - [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2499]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2499]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1502 a r:Inference; r:gives { - 2500 :kaprekar 6174 . + 2502 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2502 math:notEqualTo 0}] + skolem:lemma2870 + [ a r:Fact; r:gives {(2 5 0 2) list:quicksort (0 2 2 5)}] + [ a r:Fact; r:gives {(0 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3374 - skolem:lemma3375 - [ a r:Fact; r:gives {(0 0 2 5) list:reverse (5 2 0 0)}] - skolem:lemma2029 - skolem:lemma2030 - [ a r:Fact; r:gives {(5200 25) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 25]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1503 a r:Inference; r:gives { - 2501 :kaprekar 6174 . + 2503 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2503 math:notEqualTo 0}] + skolem:lemma2871 + [ a r:Fact; r:gives {(2 5 0 3) list:quicksort (0 2 3 5)}] + [ a r:Fact; r:gives {(0 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3376 - skolem:lemma3377 - [ a r:Fact; r:gives {(0 1 2 5) list:reverse (5 2 1 0)}] - skolem:lemma2070 - skolem:lemma2071 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2501]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1504 a r:Inference; r:gives { - 2502 :kaprekar 6174 . + 2504 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2504 math:notEqualTo 0}] + skolem:lemma2872 + [ a r:Fact; r:gives {(2 5 0 4) list:quicksort (0 2 4 5)}] + [ a r:Fact; r:gives {(0 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3378 - skolem:lemma3379 - [ a r:Fact; r:gives {(0 2 2 5) list:reverse (5 2 2 0)}] - skolem:lemma2112 - skolem:lemma2113 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2502]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 225]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1505 a r:Inference; r:gives { - 2503 :kaprekar 6174 . + 2505 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2505 math:notEqualTo 0}] + skolem:lemma2873 + [ a r:Fact; r:gives {(2 5 0 5) list:quicksort (0 2 5 5)}] + [ a r:Fact; r:gives {(0 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3380 - skolem:lemma3381 - [ a r:Fact; r:gives {(0 2 3 5) list:reverse (5 3 2 0)}] - skolem:lemma2151 - skolem:lemma2152 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2503]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 235]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1506 a r:Inference; r:gives { - 2504 :kaprekar 6174 . + 2506 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2506 math:notEqualTo 0}] + skolem:lemma2874 + [ a r:Fact; r:gives {(2 5 0 6) list:quicksort (0 2 5 6)}] + [ a r:Fact; r:gives {(0 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3382 - skolem:lemma3383 - [ a r:Fact; r:gives {(0 2 4 5) list:reverse (5 4 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2504]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 245]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1507 a r:Inference; r:gives { - 2505 :kaprekar 6174 . + 2507 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2507 math:notEqualTo 0}] + skolem:lemma2875 + [ a r:Fact; r:gives {(2 5 0 7) list:quicksort (0 2 5 7)}] + [ a r:Fact; r:gives {(0 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3384 - skolem:lemma3385 - [ a r:Fact; r:gives {(0 2 5 5) list:reverse (5 5 2 0)}] - skolem:lemma2209 - skolem:lemma2210 - [ a r:Fact; r:gives {(5520 255) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2505]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 255]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1508 a r:Inference; r:gives { - 2506 :kaprekar 6174 . + 2508 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2508 math:notEqualTo 0}] + skolem:lemma2876 + [ a r:Fact; r:gives {(2 5 0 8) list:quicksort (0 2 5 8)}] + [ a r:Fact; r:gives {(0 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3386 - skolem:lemma3387 - [ a r:Fact; r:gives {(0 2 5 6) list:reverse (6 5 2 0)}] - skolem:lemma2214 - skolem:lemma2215 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2506]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1509 a r:Inference; r:gives { - 2507 :kaprekar 6174 . + 2509 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2509 math:notEqualTo 0}] + skolem:lemma2877 + [ a r:Fact; r:gives {(2 5 0 9) list:quicksort (0 2 5 9)}] + [ a r:Fact; r:gives {(0 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3388 - skolem:lemma3389 - [ a r:Fact; r:gives {(0 2 5 7) list:reverse (7 5 2 0)}] - skolem:lemma2219 - skolem:lemma2220 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2507]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 257]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1510 a r:Inference; r:gives { - 2508 :kaprekar 6174 . + 2510 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2510 math:notEqualTo 0}] + skolem:lemma2878 + [ a r:Fact; r:gives {(2 5 1 0) list:quicksort (0 1 2 5)}] + [ a r:Fact; r:gives {(0 1 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3390 - skolem:lemma3391 - [ a r:Fact; r:gives {(0 2 5 8) list:reverse (8 5 2 0)}] - skolem:lemma2224 - skolem:lemma2225 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2508]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 258]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1511 a r:Inference; r:gives { - 2509 :kaprekar 6174 . + 2511 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2511 math:notEqualTo 0}] + skolem:lemma2879 + [ a r:Fact; r:gives {(2 5 1 1) list:quicksort (1 1 2 5)}] + [ a r:Fact; r:gives {(1 1 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3392 - skolem:lemma3393 - [ a r:Fact; r:gives {(0 2 5 9) list:reverse (9 5 2 0)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {9261 math:notEqualTo 6174}] - skolem:lemma2231 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2509]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 259]; - 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_8"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1512 a r:Inference; r:gives { - 2510 :kaprekar 6174 . + 2512 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2512 math:notEqualTo 0}] + skolem:lemma2880 + [ a r:Fact; r:gives {(2 5 1 2) list:quicksort (1 2 2 5)}] + [ a r:Fact; r:gives {(1 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3394 - skolem:lemma3395 - [ a r:Fact; r:gives {(0 1 2 5) list:reverse (5 2 1 0)}] - skolem:lemma2070 - skolem:lemma2071 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2510]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 125]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1513 a r:Inference; r:gives { - 2511 :kaprekar 6174 . + 2513 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2513 math:notEqualTo 0}] + skolem:lemma2881 + [ a r:Fact; r:gives {(2 5 1 3) list:quicksort (1 2 3 5)}] + [ a r:Fact; r:gives {(1 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3396 - skolem:lemma3397 - [ a r:Fact; r:gives {(1 1 2 5) list:reverse (5 2 1 1)}] - skolem:lemma2380 - skolem:lemma2381 - [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2511]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1125]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1514 a r:Inference; r:gives { - 2512 :kaprekar 6174 . + 2514 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2514 math:notEqualTo 0}] + skolem:lemma2882 + [ a r:Fact; r:gives {(2 5 1 4) list:quicksort (1 2 4 5)}] + [ a r:Fact; r:gives {(1 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3398 - skolem:lemma3399 - [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] - skolem:lemma2416 - skolem:lemma2417 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2512]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1225]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1515 a r:Inference; r:gives { - 2513 :kaprekar 6174 . + 2515 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2515 math:notEqualTo 0}] + skolem:lemma2883 + [ a r:Fact; r:gives {(2 5 1 5) list:quicksort (1 2 5 5)}] + [ a r:Fact; r:gives {(1 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3400 - skolem:lemma3401 - [ a r:Fact; r:gives {(1 2 3 5) list:reverse (5 3 2 1)}] - skolem:lemma2450 - skolem:lemma2451 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2513]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1235]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1516 a r:Inference; r:gives { - 2514 :kaprekar 6174 . + 2516 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2516 math:notEqualTo 0}] + skolem:lemma2884 + [ a r:Fact; r:gives {(2 5 1 6) list:quicksort (1 2 5 6)}] + [ a r:Fact; r:gives {(1 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3402 - skolem:lemma3403 - [ a r:Fact; r:gives {(1 2 4 5) list:reverse (5 4 2 1)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2514]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1245]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1517 a r:Inference; r:gives { - 2515 :kaprekar 6174 . + 2517 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2517 math:notEqualTo 0}] + skolem:lemma2885 + [ a r:Fact; r:gives {(2 5 1 7) list:quicksort (1 2 5 7)}] + [ a r:Fact; r:gives {(1 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3404 - skolem:lemma3405 - [ a r:Fact; r:gives {(1 2 5 5) list:reverse (5 5 2 1)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2515]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1255]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1518 a r:Inference; r:gives { - 2516 :kaprekar 6174 . + 2518 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2518 math:notEqualTo 0}] + skolem:lemma2886 + [ a r:Fact; r:gives {(2 5 1 8) list:quicksort (1 2 5 8)}] + [ a r:Fact; r:gives {(1 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3406 - skolem:lemma3407 - [ a r:Fact; r:gives {(1 2 5 6) list:reverse (6 5 2 1)}] - skolem:lemma2513 - skolem:lemma2514 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2516]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1256]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1519 a r:Inference; r:gives { - 2517 :kaprekar 6174 . + 2519 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2519 math:notEqualTo 0}] + skolem:lemma2887 + [ a r:Fact; r:gives {(2 5 1 9) list:quicksort (1 2 5 9)}] + [ a r:Fact; r:gives {(1 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3408 - skolem:lemma3409 - [ a r:Fact; r:gives {(1 2 5 7) list:reverse (7 5 2 1)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2517]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1257]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1520 a r:Inference; r:gives { - 2518 :kaprekar 6174 . + 2520 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2520 math:notEqualTo 0}] + skolem:lemma2888 + [ a r:Fact; r:gives {(2 5 2 0) list:quicksort (0 2 2 5)}] + [ a r:Fact; r:gives {(0 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3410 - skolem:lemma3411 - [ a r:Fact; r:gives {(1 2 5 8) list:reverse (8 5 2 1)}] - skolem:lemma2521 - skolem:lemma2522 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2518]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1258]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1521 a r:Inference; r:gives { - 2519 :kaprekar 6174 . + 2521 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2521 math:notEqualTo 0}] + skolem:lemma2889 + [ a r:Fact; r:gives {(2 5 2 1) list:quicksort (1 2 2 5)}] + [ a r:Fact; r:gives {(1 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3412 - skolem:lemma3413 - [ a r:Fact; r:gives {(1 2 5 9) list:reverse (9 5 2 1)}] - skolem:lemma2525 - skolem:lemma2526 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2519]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1259]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1522 a r:Inference; r:gives { - 2520 :kaprekar 6174 . + 2522 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2522 math:notEqualTo 0}] + skolem:lemma2890 + [ a r:Fact; r:gives {(2 5 2 2) list:quicksort (2 2 2 5)}] + [ a r:Fact; r:gives {(2 2 2 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3414 - skolem:lemma3415 - [ a r:Fact; r:gives {(0 2 2 5) list:reverse (5 2 2 0)}] - skolem:lemma2112 - skolem:lemma2113 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 225]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1523 a r:Inference; r:gives { - 2521 :kaprekar 6174 . + 2523 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2523 math:notEqualTo 0}] + skolem:lemma2891 + [ a r:Fact; r:gives {(2 5 2 3) list:quicksort (2 2 3 5)}] + [ a r:Fact; r:gives {(2 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3416 - skolem:lemma3417 - [ a r:Fact; r:gives {(1 2 2 5) list:reverse (5 2 2 1)}] - skolem:lemma2416 - skolem:lemma2417 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1225]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1524 a r:Inference; r:gives { - 2522 :kaprekar 6174 . + 2524 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2524 math:notEqualTo 0}] + skolem:lemma2892 + [ a r:Fact; r:gives {(2 5 2 4) list:quicksort (2 2 4 5)}] + [ a r:Fact; r:gives {(2 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3418 - skolem:lemma3419 - [ a r:Fact; r:gives {(2 2 2 5) list:reverse (5 2 2 2)}] - skolem:lemma2687 - skolem:lemma2688 - [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2225]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1525 a r:Inference; r:gives { - 2523 :kaprekar 6174 . + 2525 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2525 math:notEqualTo 0}] + skolem:lemma2893 + [ a r:Fact; r:gives {(2 5 2 5) list:quicksort (2 2 5 5)}] + [ a r:Fact; r:gives {(2 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3420 - skolem:lemma3421 - [ a r:Fact; r:gives {(2 2 3 5) list:reverse (5 3 2 2)}] - skolem:lemma2721 - skolem:lemma2722 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2523]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2235]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1526 a r:Inference; r:gives { - 2524 :kaprekar 6174 . + 2526 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2526 math:notEqualTo 0}] + skolem:lemma2894 + [ a r:Fact; r:gives {(2 5 2 6) list:quicksort (2 2 5 6)}] + [ a r:Fact; r:gives {(2 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3422 - skolem:lemma3423 - [ a r:Fact; r:gives {(2 2 4 5) list:reverse (5 4 2 2)}] - skolem:lemma2753 - skolem:lemma2754 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2524]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2245]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1527 a r:Inference; r:gives { - 2525 :kaprekar 6174 . + 2527 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2527 math:notEqualTo 0}] + skolem:lemma2895 + [ a r:Fact; r:gives {(2 5 2 7) list:quicksort (2 2 5 7)}] + [ a r:Fact; r:gives {(2 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3424 - skolem:lemma3425 - [ a r:Fact; r:gives {(2 2 5 5) list:reverse (5 5 2 2)}] - skolem:lemma2779 - skolem:lemma2780 - [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] - [ a r:Fact; r:gives {3267 math:notEqualTo 6174}] - skolem:lemma2781 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2525]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2255]; - 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_8"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1528 a r:Inference; r:gives { - 2526 :kaprekar 6174 . + 2528 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2528 math:notEqualTo 0}] + skolem:lemma2896 + [ a r:Fact; r:gives {(2 5 2 8) list:quicksort (2 2 5 8)}] + [ a r:Fact; r:gives {(2 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3426 - skolem:lemma3427 - [ a r:Fact; r:gives {(2 2 5 6) list:reverse (6 5 2 2)}] - skolem:lemma2784 - skolem:lemma2785 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2526]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2256]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1529 a r:Inference; r:gives { - 2527 :kaprekar 6174 . + 2529 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2529 math:notEqualTo 0}] + skolem:lemma2897 + [ a r:Fact; r:gives {(2 5 2 9) list:quicksort (2 2 5 9)}] + [ a r:Fact; r:gives {(2 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3428 - skolem:lemma3429 - [ a r:Fact; r:gives {(2 2 5 7) list:reverse (7 5 2 2)}] - skolem:lemma2788 - skolem:lemma2789 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2527]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2257]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1530 a r:Inference; r:gives { - 2528 :kaprekar 6174 . + 2530 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2530 math:notEqualTo 0}] + skolem:lemma2898 + [ a r:Fact; r:gives {(2 5 3 0) list:quicksort (0 2 3 5)}] + [ a r:Fact; r:gives {(0 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3430 - skolem:lemma3431 - [ a r:Fact; r:gives {(2 2 5 8) list:reverse (8 5 2 2)}] - skolem:lemma2792 - skolem:lemma2793 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2528]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2258]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1531 a r:Inference; r:gives { - 2529 :kaprekar 6174 . + 2531 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2531 math:notEqualTo 0}] + skolem:lemma2899 + [ a r:Fact; r:gives {(2 5 3 1) list:quicksort (1 2 3 5)}] + [ a r:Fact; r:gives {(1 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3432 - skolem:lemma3433 - [ a r:Fact; r:gives {(2 2 5 9) list:reverse (9 5 2 2)}] - skolem:lemma2796 - skolem:lemma2797 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2529]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2259]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1532 a r:Inference; r:gives { - 2530 :kaprekar 6174 . + 2532 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2532 math:notEqualTo 0}] + skolem:lemma2900 + [ a r:Fact; r:gives {(2 5 3 2) list:quicksort (2 2 3 5)}] + [ a r:Fact; r:gives {(2 2 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3434 - skolem:lemma3435 - [ a r:Fact; r:gives {(0 2 3 5) list:reverse (5 3 2 0)}] - skolem:lemma2151 - skolem:lemma2152 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2530]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 235]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1533 a r:Inference; r:gives { - 2531 :kaprekar 6174 . + 2533 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2533 math:notEqualTo 0}] + skolem:lemma2901 + [ a r:Fact; r:gives {(2 5 3 3) list:quicksort (2 3 3 5)}] + [ a r:Fact; r:gives {(2 3 3 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3436 - skolem:lemma3437 - [ a r:Fact; r:gives {(1 2 3 5) list:reverse (5 3 2 1)}] - skolem:lemma2450 - skolem:lemma2451 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1235]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1534 a r:Inference; r:gives { - 2532 :kaprekar 6174 . + 2534 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2534 math:notEqualTo 0}] + skolem:lemma2902 + [ a r:Fact; r:gives {(2 5 3 4) list:quicksort (2 3 4 5)}] + [ a r:Fact; r:gives {(2 3 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3438 - skolem:lemma3439 - [ a r:Fact; r:gives {(2 2 3 5) list:reverse (5 3 2 2)}] - skolem:lemma2721 - skolem:lemma2722 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2235]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1535 a r:Inference; r:gives { - 2533 :kaprekar 6174 . + 2535 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2535 math:notEqualTo 0}] + skolem:lemma2903 + [ a r:Fact; r:gives {(2 5 3 5) list:quicksort (2 3 5 5)}] + [ a r:Fact; r:gives {(2 3 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3440 - skolem:lemma3441 - [ a r:Fact; r:gives {(2 3 3 5) list:reverse (5 3 3 2)}] - skolem:lemma2976 - skolem:lemma2977 - [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2335]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1536 a r:Inference; r:gives { - 2534 :kaprekar 6174 . + 2536 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2536 math:notEqualTo 0}] + skolem:lemma2904 + [ a r:Fact; r:gives {(2 5 3 6) list:quicksort (2 3 5 6)}] + [ a r:Fact; r:gives {(2 3 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3442 - skolem:lemma3443 - [ a r:Fact; r:gives {(2 3 4 5) list:reverse (5 4 3 2)}] - skolem:lemma3008 - skolem:lemma3009 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2345]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1537 a r:Inference; r:gives { - 2535 :kaprekar 6174 . + 2537 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2537 math:notEqualTo 0}] + skolem:lemma2905 + [ a r:Fact; r:gives {(2 5 3 7) list:quicksort (2 3 5 7)}] + [ a r:Fact; r:gives {(2 3 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3444 - skolem:lemma3445 - [ a r:Fact; r:gives {(2 3 5 5) list:reverse (5 5 3 2)}] - skolem:lemma3038 - skolem:lemma3039 - [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2535]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2355]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1538 a r:Inference; r:gives { - 2536 :kaprekar 6174 . + 2538 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2538 math:notEqualTo 0}] + skolem:lemma2906 + [ a r:Fact; r:gives {(2 5 3 8) list:quicksort (2 3 5 8)}] + [ a r:Fact; r:gives {(2 3 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3446 - skolem:lemma3447 - [ a r:Fact; r:gives {(2 3 5 6) list:reverse (6 5 3 2)}] - skolem:lemma3042 - skolem:lemma3043 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2536]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2356]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1539 a r:Inference; r:gives { - 2537 :kaprekar 6174 . + 2539 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2539 math:notEqualTo 0}] + skolem:lemma2907 + [ a r:Fact; r:gives {(2 5 3 9) list:quicksort (2 3 5 9)}] + [ a r:Fact; r:gives {(2 3 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3448 - skolem:lemma3449 - [ a r:Fact; r:gives {(2 3 5 7) list:reverse (7 5 3 2)}] - skolem:lemma3046 - skolem:lemma3047 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2537]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2357]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1540 a r:Inference; r:gives { - 2538 :kaprekar 6174 . + 2540 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2540 math:notEqualTo 0}] + skolem:lemma2908 + [ a r:Fact; r:gives {(2 5 4 0) list:quicksort (0 2 4 5)}] + [ a r:Fact; r:gives {(0 2 4 5) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2538]; - r:rule skolem:lemma2032. + 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. skolem:lemma1541 a r:Inference; r:gives { - 2539 :kaprekar 6174 . + 2541 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2541 math:notEqualTo 0}] + skolem:lemma2909 + [ a r:Fact; r:gives {(2 5 4 1) list:quicksort (1 2 4 5)}] + [ a r:Fact; r:gives {(1 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3450 - skolem:lemma3451 - [ a r:Fact; r:gives {(2 3 5 9) list:reverse (9 5 3 2)}] - skolem:lemma3050 - skolem:lemma3051 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2539]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2359]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1542 a r:Inference; r:gives { - 2540 :kaprekar 6174 . + 2542 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2542 math:notEqualTo 0}] + skolem:lemma2910 + [ a r:Fact; r:gives {(2 5 4 2) list:quicksort (2 2 4 5)}] + [ a r:Fact; r:gives {(2 2 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3452 - skolem:lemma3453 - [ a r:Fact; r:gives {(0 2 4 5) list:reverse (5 4 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2540]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 245]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1543 a r:Inference; r:gives { - 2541 :kaprekar 6174 . + 2543 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2543 math:notEqualTo 0}] + skolem:lemma2911 + [ a r:Fact; r:gives {(2 5 4 3) list:quicksort (2 3 4 5)}] + [ a r:Fact; r:gives {(2 3 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3454 - skolem:lemma3455 - [ a r:Fact; r:gives {(1 2 4 5) list:reverse (5 4 2 1)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2541]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1245]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1544 a r:Inference; r:gives { - 2542 :kaprekar 6174 . + 2544 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2544 math:notEqualTo 0}] + skolem:lemma2912 + [ a r:Fact; r:gives {(2 5 4 4) list:quicksort (2 4 4 5)}] + [ a r:Fact; r:gives {(2 4 4 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3456 - skolem:lemma3457 - [ a r:Fact; r:gives {(2 2 4 5) list:reverse (5 4 2 2)}] - skolem:lemma2753 - skolem:lemma2754 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2245]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1545 a r:Inference; r:gives { - 2543 :kaprekar 6174 . + 2545 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2545 math:notEqualTo 0}] + skolem:lemma2913 + [ a r:Fact; r:gives {(2 5 4 5) list:quicksort (2 4 5 5)}] + [ a r:Fact; r:gives {(2 4 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3458 - skolem:lemma3459 - [ a r:Fact; r:gives {(2 3 4 5) list:reverse (5 4 3 2)}] - skolem:lemma3008 - skolem:lemma3009 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2543]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2345]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1546 a r:Inference; r:gives { - 2544 :kaprekar 6174 . + 2546 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2546 math:notEqualTo 0}] + skolem:lemma2914 + [ a r:Fact; r:gives {(2 5 4 6) list:quicksort (2 4 5 6)}] + [ a r:Fact; r:gives {(2 4 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3460 - skolem:lemma3461 - [ a r:Fact; r:gives {(2 4 4 5) list:reverse (5 4 4 2)}] - skolem:lemma3238 - skolem:lemma3239 - [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2544]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2445]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1547 a r:Inference; r:gives { - 2545 :kaprekar 6174 . + 2547 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2547 math:notEqualTo 0}] + skolem:lemma2915 + [ a r:Fact; r:gives {(2 5 4 7) list:quicksort (2 4 5 7)}] + [ a r:Fact; r:gives {(2 4 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3462 - skolem:lemma3463 - [ a r:Fact; r:gives {(2 4 5 5) list:reverse (5 5 4 2)}] - skolem:lemma3268 - skolem:lemma3269 - [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2545]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2455]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1548 a r:Inference; r:gives { - 2546 :kaprekar 6174 . + 2548 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2548 math:notEqualTo 0}] + skolem:lemma2916 + [ a r:Fact; r:gives {(2 5 4 8) list:quicksort (2 4 5 8)}] + [ a r:Fact; r:gives {(2 4 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3464 - skolem:lemma3465 - [ a r:Fact; r:gives {(2 4 5 6) list:reverse (6 5 4 2)}] - skolem:lemma3272 - skolem:lemma3273 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2546]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2456]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1549 a r:Inference; r:gives { - 2547 :kaprekar 6174 . + 2549 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2549 math:notEqualTo 0}] + skolem:lemma2917 + [ a r:Fact; r:gives {(2 5 4 9) list:quicksort (2 4 5 9)}] + [ a r:Fact; r:gives {(2 4 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3466 - skolem:lemma3467 - [ a r:Fact; r:gives {(2 4 5 7) list:reverse (7 5 4 2)}] - skolem:lemma3276 - skolem:lemma3277 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2547]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2457]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1550 a r:Inference; r:gives { - 2548 :kaprekar 6174 . + 2550 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2550 math:notEqualTo 0}] + skolem:lemma2918 + [ a r:Fact; r:gives {(2 5 5 0) list:quicksort (0 2 5 5)}] + [ a r:Fact; r:gives {(0 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3468 - skolem:lemma3469 - [ a r:Fact; r:gives {(2 4 5 8) list:reverse (8 5 4 2)}] - skolem:lemma3280 - skolem:lemma3281 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2548]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2458]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1551 a r:Inference; r:gives { - 2549 :kaprekar 6174 . + 2551 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2551 math:notEqualTo 0}] + skolem:lemma2919 + [ a r:Fact; r:gives {(2 5 5 1) list:quicksort (1 2 5 5)}] + [ a r:Fact; r:gives {(1 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3470 - skolem:lemma3471 - [ a r:Fact; r:gives {(2 4 5 9) list:reverse (9 5 4 2)}] - skolem:lemma3284 - skolem:lemma3285 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2549]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2459]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1552 a r:Inference; r:gives { - 2550 :kaprekar 6174 . + 2552 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2552 math:notEqualTo 0}] + skolem:lemma2920 + [ a r:Fact; r:gives {(2 5 5 2) list:quicksort (2 2 5 5)}] + [ a r:Fact; r:gives {(2 2 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3472 - skolem:lemma3473 - [ a r:Fact; r:gives {(0 2 5 5) list:reverse (5 5 2 0)}] - skolem:lemma2209 - skolem:lemma2210 - [ a r:Fact; r:gives {(5520 255) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2550]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 255]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1553 a r:Inference; r:gives { - 2551 :kaprekar 6174 . + 2553 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2553 math:notEqualTo 0}] + skolem:lemma2921 + [ a r:Fact; r:gives {(2 5 5 3) list:quicksort (2 3 5 5)}] + [ a r:Fact; r:gives {(2 3 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3474 - skolem:lemma3475 - [ a r:Fact; r:gives {(1 2 5 5) list:reverse (5 5 2 1)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2551]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1255]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1554 a r:Inference; r:gives { - 2552 :kaprekar 6174 . + 2554 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2554 math:notEqualTo 0}] + skolem:lemma2922 + [ a r:Fact; r:gives {(2 5 5 4) list:quicksort (2 4 5 5)}] + [ a r:Fact; r:gives {(2 4 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3476 - skolem:lemma3477 - [ a r:Fact; r:gives {(2 2 5 5) list:reverse (5 5 2 2)}] - skolem:lemma2779 - skolem:lemma2780 - [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] - [ a r:Fact; r:gives {3267 math:notEqualTo 6174}] - skolem:lemma2781 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2255]; - 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_8"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1555 a r:Inference; r:gives { - 2553 :kaprekar 6174 . + 2555 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2555 math:notEqualTo 0}] + skolem:lemma2923 + [ a r:Fact; r:gives {(2 5 5 5) list:quicksort (2 5 5 5)}] + [ a r:Fact; r:gives {(2 5 5 5) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3478 - skolem:lemma3479 - [ a r:Fact; r:gives {(2 3 5 5) list:reverse (5 5 3 2)}] - skolem:lemma3038 - skolem:lemma3039 - [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] - [ a r:Fact; r:gives {3177 math:notEqualTo 6174}] - skolem:lemma2021 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2553]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2355]; - 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_8"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1556 a r:Inference; r:gives { - 2554 :kaprekar 6174 . + 2556 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2556 math:notEqualTo 0}] + skolem:lemma2926 + [ a r:Fact; r:gives {(2 5 5 6) list:quicksort (2 5 5 6)}] + [ a r:Fact; r:gives {(2 5 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3480 - skolem:lemma3481 - [ a r:Fact; r:gives {(2 4 5 5) list:reverse (5 5 4 2)}] - skolem:lemma3268 - skolem:lemma3269 - [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2554]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2455]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1557 a r:Inference; r:gives { - 2555 :kaprekar 6174 . + 2557 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2557 math:notEqualTo 0}] + skolem:lemma2929 + [ a r:Fact; r:gives {(2 5 5 7) list:quicksort (2 5 5 7)}] + [ a r:Fact; r:gives {(2 5 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3482 - skolem:lemma3483 - [ a r:Fact; r:gives {(2 5 5 5) list:reverse (5 5 5 2)}] - skolem:lemma3484 - skolem:lemma3485 - [ a r:Fact; r:gives {(5552 2555) math:difference 2997}] - [ a r:Fact; r:gives {2997 math:notEqualTo 6174}] - skolem:lemma1999 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2555]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2555]; - 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_8"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1558 a r:Inference; r:gives { - 2556 :kaprekar 6174 . + 2558 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2558 math:notEqualTo 0}] + skolem:lemma2932 + [ a r:Fact; r:gives {(2 5 5 8) list:quicksort (2 5 5 8)}] + [ a r:Fact; r:gives {(2 5 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3486 - skolem:lemma3487 - [ a r:Fact; r:gives {(2 5 5 6) list:reverse (6 5 5 2)}] - skolem:lemma3488 - skolem:lemma3489 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2556]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2556]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1559 a r:Inference; r:gives { - 2557 :kaprekar 6174 . + 2559 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2559 math:notEqualTo 0}] + skolem:lemma2935 + [ a r:Fact; r:gives {(2 5 5 9) list:quicksort (2 5 5 9)}] + [ a r:Fact; r:gives {(2 5 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3490 - skolem:lemma3491 - [ a r:Fact; r:gives {(2 5 5 7) list:reverse (7 5 5 2)}] - skolem:lemma3492 - skolem:lemma3493 - [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2557]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1560 a r:Inference; r:gives { - 2558 :kaprekar 6174 . + 2560 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2560 math:notEqualTo 0}] + skolem:lemma2938 + [ a r:Fact; r:gives {(2 5 6 0) list:quicksort (0 2 5 6)}] + [ a r:Fact; r:gives {(0 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3494 - skolem:lemma3495 - [ a r:Fact; r:gives {(2 5 5 8) list:reverse (8 5 5 2)}] - skolem:lemma3496 - skolem:lemma3497 - [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2558]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1561 a r:Inference; r:gives { - 2559 :kaprekar 6174 . + 2561 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2561 math:notEqualTo 0}] + skolem:lemma2939 + [ a r:Fact; r:gives {(2 5 6 1) list:quicksort (1 2 5 6)}] + [ a r:Fact; r:gives {(1 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3498 - skolem:lemma3499 - [ a r:Fact; r:gives {(2 5 5 9) list:reverse (9 5 5 2)}] - skolem:lemma3500 - skolem:lemma3501 - [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2559]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2559]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1562 a r:Inference; r:gives { - 2560 :kaprekar 6174 . + 2562 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2562 math:notEqualTo 0}] + skolem:lemma2940 + [ a r:Fact; r:gives {(2 5 6 2) list:quicksort (2 2 5 6)}] + [ a r:Fact; r:gives {(2 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3502 - skolem:lemma3503 - [ a r:Fact; r:gives {(0 2 5 6) list:reverse (6 5 2 0)}] - skolem:lemma2214 - skolem:lemma2215 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2560]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1563 a r:Inference; r:gives { - 2561 :kaprekar 6174 . + 2563 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2563 math:notEqualTo 0}] + skolem:lemma2941 + [ a r:Fact; r:gives {(2 5 6 3) list:quicksort (2 3 5 6)}] + [ a r:Fact; r:gives {(2 3 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3504 - skolem:lemma3505 - [ a r:Fact; r:gives {(1 2 5 6) list:reverse (6 5 2 1)}] - skolem:lemma2513 - skolem:lemma2514 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2561]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1256]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1564 a r:Inference; r:gives { - 2562 :kaprekar 6174 . + 2564 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2564 math:notEqualTo 0}] + skolem:lemma2942 + [ a r:Fact; r:gives {(2 5 6 4) list:quicksort (2 4 5 6)}] + [ a r:Fact; r:gives {(2 4 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3506 - skolem:lemma3507 - [ a r:Fact; r:gives {(2 2 5 6) list:reverse (6 5 2 2)}] - skolem:lemma2784 - skolem:lemma2785 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2562]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2256]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1565 a r:Inference; r:gives { - 2563 :kaprekar 6174 . + 2565 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2565 math:notEqualTo 0}] + skolem:lemma2943 + [ a r:Fact; r:gives {(2 5 6 5) list:quicksort (2 5 5 6)}] + [ a r:Fact; r:gives {(2 5 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3508 - skolem:lemma3509 - [ a r:Fact; r:gives {(2 3 5 6) list:reverse (6 5 3 2)}] - skolem:lemma3042 - skolem:lemma3043 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2563]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2356]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1566 a r:Inference; r:gives { - 2564 :kaprekar 6174 . + 2566 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2566 math:notEqualTo 0}] + skolem:lemma2944 + [ a r:Fact; r:gives {(2 5 6 6) list:quicksort (2 5 6 6)}] + [ a r:Fact; r:gives {(2 5 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3510 - skolem:lemma3511 - [ a r:Fact; r:gives {(2 4 5 6) list:reverse (6 5 4 2)}] - skolem:lemma3272 - skolem:lemma3273 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2564]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2456]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1567 a r:Inference; r:gives { - 2565 :kaprekar 6174 . + 2567 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2567 math:notEqualTo 0}] + skolem:lemma2947 + [ a r:Fact; r:gives {(2 5 6 7) list:quicksort (2 5 6 7)}] + [ a r:Fact; r:gives {(2 5 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3512 - skolem:lemma3513 - [ a r:Fact; r:gives {(2 5 5 6) list:reverse (6 5 5 2)}] - skolem:lemma3488 - skolem:lemma3489 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2565]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2556]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1568 a r:Inference; r:gives { - 2566 :kaprekar 6174 . + 2568 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2568 math:notEqualTo 0}] + skolem:lemma2950 + [ a r:Fact; r:gives {(2 5 6 8) list:quicksort (2 5 6 8)}] + [ a r:Fact; r:gives {(2 5 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3514 - skolem:lemma3515 - [ a r:Fact; r:gives {(2 5 6 6) list:reverse (6 6 5 2)}] - skolem:lemma3516 - skolem:lemma3517 - [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2566]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2566]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1569 a r:Inference; r:gives { - 2567 :kaprekar 6174 . + 2569 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2569 math:notEqualTo 0}] + skolem:lemma2953 + [ a r:Fact; r:gives {(2 5 6 9) list:quicksort (2 5 6 9)}] + [ a r:Fact; r:gives {(2 5 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3518 - skolem:lemma3519 - [ a r:Fact; r:gives {(2 5 6 7) list:reverse (7 6 5 2)}] - skolem:lemma3520 - skolem:lemma3521 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2567]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1570 a r:Inference; r:gives { - 2568 :kaprekar 6174 . + 2570 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2570 math:notEqualTo 0}] + skolem:lemma2956 + [ a r:Fact; r:gives {(2 5 7 0) list:quicksort (0 2 5 7)}] + [ a r:Fact; r:gives {(0 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3522 - skolem:lemma3523 - [ a r:Fact; r:gives {(2 5 6 8) list:reverse (8 6 5 2)}] - skolem:lemma3524 - skolem:lemma3525 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2568]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1571 a r:Inference; r:gives { - 2569 :kaprekar 6174 . + 2571 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2571 math:notEqualTo 0}] + skolem:lemma2957 + [ a r:Fact; r:gives {(2 5 7 1) list:quicksort (1 2 5 7)}] + [ a r:Fact; r:gives {(1 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3526 - skolem:lemma3527 - [ a r:Fact; r:gives {(2 5 6 9) list:reverse (9 6 5 2)}] - skolem:lemma3528 - skolem:lemma3529 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2569]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1572 a r:Inference; r:gives { - 2570 :kaprekar 6174 . + 2572 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2572 math:notEqualTo 0}] + skolem:lemma2958 + [ a r:Fact; r:gives {(2 5 7 2) list:quicksort (2 2 5 7)}] + [ a r:Fact; r:gives {(2 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3530 - skolem:lemma3531 - [ a r:Fact; r:gives {(0 2 5 7) list:reverse (7 5 2 0)}] - skolem:lemma2219 - skolem:lemma2220 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2570]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 257]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1573 a r:Inference; r:gives { - 2571 :kaprekar 6174 . + 2573 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2573 math:notEqualTo 0}] + skolem:lemma2959 + [ a r:Fact; r:gives {(2 5 7 3) list:quicksort (2 3 5 7)}] + [ a r:Fact; r:gives {(2 3 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3532 - skolem:lemma3533 - [ a r:Fact; r:gives {(1 2 5 7) list:reverse (7 5 2 1)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2571]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1257]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1574 a r:Inference; r:gives { - 2572 :kaprekar 6174 . + 2574 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2574 math:notEqualTo 0}] + skolem:lemma2960 + [ a r:Fact; r:gives {(2 5 7 4) list:quicksort (2 4 5 7)}] + [ a r:Fact; r:gives {(2 4 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3534 - skolem:lemma3535 - [ a r:Fact; r:gives {(2 2 5 7) list:reverse (7 5 2 2)}] - skolem:lemma2788 - skolem:lemma2789 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2572]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2257]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1575 a r:Inference; r:gives { - 2573 :kaprekar 6174 . + 2575 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2575 math:notEqualTo 0}] + skolem:lemma2961 + [ a r:Fact; r:gives {(2 5 7 5) list:quicksort (2 5 5 7)}] + [ a r:Fact; r:gives {(2 5 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3536 - skolem:lemma3537 - [ a r:Fact; r:gives {(2 3 5 7) list:reverse (7 5 3 2)}] - skolem:lemma3046 - skolem:lemma3047 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2573]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2357]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1576 a r:Inference; r:gives { - 2574 :kaprekar 6174 . + 2576 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2576 math:notEqualTo 0}] + skolem:lemma2962 + [ a r:Fact; r:gives {(2 5 7 6) list:quicksort (2 5 6 7)}] + [ a r:Fact; r:gives {(2 5 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3538 - skolem:lemma3539 - [ a r:Fact; r:gives {(2 4 5 7) list:reverse (7 5 4 2)}] - skolem:lemma3276 - skolem:lemma3277 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2574]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2457]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1577 a r:Inference; r:gives { - 2575 :kaprekar 6174 . + 2577 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2577 math:notEqualTo 0}] + skolem:lemma2963 + [ a r:Fact; r:gives {(2 5 7 7) list:quicksort (2 5 7 7)}] + [ a r:Fact; r:gives {(2 5 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3540 - skolem:lemma3541 - [ a r:Fact; r:gives {(2 5 5 7) list:reverse (7 5 5 2)}] - skolem:lemma3492 - skolem:lemma3493 - [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2575]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2557]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1578 a r:Inference; r:gives { - 2576 :kaprekar 6174 . + 2578 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2578 math:notEqualTo 0}] + skolem:lemma2966 + [ a r:Fact; r:gives {(2 5 7 8) list:quicksort (2 5 7 8)}] + [ a r:Fact; r:gives {(2 5 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3542 - skolem:lemma3543 - [ a r:Fact; r:gives {(2 5 6 7) list:reverse (7 6 5 2)}] - skolem:lemma3520 - skolem:lemma3521 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2576]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2567]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1579 a r:Inference; r:gives { - 2577 :kaprekar 6174 . + 2579 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2579 math:notEqualTo 0}] + skolem:lemma2969 + [ a r:Fact; r:gives {(2 5 7 9) list:quicksort (2 5 7 9)}] + [ a r:Fact; r:gives {(2 5 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3544 - skolem:lemma3545 - [ a r:Fact; r:gives {(2 5 7 7) list:reverse (7 7 5 2)}] - skolem:lemma3546 - skolem:lemma3547 - [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2577]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2577]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1580 a r:Inference; r:gives { - 2578 :kaprekar 6174 . + 2580 :kaprekar (0 5). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2580 math:notEqualTo 0}] + skolem:lemma2972 + [ a r:Fact; r:gives {(2 5 8 0) list:quicksort (0 2 5 8)}] + [ a r:Fact; r:gives {(0 2 5 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2578]; - r:rule skolem:lemma2032. + 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. skolem:lemma1581 a r:Inference; r:gives { - 2579 :kaprekar 6174 . + 2581 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2581 math:notEqualTo 0}] + skolem:lemma2973 + [ a r:Fact; r:gives {(2 5 8 1) list:quicksort (1 2 5 8)}] + [ a r:Fact; r:gives {(1 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3548 - skolem:lemma3549 - [ a r:Fact; r:gives {(2 5 7 9) list:reverse (9 7 5 2)}] - skolem:lemma3550 - skolem:lemma3551 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2579]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1582 a r:Inference; r:gives { - 2580 :kaprekar 6174 . + 2582 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2582 math:notEqualTo 0}] + skolem:lemma2974 + [ a r:Fact; r:gives {(2 5 8 2) list:quicksort (2 2 5 8)}] + [ a r:Fact; r:gives {(2 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3552 - skolem:lemma3553 - [ a r:Fact; r:gives {(0 2 5 8) list:reverse (8 5 2 0)}] - skolem:lemma2224 - skolem:lemma2225 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2580]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 258]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1583 a r:Inference; r:gives { - 2581 :kaprekar 6174 . + 2583 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2583 math:notEqualTo 0}] + skolem:lemma2975 + [ a r:Fact; r:gives {(2 5 8 3) list:quicksort (2 3 5 8)}] + [ a r:Fact; r:gives {(2 3 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3554 - skolem:lemma3555 - [ a r:Fact; r:gives {(1 2 5 8) list:reverse (8 5 2 1)}] - skolem:lemma2521 - skolem:lemma2522 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2581]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1258]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1584 a r:Inference; r:gives { - 2582 :kaprekar 6174 . + 2584 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2584 math:notEqualTo 0}] + skolem:lemma2976 + [ a r:Fact; r:gives {(2 5 8 4) list:quicksort (2 4 5 8)}] + [ a r:Fact; r:gives {(2 4 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3556 - skolem:lemma3557 - [ a r:Fact; r:gives {(2 2 5 8) list:reverse (8 5 2 2)}] - skolem:lemma2792 - skolem:lemma2793 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2582]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2258]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1585 a r:Inference; r:gives { - 2583 :kaprekar 6174 . + 2585 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2585 math:notEqualTo 0}] + skolem:lemma2977 + [ a r:Fact; r:gives {(2 5 8 5) list:quicksort (2 5 5 8)}] + [ a r:Fact; r:gives {(2 5 5 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2583]; - r:rule skolem:lemma2032. + 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. skolem:lemma1586 a r:Inference; r:gives { - 2584 :kaprekar 6174 . + 2586 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2586 math:notEqualTo 0}] + skolem:lemma2978 + [ a r:Fact; r:gives {(2 5 8 6) list:quicksort (2 5 6 8)}] + [ a r:Fact; r:gives {(2 5 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3558 - skolem:lemma3559 - [ a r:Fact; r:gives {(2 4 5 8) list:reverse (8 5 4 2)}] - skolem:lemma3280 - skolem:lemma3281 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2584]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2458]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1587 a r:Inference; r:gives { - 2585 :kaprekar 6174 . + 2587 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2587 math:notEqualTo 0}] + skolem:lemma2979 + [ a r:Fact; r:gives {(2 5 8 7) list:quicksort (2 5 7 8)}] + [ a r:Fact; r:gives {(2 5 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3560 - skolem:lemma3561 - [ a r:Fact; r:gives {(2 5 5 8) list:reverse (8 5 5 2)}] - skolem:lemma3496 - skolem:lemma3497 - [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2585]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2558]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1588 a r:Inference; r:gives { - 2586 :kaprekar 6174 . + 2588 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2588 math:notEqualTo 0}] + skolem:lemma2980 + [ a r:Fact; r:gives {(2 5 8 8) list:quicksort (2 5 8 8)}] + [ a r:Fact; r:gives {(2 5 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3562 - skolem:lemma3563 - [ a r:Fact; r:gives {(2 5 6 8) list:reverse (8 6 5 2)}] - skolem:lemma3524 - skolem:lemma3525 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2586]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2568]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1589 a r:Inference; r:gives { - 2587 :kaprekar 6174 . + 2589 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2589 math:notEqualTo 0}] + skolem:lemma2983 + [ a r:Fact; r:gives {(2 5 8 9) list:quicksort (2 5 8 9)}] + [ a r:Fact; r:gives {(2 5 8 9) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2587]; - r:rule skolem:lemma2032. + 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. skolem:lemma1590 a r:Inference; r:gives { - 2588 :kaprekar 6174 . + 2590 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2590 math:notEqualTo 0}] + skolem:lemma2986 + [ a r:Fact; r:gives {(2 5 9 0) list:quicksort (0 2 5 9)}] + [ a r:Fact; r:gives {(0 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3564 - skolem:lemma3565 - [ a r:Fact; r:gives {(2 5 8 8) list:reverse (8 8 5 2)}] - skolem:lemma3566 - skolem:lemma3567 - [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2588]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2588]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1591 a r:Inference; r:gives { - 2589 :kaprekar 6174 . + 2591 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2591 math:notEqualTo 0}] + skolem:lemma2987 + [ a r:Fact; r:gives {(2 5 9 1) list:quicksort (1 2 5 9)}] + [ a r:Fact; r:gives {(1 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3568 - skolem:lemma3569 - [ a r:Fact; r:gives {(2 5 8 9) list:reverse (9 8 5 2)}] - skolem:lemma3570 - skolem:lemma3571 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2589]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1592 a r:Inference; r:gives { - 2590 :kaprekar 6174 . + 2592 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2592 math:notEqualTo 0}] + skolem:lemma2988 + [ a r:Fact; r:gives {(2 5 9 2) list:quicksort (2 2 5 9)}] + [ a r:Fact; r:gives {(2 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3572 - skolem:lemma3573 - [ a r:Fact; r:gives {(0 2 5 9) list:reverse (9 5 2 0)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {9261 math:notEqualTo 6174}] - skolem:lemma2231 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2590]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 259]; - 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_8"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1593 a r:Inference; r:gives { - 2591 :kaprekar 6174 . + 2593 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2593 math:notEqualTo 0}] + skolem:lemma2989 + [ a r:Fact; r:gives {(2 5 9 3) list:quicksort (2 3 5 9)}] + [ a r:Fact; r:gives {(2 3 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3574 - skolem:lemma3575 - [ a r:Fact; r:gives {(1 2 5 9) list:reverse (9 5 2 1)}] - skolem:lemma2525 - skolem:lemma2526 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2591]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1259]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1594 a r:Inference; r:gives { - 2592 :kaprekar 6174 . + 2594 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2594 math:notEqualTo 0}] + skolem:lemma2990 + [ a r:Fact; r:gives {(2 5 9 4) list:quicksort (2 4 5 9)}] + [ a r:Fact; r:gives {(2 4 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3576 - skolem:lemma3577 - [ a r:Fact; r:gives {(2 2 5 9) list:reverse (9 5 2 2)}] - skolem:lemma2796 - skolem:lemma2797 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2592]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2259]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1595 a r:Inference; r:gives { - 2593 :kaprekar 6174 . + 2595 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2595 math:notEqualTo 0}] + skolem:lemma2991 + [ a r:Fact; r:gives {(2 5 9 5) list:quicksort (2 5 5 9)}] + [ a r:Fact; r:gives {(2 5 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3578 - skolem:lemma3579 - [ a r:Fact; r:gives {(2 3 5 9) list:reverse (9 5 3 2)}] - skolem:lemma3050 - skolem:lemma3051 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2593]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2359]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1596 a r:Inference; r:gives { - 2594 :kaprekar 6174 . + 2596 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2596 math:notEqualTo 0}] + skolem:lemma2992 + [ a r:Fact; r:gives {(2 5 9 6) list:quicksort (2 5 6 9)}] + [ a r:Fact; r:gives {(2 5 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3580 - skolem:lemma3581 - [ a r:Fact; r:gives {(2 4 5 9) list:reverse (9 5 4 2)}] - skolem:lemma3284 - skolem:lemma3285 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2594]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2459]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1597 a r:Inference; r:gives { - 2595 :kaprekar 6174 . + 2597 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2597 math:notEqualTo 0}] + skolem:lemma2993 + [ a r:Fact; r:gives {(2 5 9 7) list:quicksort (2 5 7 9)}] + [ a r:Fact; r:gives {(2 5 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3582 - skolem:lemma3583 - [ a r:Fact; r:gives {(2 5 5 9) list:reverse (9 5 5 2)}] - skolem:lemma3500 - skolem:lemma3501 - [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2595]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2559]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1598 a r:Inference; r:gives { - 2596 :kaprekar 6174 . + 2598 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2598 math:notEqualTo 0}] + skolem:lemma2994 + [ a r:Fact; r:gives {(2 5 9 8) list:quicksort (2 5 8 9)}] + [ a r:Fact; r:gives {(2 5 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3584 - skolem:lemma3585 - [ a r:Fact; r:gives {(2 5 6 9) list:reverse (9 6 5 2)}] - skolem:lemma3528 - skolem:lemma3529 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2596]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2569]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1599 a r:Inference; r:gives { - 2597 :kaprekar 6174 . + 2599 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2599 math:notEqualTo 0}] + skolem:lemma2995 + [ a r:Fact; r:gives {(2 5 9 9) list:quicksort (2 5 9 9)}] + [ a r:Fact; r:gives {(2 5 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3586 - skolem:lemma3587 - [ a r:Fact; r:gives {(2 5 7 9) list:reverse (9 7 5 2)}] - skolem:lemma3550 - skolem:lemma3551 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2597]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2579]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1600 a r:Inference; r:gives { - 2598 :kaprekar 6174 . + 2600 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2600 math:notEqualTo 0}] + skolem:lemma2998 + [ a r:Fact; r:gives {(2 6 0 0) list:quicksort (0 0 2 6)}] + [ a r:Fact; r:gives {(0 0 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3588 - skolem:lemma3589 - [ a r:Fact; r:gives {(2 5 8 9) list:reverse (9 8 5 2)}] - skolem:lemma3570 - skolem:lemma3571 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2598]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2589]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1601 a r:Inference; r:gives { - 2599 :kaprekar 6174 . + 2601 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2601 math:notEqualTo 0}] + skolem:lemma2999 + [ a r:Fact; r:gives {(2 6 0 1) list:quicksort (0 1 2 6)}] + [ a r:Fact; r:gives {(0 1 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3590 - skolem:lemma3591 - [ a r:Fact; r:gives {(2 5 9 9) list:reverse (9 9 5 2)}] - skolem:lemma3592 - skolem:lemma3593 - [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2599]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1602 a r:Inference; r:gives { - 2600 :kaprekar 6174 . + 2602 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2602 math:notEqualTo 0}] + skolem:lemma3000 + [ a r:Fact; r:gives {(2 6 0 2) list:quicksort (0 2 2 6)}] + [ a r:Fact; r:gives {(0 2 2 6) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2600]; - r:rule skolem:lemma2032. + 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. skolem:lemma1603 a r:Inference; r:gives { - 2601 :kaprekar 6174 . + 2603 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2603 math:notEqualTo 0}] + skolem:lemma3001 + [ a r:Fact; r:gives {(2 6 0 3) list:quicksort (0 2 3 6)}] + [ a r:Fact; r:gives {(0 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3594 - skolem:lemma3595 - [ a r:Fact; r:gives {(0 1 2 6) list:reverse (6 2 1 0)}] - skolem:lemma2075 - skolem:lemma2076 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2601]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 126]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1604 a r:Inference; r:gives { - 2602 :kaprekar 6174 . + 2604 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3596 - skolem:lemma3597 - [ a r:Fact; r:gives {(0 2 2 6) list:reverse (6 2 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ a r:Fact; r:gives {2604 math:notEqualTo 0}] + skolem:lemma3002 + [ a r:Fact; r:gives {(2 6 0 4) list:quicksort (0 2 4 6)}] + [ a r:Fact; r:gives {(0 2 4 6) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2602]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 226]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1605 a r:Inference; r:gives { - 2603 :kaprekar 6174 . + 2605 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2605 math:notEqualTo 0}] + skolem:lemma3003 + [ a r:Fact; r:gives {(2 6 0 5) list:quicksort (0 2 5 6)}] + [ a r:Fact; r:gives {(0 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3598 - skolem:lemma3599 - [ a r:Fact; r:gives {(0 2 3 6) list:reverse (6 3 2 0)}] - skolem:lemma2155 - skolem:lemma2156 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2603]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 236]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1606 a r:Inference; r:gives { - 2604 :kaprekar 6174 . + 2606 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2606 math:notEqualTo 0}] + skolem:lemma3004 + [ a r:Fact; r:gives {(2 6 0 6) list:quicksort (0 2 6 6)}] + [ a r:Fact; r:gives {(0 2 6 6) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2604]; - r:rule skolem:lemma2032. + 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. skolem:lemma1607 a r:Inference; r:gives { - 2605 :kaprekar 6174 . + 2607 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2607 math:notEqualTo 0}] + skolem:lemma3005 + [ a r:Fact; r:gives {(2 6 0 7) list:quicksort (0 2 6 7)}] + [ a r:Fact; r:gives {(0 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3600 - skolem:lemma3601 - [ a r:Fact; r:gives {(0 2 5 6) list:reverse (6 5 2 0)}] - skolem:lemma2214 - skolem:lemma2215 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2605]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1608 a r:Inference; r:gives { - 2606 :kaprekar 6174 . + 2608 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2608 math:notEqualTo 0}] + skolem:lemma3006 + [ a r:Fact; r:gives {(2 6 0 8) list:quicksort (0 2 6 8)}] + [ a r:Fact; r:gives {(0 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3602 - skolem:lemma3603 - [ a r:Fact; r:gives {(0 2 6 6) list:reverse (6 6 2 0)}] - skolem:lemma2242 - skolem:lemma2243 - [ a r:Fact; r:gives {(6620 266) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2606]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 266]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1609 a r:Inference; r:gives { - 2607 :kaprekar 6174 . + 2609 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2609 math:notEqualTo 0}] + skolem:lemma3007 + [ a r:Fact; r:gives {(2 6 0 9) list:quicksort (0 2 6 9)}] + [ a r:Fact; r:gives {(0 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3604 - skolem:lemma3605 - [ a r:Fact; r:gives {(0 2 6 7) list:reverse (7 6 2 0)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2607]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 267]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1610 a r:Inference; r:gives { - 2608 :kaprekar 6174 . + 2610 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2610 math:notEqualTo 0}] + skolem:lemma3008 + [ a r:Fact; r:gives {(2 6 1 0) list:quicksort (0 1 2 6)}] + [ a r:Fact; r:gives {(0 1 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3606 - skolem:lemma3607 - [ a r:Fact; r:gives {(0 2 6 8) list:reverse (8 6 2 0)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2608]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 268]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1611 a r:Inference; r:gives { - 2609 :kaprekar 6174 . + 2611 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2611 math:notEqualTo 0}] + skolem:lemma3009 + [ a r:Fact; r:gives {(2 6 1 1) list:quicksort (1 1 2 6)}] + [ a r:Fact; r:gives {(1 1 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3608 - skolem:lemma3609 - [ a r:Fact; r:gives {(0 2 6 9) list:reverse (9 6 2 0)}] - skolem:lemma2257 - skolem:lemma2258 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {9351 math:notEqualTo 6174}] - skolem:lemma2259 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2609]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 269]; - 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_8"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1612 a r:Inference; r:gives { - 2610 :kaprekar 6174 . + 2612 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2612 math:notEqualTo 0}] + skolem:lemma3010 + [ a r:Fact; r:gives {(2 6 1 2) list:quicksort (1 2 2 6)}] + [ a r:Fact; r:gives {(1 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3610 - skolem:lemma3611 - [ a r:Fact; r:gives {(0 1 2 6) list:reverse (6 2 1 0)}] - skolem:lemma2075 - skolem:lemma2076 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2610]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 126]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1613 a r:Inference; r:gives { - 2611 :kaprekar 6174 . + 2613 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2613 math:notEqualTo 0}] + skolem:lemma3011 + [ a r:Fact; r:gives {(2 6 1 3) list:quicksort (1 2 3 6)}] + [ a r:Fact; r:gives {(1 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3612 - skolem:lemma3613 - [ a r:Fact; r:gives {(1 1 2 6) list:reverse (6 2 1 1)}] - skolem:lemma2384 - skolem:lemma2385 - [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2611]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1126]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1614 a r:Inference; r:gives { - 2612 :kaprekar 6174 . + 2614 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2614 math:notEqualTo 0}] + skolem:lemma3012 + [ a r:Fact; r:gives {(2 6 1 4) list:quicksort (1 2 4 6)}] + [ a r:Fact; r:gives {(1 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3614 - skolem:lemma3615 - [ a r:Fact; r:gives {(1 2 2 6) list:reverse (6 2 2 1)}] - skolem:lemma2420 - skolem:lemma2421 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2612]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1226]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1615 a r:Inference; r:gives { - 2613 :kaprekar 6174 . + 2615 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2615 math:notEqualTo 0}] + skolem:lemma3013 + [ a r:Fact; r:gives {(2 6 1 5) list:quicksort (1 2 5 6)}] + [ a r:Fact; r:gives {(1 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3616 - skolem:lemma3617 - [ a r:Fact; r:gives {(1 2 3 6) list:reverse (6 3 2 1)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2613]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1236]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1616 a r:Inference; r:gives { - 2614 :kaprekar 6174 . + 2616 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2616 math:notEqualTo 0}] + skolem:lemma3014 + [ a r:Fact; r:gives {(2 6 1 6) list:quicksort (1 2 6 6)}] + [ a r:Fact; r:gives {(1 2 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3618 - skolem:lemma3619 - [ a r:Fact; r:gives {(1 2 4 6) list:reverse (6 4 2 1)}] - skolem:lemma2486 - skolem:lemma2487 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2614]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1246]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1617 a r:Inference; r:gives { - 2615 :kaprekar 6174 . + 2617 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2617 math:notEqualTo 0}] + skolem:lemma3015 + [ a r:Fact; r:gives {(2 6 1 7) list:quicksort (1 2 6 7)}] + [ a r:Fact; r:gives {(1 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3620 - skolem:lemma3621 - [ a r:Fact; r:gives {(1 2 5 6) list:reverse (6 5 2 1)}] - skolem:lemma2513 - skolem:lemma2514 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2615]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1256]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1618 a r:Inference; r:gives { - 2616 :kaprekar 6174 . + 2618 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2618 math:notEqualTo 0}] + skolem:lemma3016 + [ a r:Fact; r:gives {(2 6 1 8) list:quicksort (1 2 6 8)}] + [ a r:Fact; r:gives {(1 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3622 - skolem:lemma3623 - [ a r:Fact; r:gives {(1 2 6 6) list:reverse (6 6 2 1)}] - skolem:lemma2541 - skolem:lemma2542 - [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2616]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1266]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1619 a r:Inference; r:gives { - 2617 :kaprekar 6174 . + 2619 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2619 math:notEqualTo 0}] + skolem:lemma3017 + [ a r:Fact; r:gives {(2 6 1 9) list:quicksort (1 2 6 9)}] + [ a r:Fact; r:gives {(1 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3624 - skolem:lemma3625 - [ a r:Fact; r:gives {(1 2 6 7) list:reverse (7 6 2 1)}] - skolem:lemma2546 - skolem:lemma2547 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2617]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1267]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1620 a r:Inference; r:gives { - 2618 :kaprekar 6174 . + 2620 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2620 math:notEqualTo 0}] + skolem:lemma3018 + [ a r:Fact; r:gives {(2 6 2 0) list:quicksort (0 2 2 6)}] + [ a r:Fact; r:gives {(0 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3626 - skolem:lemma3627 - [ a r:Fact; r:gives {(1 2 6 8) list:reverse (8 6 2 1)}] - skolem:lemma2550 - skolem:lemma2551 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2618]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1268]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1621 a r:Inference; r:gives { - 2619 :kaprekar 6174 . + 2621 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2621 math:notEqualTo 0}] + skolem:lemma3019 + [ a r:Fact; r:gives {(2 6 2 1) list:quicksort (1 2 2 6)}] + [ a r:Fact; r:gives {(1 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3628 - skolem:lemma3629 - [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2619]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1622 a r:Inference; r:gives { - 2620 :kaprekar 6174 . + 2622 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2622 math:notEqualTo 0}] + skolem:lemma3020 + [ a r:Fact; r:gives {(2 6 2 2) list:quicksort (2 2 2 6)}] + [ a r:Fact; r:gives {(2 2 2 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3630 - skolem:lemma3631 - [ a r:Fact; r:gives {(0 2 2 6) list:reverse (6 2 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 226]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1623 a r:Inference; r:gives { - 2621 :kaprekar 6174 . + 2623 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2623 math:notEqualTo 0}] + skolem:lemma3021 + [ a r:Fact; r:gives {(2 6 2 3) list:quicksort (2 2 3 6)}] + [ a r:Fact; r:gives {(2 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3632 - skolem:lemma3633 - [ a r:Fact; r:gives {(1 2 2 6) list:reverse (6 2 2 1)}] - skolem:lemma2420 - skolem:lemma2421 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1226]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1624 a r:Inference; r:gives { - 2622 :kaprekar 6174 . + 2624 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2624 math:notEqualTo 0}] + skolem:lemma3022 + [ a r:Fact; r:gives {(2 6 2 4) list:quicksort (2 2 4 6)}] + [ a r:Fact; r:gives {(2 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3634 - skolem:lemma3635 - [ a r:Fact; r:gives {(2 2 2 6) list:reverse (6 2 2 2)}] - skolem:lemma2691 - skolem:lemma2692 - [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2226]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1625 a r:Inference; r:gives { - 2623 :kaprekar 6174 . + 2625 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2625 math:notEqualTo 0}] + skolem:lemma3023 + [ a r:Fact; r:gives {(2 6 2 5) list:quicksort (2 2 5 6)}] + [ a r:Fact; r:gives {(2 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3636 - skolem:lemma3637 - [ a r:Fact; r:gives {(2 2 3 6) list:reverse (6 3 2 2)}] - skolem:lemma2725 - skolem:lemma2726 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2236]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1626 a r:Inference; r:gives { - 2624 :kaprekar 6174 . + 2626 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2626 math:notEqualTo 0}] + skolem:lemma3024 + [ a r:Fact; r:gives {(2 6 2 6) list:quicksort (2 2 6 6)}] + [ a r:Fact; r:gives {(2 2 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3638 - skolem:lemma3639 - [ a r:Fact; r:gives {(2 2 4 6) list:reverse (6 4 2 2)}] - skolem:lemma2757 - skolem:lemma2758 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2624]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2246]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1627 a r:Inference; r:gives { - 2625 :kaprekar 6174 . + 2627 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2627 math:notEqualTo 0}] + skolem:lemma3025 + [ a r:Fact; r:gives {(2 6 2 7) list:quicksort (2 2 6 7)}] + [ a r:Fact; r:gives {(2 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3640 - skolem:lemma3641 - [ a r:Fact; r:gives {(2 2 5 6) list:reverse (6 5 2 2)}] - skolem:lemma2784 - skolem:lemma2785 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2625]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2256]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1628 a r:Inference; r:gives { - 2626 :kaprekar 6174 . + 2628 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2628 math:notEqualTo 0}] + skolem:lemma3026 + [ a r:Fact; r:gives {(2 6 2 8) list:quicksort (2 2 6 8)}] + [ a r:Fact; r:gives {(2 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3642 - skolem:lemma3643 - [ a r:Fact; r:gives {(2 2 6 6) list:reverse (6 6 2 2)}] - skolem:lemma2812 - skolem:lemma2813 - [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] - [ a r:Fact; r:gives {4356 math:notEqualTo 6174}] - skolem:lemma2814 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2626]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2266]; - 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_8"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1629 a r:Inference; r:gives { - 2627 :kaprekar 6174 . + 2629 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2629 math:notEqualTo 0}] + skolem:lemma3027 + [ a r:Fact; r:gives {(2 6 2 9) list:quicksort (2 2 6 9)}] + [ a r:Fact; r:gives {(2 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3644 - skolem:lemma3645 - [ a r:Fact; r:gives {(2 2 6 7) list:reverse (7 6 2 2)}] - skolem:lemma2817 - skolem:lemma2818 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2627]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2267]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1630 a r:Inference; r:gives { - 2628 :kaprekar 6174 . + 2630 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2630 math:notEqualTo 0}] + skolem:lemma3028 + [ a r:Fact; r:gives {(2 6 3 0) list:quicksort (0 2 3 6)}] + [ a r:Fact; r:gives {(0 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3646 - skolem:lemma3647 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2628]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1631 a r:Inference; r:gives { - 2629 :kaprekar 6174 . + 2631 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2631 math:notEqualTo 0}] + skolem:lemma3029 + [ a r:Fact; r:gives {(2 6 3 1) list:quicksort (1 2 3 6)}] + [ a r:Fact; r:gives {(1 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3648 - skolem:lemma3649 - [ a r:Fact; r:gives {(2 2 6 9) list:reverse (9 6 2 2)}] - skolem:lemma2825 - skolem:lemma2826 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2629]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2269]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1632 a r:Inference; r:gives { - 2630 :kaprekar 6174 . + 2632 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2632 math:notEqualTo 0}] + skolem:lemma3030 + [ a r:Fact; r:gives {(2 6 3 2) list:quicksort (2 2 3 6)}] + [ a r:Fact; r:gives {(2 2 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3650 - skolem:lemma3651 - [ a r:Fact; r:gives {(0 2 3 6) list:reverse (6 3 2 0)}] - skolem:lemma2155 - skolem:lemma2156 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2630]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 236]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1633 a r:Inference; r:gives { - 2631 :kaprekar 6174 . + 2633 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2633 math:notEqualTo 0}] + skolem:lemma3031 + [ a r:Fact; r:gives {(2 6 3 3) list:quicksort (2 3 3 6)}] + [ a r:Fact; r:gives {(2 3 3 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3652 - skolem:lemma3653 - [ a r:Fact; r:gives {(1 2 3 6) list:reverse (6 3 2 1)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2631]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1236]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1634 a r:Inference; r:gives { - 2632 :kaprekar 6174 . + 2634 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2634 math:notEqualTo 0}] + skolem:lemma3032 + [ a r:Fact; r:gives {(2 6 3 4) list:quicksort (2 3 4 6)}] + [ a r:Fact; r:gives {(2 3 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3654 - skolem:lemma3655 - [ a r:Fact; r:gives {(2 2 3 6) list:reverse (6 3 2 2)}] - skolem:lemma2725 - skolem:lemma2726 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2236]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1635 a r:Inference; r:gives { - 2633 :kaprekar 6174 . + 2635 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2635 math:notEqualTo 0}] + skolem:lemma3033 + [ a r:Fact; r:gives {(2 6 3 5) list:quicksort (2 3 5 6)}] + [ a r:Fact; r:gives {(2 3 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3656 - skolem:lemma3657 - [ a r:Fact; r:gives {(2 3 3 6) list:reverse (6 3 3 2)}] - skolem:lemma2980 - skolem:lemma2981 - [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2633]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2336]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1636 a r:Inference; r:gives { - 2634 :kaprekar 6174 . + 2636 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2636 math:notEqualTo 0}] + skolem:lemma3034 + [ a r:Fact; r:gives {(2 6 3 6) list:quicksort (2 3 6 6)}] + [ a r:Fact; r:gives {(2 3 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3658 - skolem:lemma3659 - [ a r:Fact; r:gives {(2 3 4 6) list:reverse (6 4 3 2)}] - skolem:lemma3012 - skolem:lemma3013 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2634]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2346]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1637 a r:Inference; r:gives { - 2635 :kaprekar 6174 . + 2637 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2637 math:notEqualTo 0}] + skolem:lemma3035 + [ a r:Fact; r:gives {(2 6 3 7) list:quicksort (2 3 6 7)}] + [ a r:Fact; r:gives {(2 3 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3660 - skolem:lemma3661 - [ a r:Fact; r:gives {(2 3 5 6) list:reverse (6 5 3 2)}] - skolem:lemma3042 - skolem:lemma3043 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2635]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2356]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1638 a r:Inference; r:gives { - 2636 :kaprekar 6174 . + 2638 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2638 math:notEqualTo 0}] + skolem:lemma3036 + [ a r:Fact; r:gives {(2 6 3 8) list:quicksort (2 3 6 8)}] + [ a r:Fact; r:gives {(2 3 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3662 - skolem:lemma3663 - [ a r:Fact; r:gives {(2 3 6 6) list:reverse (6 6 3 2)}] - skolem:lemma3066 - skolem:lemma3067 - [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2636]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2366]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1639 a r:Inference; r:gives { - 2637 :kaprekar 6174 . + 2639 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2639 math:notEqualTo 0}] + skolem:lemma3037 + [ a r:Fact; r:gives {(2 6 3 9) list:quicksort (2 3 6 9)}] + [ a r:Fact; r:gives {(2 3 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3664 - skolem:lemma3665 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2637]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1640 a r:Inference; r:gives { - 2638 :kaprekar 6174 . + 2640 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2640 math:notEqualTo 0}] + skolem:lemma3038 + [ a r:Fact; r:gives {(2 6 4 0) list:quicksort (0 2 4 6)}] + [ a r:Fact; r:gives {(0 2 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3666 - skolem:lemma3667 - [ a r:Fact; r:gives {(2 3 6 8) list:reverse (8 6 3 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2638]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2368]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1641 a r:Inference; r:gives { - 2639 :kaprekar 6174 . + 2641 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3668 - skolem:lemma3669 - [ a r:Fact; r:gives {(2 3 6 9) list:reverse (9 6 3 2)}] - skolem:lemma3078 - skolem:lemma3079 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ a r:Fact; r:gives {2641 math:notEqualTo 0}] + skolem:lemma3039 + [ a r:Fact; r:gives {(2 6 4 1) list:quicksort (1 2 4 6)}] + [ a r:Fact; r:gives {(1 2 4 6) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2639]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2369]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1642 a r:Inference; r:gives { - 2640 :kaprekar 6174 . + 2642 :kaprekar (0 2). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2642 math:notEqualTo 0}] + skolem:lemma3040 + [ a r:Fact; r:gives {(2 6 4 2) list:quicksort (2 2 4 6)}] + [ a r:Fact; r:gives {(2 2 4 6) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2640]; - r:rule skolem:lemma2032. + 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. skolem:lemma1643 a r:Inference; r:gives { - 2641 :kaprekar 6174 . + 2643 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2643 math:notEqualTo 0}] + skolem:lemma3041 + [ a r:Fact; r:gives {(2 6 4 3) list:quicksort (2 3 4 6)}] + [ a r:Fact; r:gives {(2 3 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3670 - skolem:lemma3671 - [ a r:Fact; r:gives {(1 2 4 6) list:reverse (6 4 2 1)}] - skolem:lemma2486 - skolem:lemma2487 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2641]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1246]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1644 a r:Inference; r:gives { - 2642 :kaprekar 6174 . + 2644 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2644 math:notEqualTo 0}] + skolem:lemma3042 + [ a r:Fact; r:gives {(2 6 4 4) list:quicksort (2 4 4 6)}] + [ a r:Fact; r:gives {(2 4 4 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3672 - skolem:lemma3673 - [ a r:Fact; r:gives {(2 2 4 6) list:reverse (6 4 2 2)}] - skolem:lemma2757 - skolem:lemma2758 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2246]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1645 a r:Inference; r:gives { - 2643 :kaprekar 6174 . + 2645 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2645 math:notEqualTo 0}] + skolem:lemma3043 + [ a r:Fact; r:gives {(2 6 4 5) list:quicksort (2 4 5 6)}] + [ a r:Fact; r:gives {(2 4 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3674 - skolem:lemma3675 - [ a r:Fact; r:gives {(2 3 4 6) list:reverse (6 4 3 2)}] - skolem:lemma3012 - skolem:lemma3013 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2643]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2346]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1646 a r:Inference; r:gives { - 2644 :kaprekar 6174 . + 2646 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2646 math:notEqualTo 0}] + skolem:lemma3044 + [ a r:Fact; r:gives {(2 6 4 6) list:quicksort (2 4 6 6)}] + [ a r:Fact; r:gives {(2 4 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3676 - skolem:lemma3677 - [ a r:Fact; r:gives {(2 4 4 6) list:reverse (6 4 4 2)}] - skolem:lemma3242 - skolem:lemma3243 - [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2644]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2446]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1647 a r:Inference; r:gives { - 2645 :kaprekar 6174 . + 2647 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2647 math:notEqualTo 0}] + skolem:lemma3045 + [ a r:Fact; r:gives {(2 6 4 7) list:quicksort (2 4 6 7)}] + [ a r:Fact; r:gives {(2 4 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3678 - skolem:lemma3679 - [ a r:Fact; r:gives {(2 4 5 6) list:reverse (6 5 4 2)}] - skolem:lemma3272 - skolem:lemma3273 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2645]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2456]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1648 a r:Inference; r:gives { - 2646 :kaprekar 6174 . + 2648 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2648 math:notEqualTo 0}] + skolem:lemma3046 + [ a r:Fact; r:gives {(2 6 4 8) list:quicksort (2 4 6 8)}] + [ a r:Fact; r:gives {(2 4 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3680 - skolem:lemma3681 - [ a r:Fact; r:gives {(2 4 6 6) list:reverse (6 6 4 2)}] - skolem:lemma3298 - skolem:lemma3299 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2646]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2466]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1649 a r:Inference; r:gives { - 2647 :kaprekar 6174 . + 2649 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2649 math:notEqualTo 0}] + skolem:lemma3047 + [ a r:Fact; r:gives {(2 6 4 9) list:quicksort (2 4 6 9)}] + [ a r:Fact; r:gives {(2 4 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3682 - skolem:lemma3683 - [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] - skolem:lemma3302 - skolem:lemma3303 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2647]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2467]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1650 a r:Inference; r:gives { - 2648 :kaprekar 6174 . + 2650 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2650 math:notEqualTo 0}] + skolem:lemma3048 + [ a r:Fact; r:gives {(2 6 5 0) list:quicksort (0 2 5 6)}] + [ a r:Fact; r:gives {(0 2 5 6) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2648]; - r:rule skolem:lemma2032. + 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. skolem:lemma1651 a r:Inference; r:gives { - 2649 :kaprekar 6174 . + 2651 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2651 math:notEqualTo 0}] + skolem:lemma3049 + [ a r:Fact; r:gives {(2 6 5 1) list:quicksort (1 2 5 6)}] + [ a r:Fact; r:gives {(1 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3684 - skolem:lemma3685 - [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] - skolem:lemma3306 - skolem:lemma3307 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2649]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2469]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1652 a r:Inference; r:gives { - 2650 :kaprekar 6174 . + 2652 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2652 math:notEqualTo 0}] + skolem:lemma3050 + [ a r:Fact; r:gives {(2 6 5 2) list:quicksort (2 2 5 6)}] + [ a r:Fact; r:gives {(2 2 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3686 - skolem:lemma3687 - [ a r:Fact; r:gives {(0 2 5 6) list:reverse (6 5 2 0)}] - skolem:lemma2214 - skolem:lemma2215 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2650]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 256]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1653 a r:Inference; r:gives { - 2651 :kaprekar 6174 . + 2653 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2653 math:notEqualTo 0}] + skolem:lemma3051 + [ a r:Fact; r:gives {(2 6 5 3) list:quicksort (2 3 5 6)}] + [ a r:Fact; r:gives {(2 3 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3688 - skolem:lemma3689 - [ a r:Fact; r:gives {(1 2 5 6) list:reverse (6 5 2 1)}] - skolem:lemma2513 - skolem:lemma2514 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2651]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1256]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1654 a r:Inference; r:gives { - 2652 :kaprekar 6174 . + 2654 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2654 math:notEqualTo 0}] + skolem:lemma3052 + [ a r:Fact; r:gives {(2 6 5 4) list:quicksort (2 4 5 6)}] + [ a r:Fact; r:gives {(2 4 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3690 - skolem:lemma3691 - [ a r:Fact; r:gives {(2 2 5 6) list:reverse (6 5 2 2)}] - skolem:lemma2784 - skolem:lemma2785 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2256]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1655 a r:Inference; r:gives { - 2653 :kaprekar 6174 . + 2655 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2655 math:notEqualTo 0}] + skolem:lemma3053 + [ a r:Fact; r:gives {(2 6 5 5) list:quicksort (2 5 5 6)}] + [ a r:Fact; r:gives {(2 5 5 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3692 - skolem:lemma3693 - [ a r:Fact; r:gives {(2 3 5 6) list:reverse (6 5 3 2)}] - skolem:lemma3042 - skolem:lemma3043 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2653]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2356]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1656 a r:Inference; r:gives { - 2654 :kaprekar 6174 . + 2656 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2656 math:notEqualTo 0}] + skolem:lemma3054 + [ a r:Fact; r:gives {(2 6 5 6) list:quicksort (2 5 6 6)}] + [ a r:Fact; r:gives {(2 5 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3694 - skolem:lemma3695 - [ a r:Fact; r:gives {(2 4 5 6) list:reverse (6 5 4 2)}] - skolem:lemma3272 - skolem:lemma3273 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2654]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2456]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1657 a r:Inference; r:gives { - 2655 :kaprekar 6174 . + 2657 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2657 math:notEqualTo 0}] + skolem:lemma3055 + [ a r:Fact; r:gives {(2 6 5 7) list:quicksort (2 5 6 7)}] + [ a r:Fact; r:gives {(2 5 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3696 - skolem:lemma3697 - [ a r:Fact; r:gives {(2 5 5 6) list:reverse (6 5 5 2)}] - skolem:lemma3488 - skolem:lemma3489 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2655]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2556]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1658 a r:Inference; r:gives { - 2656 :kaprekar 6174 . + 2658 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2658 math:notEqualTo 0}] + skolem:lemma3056 + [ a r:Fact; r:gives {(2 6 5 8) list:quicksort (2 5 6 8)}] + [ a r:Fact; r:gives {(2 5 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3698 - skolem:lemma3699 - [ a r:Fact; r:gives {(2 5 6 6) list:reverse (6 6 5 2)}] - skolem:lemma3516 - skolem:lemma3517 - [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2656]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2566]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1659 a r:Inference; r:gives { - 2657 :kaprekar 6174 . + 2659 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2659 math:notEqualTo 0}] + skolem:lemma3057 + [ a r:Fact; r:gives {(2 6 5 9) list:quicksort (2 5 6 9)}] + [ a r:Fact; r:gives {(2 5 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3700 - skolem:lemma3701 - [ a r:Fact; r:gives {(2 5 6 7) list:reverse (7 6 5 2)}] - skolem:lemma3520 - skolem:lemma3521 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2657]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2567]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1660 a r:Inference; r:gives { - 2658 :kaprekar 6174 . + 2660 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2660 math:notEqualTo 0}] + skolem:lemma3058 + [ a r:Fact; r:gives {(2 6 6 0) list:quicksort (0 2 6 6)}] + [ a r:Fact; r:gives {(0 2 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3702 - skolem:lemma3703 - [ a r:Fact; r:gives {(2 5 6 8) list:reverse (8 6 5 2)}] - skolem:lemma3524 - skolem:lemma3525 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2658]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2568]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1661 a r:Inference; r:gives { - 2659 :kaprekar 6174 . + 2661 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2661 math:notEqualTo 0}] + skolem:lemma3059 + [ a r:Fact; r:gives {(2 6 6 1) list:quicksort (1 2 6 6)}] + [ a r:Fact; r:gives {(1 2 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3704 - skolem:lemma3705 - [ a r:Fact; r:gives {(2 5 6 9) list:reverse (9 6 5 2)}] - skolem:lemma3528 - skolem:lemma3529 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2659]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2569]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1662 a r:Inference; r:gives { - 2660 :kaprekar 6174 . + 2662 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2662 math:notEqualTo 0}] + skolem:lemma3060 + [ a r:Fact; r:gives {(2 6 6 2) list:quicksort (2 2 6 6)}] + [ a r:Fact; r:gives {(2 2 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3706 - skolem:lemma3707 - [ a r:Fact; r:gives {(0 2 6 6) list:reverse (6 6 2 0)}] - skolem:lemma2242 - skolem:lemma2243 - [ a r:Fact; r:gives {(6620 266) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2660]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 266]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1663 a r:Inference; r:gives { - 2661 :kaprekar 6174 . + 2663 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2663 math:notEqualTo 0}] + skolem:lemma3061 + [ a r:Fact; r:gives {(2 6 6 3) list:quicksort (2 3 6 6)}] + [ a r:Fact; r:gives {(2 3 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3708 - skolem:lemma3709 - [ a r:Fact; r:gives {(1 2 6 6) list:reverse (6 6 2 1)}] - skolem:lemma2541 - skolem:lemma2542 - [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2661]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1266]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1664 a r:Inference; r:gives { - 2662 :kaprekar 6174 . + 2664 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2664 math:notEqualTo 0}] + skolem:lemma3062 + [ a r:Fact; r:gives {(2 6 6 4) list:quicksort (2 4 6 6)}] + [ a r:Fact; r:gives {(2 4 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3710 - skolem:lemma3711 - [ a r:Fact; r:gives {(2 2 6 6) list:reverse (6 6 2 2)}] - skolem:lemma2812 - skolem:lemma2813 - [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] - [ a r:Fact; r:gives {4356 math:notEqualTo 6174}] - skolem:lemma2814 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2266]; - 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_8"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1665 a r:Inference; r:gives { - 2663 :kaprekar 6174 . + 2665 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2665 math:notEqualTo 0}] + skolem:lemma3063 + [ a r:Fact; r:gives {(2 6 6 5) list:quicksort (2 5 6 6)}] + [ a r:Fact; r:gives {(2 5 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3712 - skolem:lemma3713 - [ a r:Fact; r:gives {(2 3 6 6) list:reverse (6 6 3 2)}] - skolem:lemma3066 - skolem:lemma3067 - [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] - [ a r:Fact; r:gives {4266 math:notEqualTo 6174}] - skolem:lemma2510 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2663]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2366]; - 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_8"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1666 a r:Inference; r:gives { - 2664 :kaprekar 6174 . + 2666 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2666 math:notEqualTo 0}] + skolem:lemma3064 + [ a r:Fact; r:gives {(2 6 6 6) list:quicksort (2 6 6 6)}] + [ a r:Fact; r:gives {(2 6 6 6) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3714 - skolem:lemma3715 - [ a r:Fact; r:gives {(2 4 6 6) list:reverse (6 6 4 2)}] - skolem:lemma3298 - skolem:lemma3299 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2664]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2466]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1667 a r:Inference; r:gives { - 2665 :kaprekar 6174 . + 2667 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2667 math:notEqualTo 0}] + skolem:lemma3067 + [ a r:Fact; r:gives {(2 6 6 7) list:quicksort (2 6 6 7)}] + [ a r:Fact; r:gives {(2 6 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3716 - skolem:lemma3717 - [ a r:Fact; r:gives {(2 5 6 6) list:reverse (6 6 5 2)}] - skolem:lemma3516 - skolem:lemma3517 - [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] - [ a r:Fact; r:gives {4086 math:notEqualTo 6174}] - skolem:lemma2067 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2665]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2566]; - 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_8"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1668 a r:Inference; r:gives { - 2666 :kaprekar 6174 . + 2668 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2668 math:notEqualTo 0}] + skolem:lemma3070 + [ a r:Fact; r:gives {(2 6 6 8) list:quicksort (2 6 6 8)}] + [ a r:Fact; r:gives {(2 6 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3718 - skolem:lemma3719 - [ a r:Fact; r:gives {(2 6 6 6) list:reverse (6 6 6 2)}] - skolem:lemma3720 - skolem:lemma3721 - [ a r:Fact; r:gives {(6662 2666) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2666]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2666]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1669 a r:Inference; r:gives { - 2667 :kaprekar 6174 . + 2669 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2669 math:notEqualTo 0}] + skolem:lemma3073 + [ a r:Fact; r:gives {(2 6 6 9) list:quicksort (2 6 6 9)}] + [ a r:Fact; r:gives {(2 6 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3722 - skolem:lemma3723 - [ a r:Fact; r:gives {(2 6 6 7) list:reverse (7 6 6 2)}] - skolem:lemma3724 - skolem:lemma3725 - [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2667]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2667]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1670 a r:Inference; r:gives { - 2668 :kaprekar 6174 . + 2670 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2670 math:notEqualTo 0}] + skolem:lemma3076 + [ a r:Fact; r:gives {(2 6 7 0) list:quicksort (0 2 6 7)}] + [ a r:Fact; r:gives {(0 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3726 - skolem:lemma3727 - [ a r:Fact; r:gives {(2 6 6 8) list:reverse (8 6 6 2)}] - skolem:lemma3728 - skolem:lemma3729 - [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2668]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2668]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1671 a r:Inference; r:gives { - 2669 :kaprekar 6174 . + 2671 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2671 math:notEqualTo 0}] + skolem:lemma3077 + [ a r:Fact; r:gives {(2 6 7 1) list:quicksort (1 2 6 7)}] + [ a r:Fact; r:gives {(1 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3730 - skolem:lemma3731 - [ a r:Fact; r:gives {(2 6 6 9) list:reverse (9 6 6 2)}] - skolem:lemma3732 - skolem:lemma3733 - [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2669]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2669]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1672 a r:Inference; r:gives { - 2670 :kaprekar 6174 . + 2672 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2672 math:notEqualTo 0}] + skolem:lemma3078 + [ a r:Fact; r:gives {(2 6 7 2) list:quicksort (2 2 6 7)}] + [ a r:Fact; r:gives {(2 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3734 - skolem:lemma3735 - [ a r:Fact; r:gives {(0 2 6 7) list:reverse (7 6 2 0)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2670]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 267]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1673 a r:Inference; r:gives { - 2671 :kaprekar 6174 . + 2673 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2673 math:notEqualTo 0}] + skolem:lemma3079 + [ a r:Fact; r:gives {(2 6 7 3) list:quicksort (2 3 6 7)}] + [ a r:Fact; r:gives {(2 3 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3736 - skolem:lemma3737 - [ a r:Fact; r:gives {(1 2 6 7) list:reverse (7 6 2 1)}] - skolem:lemma2546 - skolem:lemma2547 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2671]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1267]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1674 a r:Inference; r:gives { - 2672 :kaprekar 6174 . + 2674 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3738 - skolem:lemma3739 - [ a r:Fact; r:gives {(2 2 6 7) list:reverse (7 6 2 2)}] - skolem:lemma2817 + [ a r:Fact; r:gives {2674 math:notEqualTo 0}] + skolem:lemma3080 + [ a r:Fact; r:gives {(2 6 7 4) list:quicksort (2 4 6 7)}] + [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] skolem:lemma2818 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + 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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2672]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2267]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1675 a r:Inference; r:gives { - 2673 :kaprekar 6174 . + 2675 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2675 math:notEqualTo 0}] + skolem:lemma3081 + [ a r:Fact; r:gives {(2 6 7 5) list:quicksort (2 5 6 7)}] + [ a r:Fact; r:gives {(2 5 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3740 - skolem:lemma3741 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2673]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1676 a r:Inference; r:gives { - 2674 :kaprekar 6174 . + 2676 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2676 math:notEqualTo 0}] + skolem:lemma3082 + [ a r:Fact; r:gives {(2 6 7 6) list:quicksort (2 6 6 7)}] + [ a r:Fact; r:gives {(2 6 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3742 - skolem:lemma3743 - [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] - skolem:lemma3302 - skolem:lemma3303 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2674]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2467]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1677 a r:Inference; r:gives { - 2675 :kaprekar 6174 . + 2677 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2677 math:notEqualTo 0}] + skolem:lemma3083 + [ a r:Fact; r:gives {(2 6 7 7) list:quicksort (2 6 7 7)}] + [ a r:Fact; r:gives {(2 6 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3744 - skolem:lemma3745 - [ a r:Fact; r:gives {(2 5 6 7) list:reverse (7 6 5 2)}] - skolem:lemma3520 - skolem:lemma3521 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2675]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2567]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1678 a r:Inference; r:gives { - 2676 :kaprekar 6174 . + 2678 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2678 math:notEqualTo 0}] + skolem:lemma3086 + [ a r:Fact; r:gives {(2 6 7 8) list:quicksort (2 6 7 8)}] + [ a r:Fact; r:gives {(2 6 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3746 - skolem:lemma3747 - [ a r:Fact; r:gives {(2 6 6 7) list:reverse (7 6 6 2)}] - skolem:lemma3724 - skolem:lemma3725 - [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2676]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2667]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1679 a r:Inference; r:gives { - 2677 :kaprekar 6174 . + 2679 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2679 math:notEqualTo 0}] + skolem:lemma3089 + [ a r:Fact; r:gives {(2 6 7 9) list:quicksort (2 6 7 9)}] + [ a r:Fact; r:gives {(2 6 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3748 - skolem:lemma3749 - [ a r:Fact; r:gives {(2 6 7 7) list:reverse (7 7 6 2)}] - skolem:lemma3750 - skolem:lemma3751 - [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2677]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2677]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1680 a r:Inference; r:gives { - 2678 :kaprekar 6174 . + 2680 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2680 math:notEqualTo 0}] + skolem:lemma3092 + [ a r:Fact; r:gives {(2 6 8 0) list:quicksort (0 2 6 8)}] + [ a r:Fact; r:gives {(0 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3752 - skolem:lemma3753 - [ a r:Fact; r:gives {(2 6 7 8) list:reverse (8 7 6 2)}] - skolem:lemma3754 - skolem:lemma3755 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2678]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1681 a r:Inference; r:gives { - 2679 :kaprekar 6174 . + 2681 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2681 math:notEqualTo 0}] + skolem:lemma3093 + [ a r:Fact; r:gives {(2 6 8 1) list:quicksort (1 2 6 8)}] + [ a r:Fact; r:gives {(1 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3756 - skolem:lemma3757 - [ a r:Fact; r:gives {(2 6 7 9) list:reverse (9 7 6 2)}] - skolem:lemma3758 - skolem:lemma3759 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2679]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1682 a r:Inference; r:gives { - 2680 :kaprekar 6174 . + 2682 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2682 math:notEqualTo 0}] + skolem:lemma3094 + [ a r:Fact; r:gives {(2 6 8 2) list:quicksort (2 2 6 8)}] + [ a r:Fact; r:gives {(2 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3760 - skolem:lemma3761 - [ a r:Fact; r:gives {(0 2 6 8) list:reverse (8 6 2 0)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2680]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 268]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1683 a r:Inference; r:gives { - 2681 :kaprekar 6174 . + 2683 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2683 math:notEqualTo 0}] + skolem:lemma3095 + [ a r:Fact; r:gives {(2 6 8 3) list:quicksort (2 3 6 8)}] + [ a r:Fact; r:gives {(2 3 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3762 - skolem:lemma3763 - [ a r:Fact; r:gives {(1 2 6 8) list:reverse (8 6 2 1)}] - skolem:lemma2550 - skolem:lemma2551 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2681]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1268]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1684 a r:Inference; r:gives { - 2682 :kaprekar 6174 . + 2684 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3764 - skolem:lemma3765 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] + [ a r:Fact; r:gives {2684 math:notEqualTo 0}] + skolem:lemma3096 + [ a r:Fact; r:gives {(2 6 8 4) list:quicksort (2 4 6 8)}] + [ a r:Fact; r:gives {(2 4 6 8) list:reverse (8 6 4 2)}] skolem:lemma2821 skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2682]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1685 a r:Inference; r:gives { - 2683 :kaprekar 6174 . + 2685 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2685 math:notEqualTo 0}] + skolem:lemma3097 + [ a r:Fact; r:gives {(2 6 8 5) list:quicksort (2 5 6 8)}] + [ a r:Fact; r:gives {(2 5 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3766 - skolem:lemma3767 - [ a r:Fact; r:gives {(2 3 6 8) list:reverse (8 6 3 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2683]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2368]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1686 a r:Inference; r:gives { - 2684 :kaprekar 6174 . + 2686 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2686 math:notEqualTo 0}] + skolem:lemma3098 + [ a r:Fact; r:gives {(2 6 8 6) list:quicksort (2 6 6 8)}] + [ a r:Fact; r:gives {(2 6 6 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2684]; - r:rule skolem:lemma2032. + 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. skolem:lemma1687 a r:Inference; r:gives { - 2685 :kaprekar 6174 . + 2687 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2687 math:notEqualTo 0}] + skolem:lemma3099 + [ a r:Fact; r:gives {(2 6 8 7) list:quicksort (2 6 7 8)}] + [ a r:Fact; r:gives {(2 6 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3768 - skolem:lemma3769 - [ a r:Fact; r:gives {(2 5 6 8) list:reverse (8 6 5 2)}] - skolem:lemma3524 - skolem:lemma3525 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2685]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2568]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1688 a r:Inference; r:gives { - 2686 :kaprekar 6174 . + 2688 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2688 math:notEqualTo 0}] + skolem:lemma3100 + [ a r:Fact; r:gives {(2 6 8 8) list:quicksort (2 6 8 8)}] + [ a r:Fact; r:gives {(2 6 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3770 - skolem:lemma3771 - [ a r:Fact; r:gives {(2 6 6 8) list:reverse (8 6 6 2)}] - skolem:lemma3728 - skolem:lemma3729 - [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2686]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2668]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1689 a r:Inference; r:gives { - 2687 :kaprekar 6174 . + 2689 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2689 math:notEqualTo 0}] + skolem:lemma3103 + [ a r:Fact; r:gives {(2 6 8 9) list:quicksort (2 6 8 9)}] + [ a r:Fact; r:gives {(2 6 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3772 - skolem:lemma3773 - [ a r:Fact; r:gives {(2 6 7 8) list:reverse (8 7 6 2)}] - skolem:lemma3754 - skolem:lemma3755 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2687]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2678]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1690 a r:Inference; r:gives { - 2688 :kaprekar 6174 . + 2690 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2690 math:notEqualTo 0}] + skolem:lemma3106 + [ a r:Fact; r:gives {(2 6 9 0) list:quicksort (0 2 6 9)}] + [ a r:Fact; r:gives {(0 2 6 9) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2688]; - r:rule skolem:lemma2032. + 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. skolem:lemma1691 a r:Inference; r:gives { - 2689 :kaprekar 6174 . + 2691 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2691 math:notEqualTo 0}] + skolem:lemma3107 + [ a r:Fact; r:gives {(2 6 9 1) list:quicksort (1 2 6 9)}] + [ a r:Fact; r:gives {(1 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3774 - skolem:lemma3775 - [ a r:Fact; r:gives {(2 6 8 9) list:reverse (9 8 6 2)}] - skolem:lemma3776 - skolem:lemma3777 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2689]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1692 a r:Inference; r:gives { - 2690 :kaprekar 6174 . + 2692 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2692 math:notEqualTo 0}] + skolem:lemma3108 + [ a r:Fact; r:gives {(2 6 9 2) list:quicksort (2 2 6 9)}] + [ a r:Fact; r:gives {(2 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3778 - skolem:lemma3779 - [ a r:Fact; r:gives {(0 2 6 9) list:reverse (9 6 2 0)}] - skolem:lemma2257 - skolem:lemma2258 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {9351 math:notEqualTo 6174}] - skolem:lemma2259 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2690]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 269]; - 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_8"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1693 a r:Inference; r:gives { - 2691 :kaprekar 6174 . + 2693 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2693 math:notEqualTo 0}] + skolem:lemma3109 + [ a r:Fact; r:gives {(2 6 9 3) list:quicksort (2 3 6 9)}] + [ a r:Fact; r:gives {(2 3 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3780 - skolem:lemma3781 - [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2691]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1694 a r:Inference; r:gives { - 2692 :kaprekar 6174 . + 2694 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3782 - skolem:lemma3783 - [ a r:Fact; r:gives {(2 2 6 9) list:reverse (9 6 2 2)}] + [ a r:Fact; r:gives {2694 math:notEqualTo 0}] + skolem:lemma3110 + [ a r:Fact; r:gives {(2 6 9 4) list:quicksort (2 4 6 9)}] + [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] + skolem:lemma2824 skolem:lemma2825 - skolem:lemma2826 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2692]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2269]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1695 a r:Inference; r:gives { - 2693 :kaprekar 6174 . + 2695 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2695 math:notEqualTo 0}] + skolem:lemma3111 + [ a r:Fact; r:gives {(2 6 9 5) list:quicksort (2 5 6 9)}] + [ a r:Fact; r:gives {(2 5 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3784 - skolem:lemma3785 - [ a r:Fact; r:gives {(2 3 6 9) list:reverse (9 6 3 2)}] - skolem:lemma3078 - skolem:lemma3079 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2693]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2369]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1696 a r:Inference; r:gives { - 2694 :kaprekar 6174 . + 2696 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2696 math:notEqualTo 0}] + skolem:lemma3112 + [ a r:Fact; r:gives {(2 6 9 6) list:quicksort (2 6 6 9)}] + [ a r:Fact; r:gives {(2 6 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3786 - skolem:lemma3787 - [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] - skolem:lemma3306 - skolem:lemma3307 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2694]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2469]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1697 a r:Inference; r:gives { - 2695 :kaprekar 6174 . + 2697 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2697 math:notEqualTo 0}] + skolem:lemma3113 + [ a r:Fact; r:gives {(2 6 9 7) list:quicksort (2 6 7 9)}] + [ a r:Fact; r:gives {(2 6 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3788 - skolem:lemma3789 - [ a r:Fact; r:gives {(2 5 6 9) list:reverse (9 6 5 2)}] - skolem:lemma3528 - skolem:lemma3529 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2695]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2569]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1698 a r:Inference; r:gives { - 2696 :kaprekar 6174 . + 2698 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2698 math:notEqualTo 0}] + skolem:lemma3114 + [ a r:Fact; r:gives {(2 6 9 8) list:quicksort (2 6 8 9)}] + [ a r:Fact; r:gives {(2 6 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3790 - skolem:lemma3791 - [ a r:Fact; r:gives {(2 6 6 9) list:reverse (9 6 6 2)}] - skolem:lemma3732 - skolem:lemma3733 - [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2696]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2669]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1699 a r:Inference; r:gives { - 2697 :kaprekar 6174 . + 2699 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2699 math:notEqualTo 0}] + skolem:lemma3115 + [ a r:Fact; r:gives {(2 6 9 9) list:quicksort (2 6 9 9)}] + [ a r:Fact; r:gives {(2 6 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3792 - skolem:lemma3793 - [ a r:Fact; r:gives {(2 6 7 9) list:reverse (9 7 6 2)}] - skolem:lemma3758 - skolem:lemma3759 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2697]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2679]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1700 a r:Inference; r:gives { - 2698 :kaprekar 6174 . + 2700 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2700 math:notEqualTo 0}] + skolem:lemma3118 + [ a r:Fact; r:gives {(2 7 0 0) list:quicksort (0 0 2 7)}] + [ a r:Fact; r:gives {(0 0 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3794 - skolem:lemma3795 - [ a r:Fact; r:gives {(2 6 8 9) list:reverse (9 8 6 2)}] - skolem:lemma3776 - skolem:lemma3777 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2698]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2689]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1701 a r:Inference; r:gives { - 2699 :kaprekar 6174 . + 2701 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2701 math:notEqualTo 0}] + skolem:lemma3119 + [ a r:Fact; r:gives {(2 7 0 1) list:quicksort (0 1 2 7)}] + [ a r:Fact; r:gives {(0 1 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3796 - skolem:lemma3797 - [ a r:Fact; r:gives {(2 6 9 9) list:reverse (9 9 6 2)}] - skolem:lemma3798 - skolem:lemma3799 - [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2699]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2699]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1702 a r:Inference; r:gives { - 2700 :kaprekar 6174 . + 2702 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2702 math:notEqualTo 0}] + skolem:lemma3120 + [ a r:Fact; r:gives {(2 7 0 2) list:quicksort (0 2 2 7)}] + [ a r:Fact; r:gives {(0 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3800 - skolem:lemma3801 - [ a r:Fact; r:gives {(0 0 2 7) list:reverse (7 2 0 0)}] - skolem:lemma2035 - skolem:lemma2036 - [ a r:Fact; r:gives {(7200 27) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2700]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 27]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1703 a r:Inference; r:gives { - 2701 :kaprekar 6174 . + 2703 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2703 math:notEqualTo 0}] + skolem:lemma3121 + [ a r:Fact; r:gives {(2 7 0 3) list:quicksort (0 2 3 7)}] + [ a r:Fact; r:gives {(0 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3802 - skolem:lemma3803 - [ a r:Fact; r:gives {(0 1 2 7) list:reverse (7 2 1 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2701]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 127]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1704 a r:Inference; r:gives { - 2702 :kaprekar 6174 . + 2704 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3804 - skolem:lemma3805 - [ a r:Fact; r:gives {(0 2 2 7) list:reverse (7 2 2 0)}] - skolem:lemma2122 + [ a r:Fact; r:gives {2704 math:notEqualTo 0}] + skolem:lemma3122 + [ a r:Fact; r:gives {(2 7 0 4) list:quicksort (0 2 4 7)}] + [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] skolem:lemma2123 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] 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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2702]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 227]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1705 a r:Inference; r:gives { - 2703 :kaprekar 6174 . + 2705 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2705 math:notEqualTo 0}] + skolem:lemma3123 + [ a r:Fact; r:gives {(2 7 0 5) list:quicksort (0 2 5 7)}] + [ a r:Fact; r:gives {(0 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3806 - skolem:lemma3807 - [ a r:Fact; r:gives {(0 2 3 7) list:reverse (7 3 2 0)}] - skolem:lemma2159 - skolem:lemma2160 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2703]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 237]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1706 a r:Inference; r:gives { - 2704 :kaprekar 6174 . + 2706 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2706 math:notEqualTo 0}] + skolem:lemma3124 + [ a r:Fact; r:gives {(2 7 0 6) list:quicksort (0 2 6 7)}] + [ a r:Fact; r:gives {(0 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3808 - skolem:lemma3809 - [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] - skolem:lemma2187 - skolem:lemma2188 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2704]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 247]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1707 a r:Inference; r:gives { - 2705 :kaprekar 6174 . + 2707 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2707 math:notEqualTo 0}] + skolem:lemma3125 + [ a r:Fact; r:gives {(2 7 0 7) list:quicksort (0 2 7 7)}] + [ a r:Fact; r:gives {(0 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3810 - skolem:lemma3811 - [ a r:Fact; r:gives {(0 2 5 7) list:reverse (7 5 2 0)}] - skolem:lemma2219 - skolem:lemma2220 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2705]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 257]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1708 a r:Inference; r:gives { - 2706 :kaprekar 6174 . + 2708 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2708 math:notEqualTo 0}] + skolem:lemma3126 + [ a r:Fact; r:gives {(2 7 0 8) list:quicksort (0 2 7 8)}] + [ a r:Fact; r:gives {(0 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3812 - skolem:lemma3813 - [ a r:Fact; r:gives {(0 2 6 7) list:reverse (7 6 2 0)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2706]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 267]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1709 a r:Inference; r:gives { - 2707 :kaprekar 6174 . + 2709 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2709 math:notEqualTo 0}] + skolem:lemma3127 + [ a r:Fact; r:gives {(2 7 0 9) list:quicksort (0 2 7 9)}] + [ a r:Fact; r:gives {(0 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3814 - skolem:lemma3815 - [ a r:Fact; r:gives {(0 2 7 7) list:reverse (7 7 2 0)}] - skolem:lemma2276 - skolem:lemma2277 - [ a r:Fact; r:gives {(7720 277) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2707]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 277]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1710 a r:Inference; r:gives { - 2708 :kaprekar 6174 . + 2710 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2710 math:notEqualTo 0}] + skolem:lemma3128 + [ a r:Fact; r:gives {(2 7 1 0) list:quicksort (0 1 2 7)}] + [ a r:Fact; r:gives {(0 1 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3816 - skolem:lemma3817 - [ a r:Fact; r:gives {(0 2 7 8) list:reverse (8 7 2 0)}] - skolem:lemma2281 - skolem:lemma2282 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2708]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 278]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1711 a r:Inference; r:gives { - 2709 :kaprekar 6174 . + 2711 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2711 math:notEqualTo 0}] + skolem:lemma3129 + [ a r:Fact; r:gives {(2 7 1 1) list:quicksort (1 1 2 7)}] + [ a r:Fact; r:gives {(1 1 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3818 - skolem:lemma3819 - [ a r:Fact; r:gives {(0 2 7 9) list:reverse (9 7 2 0)}] - skolem:lemma2286 - skolem:lemma2287 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {9441 math:notEqualTo 6174}] - skolem:lemma2288 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2709]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 279]; - 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_8"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1712 a r:Inference; r:gives { - 2710 :kaprekar 6174 . + 2712 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2712 math:notEqualTo 0}] + skolem:lemma3130 + [ a r:Fact; r:gives {(2 7 1 2) list:quicksort (1 2 2 7)}] + [ a r:Fact; r:gives {(1 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3820 - skolem:lemma3821 - [ a r:Fact; r:gives {(0 1 2 7) list:reverse (7 2 1 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2710]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 127]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1713 a r:Inference; r:gives { - 2711 :kaprekar 6174 . + 2713 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2713 math:notEqualTo 0}] + skolem:lemma3131 + [ a r:Fact; r:gives {(2 7 1 3) list:quicksort (1 2 3 7)}] + [ a r:Fact; r:gives {(1 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3822 - skolem:lemma3823 - [ a r:Fact; r:gives {(1 1 2 7) list:reverse (7 2 1 1)}] - skolem:lemma2388 - skolem:lemma2389 - [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2711]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1127]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1714 a r:Inference; r:gives { - 2712 :kaprekar 6174 . + 2714 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2714 math:notEqualTo 0}] + skolem:lemma3132 + [ a r:Fact; r:gives {(2 7 1 4) list:quicksort (1 2 4 7)}] + [ a r:Fact; r:gives {(1 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3824 - skolem:lemma3825 - [ a r:Fact; r:gives {(1 2 2 7) list:reverse (7 2 2 1)}] - skolem:lemma2424 - skolem:lemma2425 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2712]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1227]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1715 a r:Inference; r:gives { - 2713 :kaprekar 6174 . + 2715 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2715 math:notEqualTo 0}] + skolem:lemma3133 + [ a r:Fact; r:gives {(2 7 1 5) list:quicksort (1 2 5 7)}] + [ a r:Fact; r:gives {(1 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3826 - skolem:lemma3827 - [ a r:Fact; r:gives {(1 2 3 7) list:reverse (7 3 2 1)}] - skolem:lemma2458 - skolem:lemma2459 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2713]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1237]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1716 a r:Inference; r:gives { - 2714 :kaprekar 6174 . + 2716 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2716 math:notEqualTo 0}] + skolem:lemma3134 + [ a r:Fact; r:gives {(2 7 1 6) list:quicksort (1 2 6 7)}] + [ a r:Fact; r:gives {(1 2 6 7) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2714]; - r:rule skolem:lemma2032. + 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. skolem:lemma1717 a r:Inference; r:gives { - 2715 :kaprekar 6174 . + 2717 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2717 math:notEqualTo 0}] + skolem:lemma3135 + [ a r:Fact; r:gives {(2 7 1 7) list:quicksort (1 2 7 7)}] + [ a r:Fact; r:gives {(1 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3828 - skolem:lemma3829 - [ a r:Fact; r:gives {(1 2 5 7) list:reverse (7 5 2 1)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2715]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1257]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1718 a r:Inference; r:gives { - 2716 :kaprekar 6174 . + 2718 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2718 math:notEqualTo 0}] + skolem:lemma3136 + [ a r:Fact; r:gives {(2 7 1 8) list:quicksort (1 2 7 8)}] + [ a r:Fact; r:gives {(1 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3830 - skolem:lemma3831 - [ a r:Fact; r:gives {(1 2 6 7) list:reverse (7 6 2 1)}] - skolem:lemma2546 - skolem:lemma2547 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2716]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1267]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1719 a r:Inference; r:gives { - 2717 :kaprekar 6174 . + 2719 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2719 math:notEqualTo 0}] + skolem:lemma3137 + [ a r:Fact; r:gives {(2 7 1 9) list:quicksort (1 2 7 9)}] + [ a r:Fact; r:gives {(1 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3832 - skolem:lemma3833 - [ a r:Fact; r:gives {(1 2 7 7) list:reverse (7 7 2 1)}] - skolem:lemma2570 - skolem:lemma2571 - [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2717]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1277]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1720 a r:Inference; r:gives { - 2718 :kaprekar 6174 . + 2720 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3834 - skolem:lemma3835 - [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ a r:Fact; r:gives {2720 math:notEqualTo 0}] + skolem:lemma3138 + [ a r:Fact; r:gives {(2 7 2 0) list:quicksort (0 2 2 7)}] + [ a r:Fact; r:gives {(0 2 2 7) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2718]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1721 a r:Inference; r:gives { - 2719 :kaprekar 6174 . + 2721 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2721 math:notEqualTo 0}] + skolem:lemma3139 + [ a r:Fact; r:gives {(2 7 2 1) list:quicksort (1 2 2 7)}] + [ a r:Fact; r:gives {(1 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3836 - skolem:lemma3837 - [ a r:Fact; r:gives {(1 2 7 9) list:reverse (9 7 2 1)}] - skolem:lemma2579 - skolem:lemma2580 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2719]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1279]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1722 a r:Inference; r:gives { - 2720 :kaprekar 6174 . + 2722 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2722 math:notEqualTo 0}] + skolem:lemma3140 + [ a r:Fact; r:gives {(2 7 2 2) list:quicksort (2 2 2 7)}] + [ a r:Fact; r:gives {(2 2 2 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3838 - skolem:lemma3839 - [ a r:Fact; r:gives {(0 2 2 7) list:reverse (7 2 2 0)}] - skolem:lemma2122 - skolem:lemma2123 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 227]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1723 a r:Inference; r:gives { - 2721 :kaprekar 6174 . + 2723 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2723 math:notEqualTo 0}] + skolem:lemma3141 + [ a r:Fact; r:gives {(2 7 2 3) list:quicksort (2 2 3 7)}] + [ a r:Fact; r:gives {(2 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3840 - skolem:lemma3841 - [ a r:Fact; r:gives {(1 2 2 7) list:reverse (7 2 2 1)}] - skolem:lemma2424 - skolem:lemma2425 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1227]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1724 a r:Inference; r:gives { - 2722 :kaprekar 6174 . + 2724 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2724 math:notEqualTo 0}] + skolem:lemma3142 + [ a r:Fact; r:gives {(2 7 2 4) list:quicksort (2 2 4 7)}] + [ a r:Fact; r:gives {(2 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3842 - skolem:lemma3843 - [ a r:Fact; r:gives {(2 2 2 7) list:reverse (7 2 2 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2227]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1725 a r:Inference; r:gives { - 2723 :kaprekar 6174 . + 2725 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2725 math:notEqualTo 0}] + skolem:lemma3143 + [ a r:Fact; r:gives {(2 7 2 5) list:quicksort (2 2 5 7)}] + [ a r:Fact; r:gives {(2 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3844 - skolem:lemma3845 - [ a r:Fact; r:gives {(2 2 3 7) list:reverse (7 3 2 2)}] - skolem:lemma2729 - skolem:lemma2730 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2723]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2237]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1726 a r:Inference; r:gives { - 2724 :kaprekar 6174 . + 2726 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2726 math:notEqualTo 0}] + skolem:lemma3144 + [ a r:Fact; r:gives {(2 7 2 6) list:quicksort (2 2 6 7)}] + [ a r:Fact; r:gives {(2 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3846 - skolem:lemma3847 - [ a r:Fact; r:gives {(2 2 4 7) list:reverse (7 4 2 2)}] - skolem:lemma2761 - skolem:lemma2762 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2724]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2247]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1727 a r:Inference; r:gives { - 2725 :kaprekar 6174 . + 2727 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2727 math:notEqualTo 0}] + skolem:lemma3145 + [ a r:Fact; r:gives {(2 7 2 7) list:quicksort (2 2 7 7)}] + [ a r:Fact; r:gives {(2 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3848 - skolem:lemma3849 - [ a r:Fact; r:gives {(2 2 5 7) list:reverse (7 5 2 2)}] - skolem:lemma2788 - skolem:lemma2789 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2725]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2257]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1728 a r:Inference; r:gives { - 2726 :kaprekar 6174 . + 2728 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2728 math:notEqualTo 0}] + skolem:lemma3146 + [ a r:Fact; r:gives {(2 7 2 8) list:quicksort (2 2 7 8)}] + [ a r:Fact; r:gives {(2 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3850 - skolem:lemma3851 - [ a r:Fact; r:gives {(2 2 6 7) list:reverse (7 6 2 2)}] - skolem:lemma2817 - skolem:lemma2818 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2726]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2267]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1729 a r:Inference; r:gives { - 2727 :kaprekar 6174 . + 2729 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2729 math:notEqualTo 0}] + skolem:lemma3147 + [ a r:Fact; r:gives {(2 7 2 9) list:quicksort (2 2 7 9)}] + [ a r:Fact; r:gives {(2 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3852 - skolem:lemma3853 - [ a r:Fact; r:gives {(2 2 7 7) list:reverse (7 7 2 2)}] - skolem:lemma2843 - skolem:lemma2844 - [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] - [ a r:Fact; r:gives {5445 math:notEqualTo 6174}] - skolem:lemma2845 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2727]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2277]; - 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_8"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1730 a r:Inference; r:gives { - 2728 :kaprekar 6174 . + 2730 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2730 math:notEqualTo 0}] + skolem:lemma3148 + [ a r:Fact; r:gives {(2 7 3 0) list:quicksort (0 2 3 7)}] + [ a r:Fact; r:gives {(0 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3854 - skolem:lemma3855 - [ a r:Fact; r:gives {(2 2 7 8) list:reverse (8 7 2 2)}] - skolem:lemma2848 - skolem:lemma2849 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2728]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2278]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1731 a r:Inference; r:gives { - 2729 :kaprekar 6174 . + 2731 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2731 math:notEqualTo 0}] + skolem:lemma3149 + [ a r:Fact; r:gives {(2 7 3 1) list:quicksort (1 2 3 7)}] + [ a r:Fact; r:gives {(1 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3856 - skolem:lemma3857 - [ a r:Fact; r:gives {(2 2 7 9) list:reverse (9 7 2 2)}] - skolem:lemma2852 - skolem:lemma2853 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2729]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2279]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1732 a r:Inference; r:gives { - 2730 :kaprekar 6174 . + 2732 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2732 math:notEqualTo 0}] + skolem:lemma3150 + [ a r:Fact; r:gives {(2 7 3 2) list:quicksort (2 2 3 7)}] + [ a r:Fact; r:gives {(2 2 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3858 - skolem:lemma3859 - [ a r:Fact; r:gives {(0 2 3 7) list:reverse (7 3 2 0)}] - skolem:lemma2159 - skolem:lemma2160 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2730]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 237]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1733 a r:Inference; r:gives { - 2731 :kaprekar 6174 . + 2733 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2733 math:notEqualTo 0}] + skolem:lemma3151 + [ a r:Fact; r:gives {(2 7 3 3) list:quicksort (2 3 3 7)}] + [ a r:Fact; r:gives {(2 3 3 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3860 - skolem:lemma3861 - [ a r:Fact; r:gives {(1 2 3 7) list:reverse (7 3 2 1)}] - skolem:lemma2458 - skolem:lemma2459 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2731]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1237]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1734 a r:Inference; r:gives { - 2732 :kaprekar 6174 . + 2734 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2734 math:notEqualTo 0}] + skolem:lemma3152 + [ a r:Fact; r:gives {(2 7 3 4) list:quicksort (2 3 4 7)}] + [ a r:Fact; r:gives {(2 3 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3862 - skolem:lemma3863 - [ a r:Fact; r:gives {(2 2 3 7) list:reverse (7 3 2 2)}] - skolem:lemma2729 - skolem:lemma2730 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2237]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1735 a r:Inference; r:gives { - 2733 :kaprekar 6174 . + 2735 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2735 math:notEqualTo 0}] + skolem:lemma3153 + [ a r:Fact; r:gives {(2 7 3 5) list:quicksort (2 3 5 7)}] + [ a r:Fact; r:gives {(2 3 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3864 - skolem:lemma3865 - [ a r:Fact; r:gives {(2 3 3 7) list:reverse (7 3 3 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2733]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2337]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1736 a r:Inference; r:gives { - 2734 :kaprekar 6174 . + 2736 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2736 math:notEqualTo 0}] + skolem:lemma3154 + [ a r:Fact; r:gives {(2 7 3 6) list:quicksort (2 3 6 7)}] + [ a r:Fact; r:gives {(2 3 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3866 - skolem:lemma3867 - [ a r:Fact; r:gives {(2 3 4 7) list:reverse (7 4 3 2)}] - skolem:lemma3016 - skolem:lemma3017 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2734]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2347]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1737 a r:Inference; r:gives { - 2735 :kaprekar 6174 . + 2737 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2737 math:notEqualTo 0}] + skolem:lemma3155 + [ a r:Fact; r:gives {(2 7 3 7) list:quicksort (2 3 7 7)}] + [ a r:Fact; r:gives {(2 3 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3868 - skolem:lemma3869 - [ a r:Fact; r:gives {(2 3 5 7) list:reverse (7 5 3 2)}] - skolem:lemma3046 - skolem:lemma3047 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2735]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2357]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1738 a r:Inference; r:gives { - 2736 :kaprekar 6174 . + 2738 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2738 math:notEqualTo 0}] + skolem:lemma3156 + [ a r:Fact; r:gives {(2 7 3 8) list:quicksort (2 3 7 8)}] + [ a r:Fact; r:gives {(2 3 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3870 - skolem:lemma3871 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2736]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1739 a r:Inference; r:gives { - 2737 :kaprekar 6174 . + 2739 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2739 math:notEqualTo 0}] + skolem:lemma3157 + [ a r:Fact; r:gives {(2 7 3 9) list:quicksort (2 3 7 9)}] + [ a r:Fact; r:gives {(2 3 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3872 - skolem:lemma3873 - [ a r:Fact; r:gives {(2 3 7 7) list:reverse (7 7 3 2)}] - skolem:lemma3096 - skolem:lemma3097 - [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2737]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2377]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1740 a r:Inference; r:gives { - 2738 :kaprekar 6174 . + 2740 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2740 math:notEqualTo 0}] + skolem:lemma3158 + [ a r:Fact; r:gives {(2 7 4 0) list:quicksort (0 2 4 7)}] + [ a r:Fact; r:gives {(0 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3874 - skolem:lemma3875 - [ a r:Fact; r:gives {(2 3 7 8) list:reverse (8 7 3 2)}] - skolem:lemma3100 - skolem:lemma3101 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2738]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2378]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1741 a r:Inference; r:gives { - 2739 :kaprekar 6174 . + 2741 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2741 math:notEqualTo 0}] + skolem:lemma3159 + [ a r:Fact; r:gives {(2 7 4 1) list:quicksort (1 2 4 7)}] + [ a r:Fact; r:gives {(1 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3876 - skolem:lemma3877 - [ a r:Fact; r:gives {(2 3 7 9) list:reverse (9 7 3 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2739]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2379]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1742 a r:Inference; r:gives { - 2740 :kaprekar 6174 . + 2742 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2742 math:notEqualTo 0}] + skolem:lemma3160 + [ a r:Fact; r:gives {(2 7 4 2) list:quicksort (2 2 4 7)}] + [ a r:Fact; r:gives {(2 2 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3878 - skolem:lemma3879 - [ a r:Fact; r:gives {(0 2 4 7) list:reverse (7 4 2 0)}] - skolem:lemma2187 - skolem:lemma2188 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2740]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 247]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1743 a r:Inference; r:gives { - 2741 :kaprekar 6174 . + 2743 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2743 math:notEqualTo 0}] + skolem:lemma3161 + [ a r:Fact; r:gives {(2 7 4 3) list:quicksort (2 3 4 7)}] + [ a r:Fact; r:gives {(2 3 4 7) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2741]; - r:rule skolem:lemma2032. + 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. skolem:lemma1744 a r:Inference; r:gives { - 2742 :kaprekar 6174 . + 2744 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2744 math:notEqualTo 0}] + skolem:lemma3162 + [ a r:Fact; r:gives {(2 7 4 4) list:quicksort (2 4 4 7)}] + [ a r:Fact; r:gives {(2 4 4 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3880 - skolem:lemma3881 - [ a r:Fact; r:gives {(2 2 4 7) list:reverse (7 4 2 2)}] - skolem:lemma2761 - skolem:lemma2762 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2247]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1745 a r:Inference; r:gives { - 2743 :kaprekar 6174 . + 2745 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2745 math:notEqualTo 0}] + skolem:lemma3163 + [ a r:Fact; r:gives {(2 7 4 5) list:quicksort (2 4 5 7)}] + [ a r:Fact; r:gives {(2 4 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3882 - skolem:lemma3883 - [ a r:Fact; r:gives {(2 3 4 7) list:reverse (7 4 3 2)}] - skolem:lemma3016 - skolem:lemma3017 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2743]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2347]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1746 a r:Inference; r:gives { - 2744 :kaprekar 6174 . + 2746 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2746 math:notEqualTo 0}] + skolem:lemma3164 + [ a r:Fact; r:gives {(2 7 4 6) list:quicksort (2 4 6 7)}] + [ a r:Fact; r:gives {(2 4 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3884 - skolem:lemma3885 - [ a r:Fact; r:gives {(2 4 4 7) list:reverse (7 4 4 2)}] - skolem:lemma3246 - skolem:lemma3247 - [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2744]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2447]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1747 a r:Inference; r:gives { - 2745 :kaprekar 6174 . + 2747 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2747 math:notEqualTo 0}] + skolem:lemma3165 + [ a r:Fact; r:gives {(2 7 4 7) list:quicksort (2 4 7 7)}] + [ a r:Fact; r:gives {(2 4 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3886 - skolem:lemma3887 - [ a r:Fact; r:gives {(2 4 5 7) list:reverse (7 5 4 2)}] - skolem:lemma3276 - skolem:lemma3277 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2745]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2457]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1748 a r:Inference; r:gives { - 2746 :kaprekar 6174 . + 2748 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2748 math:notEqualTo 0}] + skolem:lemma3166 + [ a r:Fact; r:gives {(2 7 4 8) list:quicksort (2 4 7 8)}] + [ a r:Fact; r:gives {(2 4 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3888 - skolem:lemma3889 - [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] - skolem:lemma3302 - skolem:lemma3303 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2746]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2467]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1749 a r:Inference; r:gives { - 2747 :kaprekar 6174 . + 2749 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2749 math:notEqualTo 0}] + skolem:lemma3167 + [ a r:Fact; r:gives {(2 7 4 9) list:quicksort (2 4 7 9)}] + [ a r:Fact; r:gives {(2 4 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3890 - skolem:lemma3891 - [ a r:Fact; r:gives {(2 4 7 7) list:reverse (7 7 4 2)}] - skolem:lemma3322 - skolem:lemma3323 - [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2747]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2477]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1750 a r:Inference; r:gives { - 2748 :kaprekar 6174 . + 2750 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2750 math:notEqualTo 0}] + skolem:lemma3168 + [ a r:Fact; r:gives {(2 7 5 0) list:quicksort (0 2 5 7)}] + [ a r:Fact; r:gives {(0 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3892 - skolem:lemma3893 - [ a r:Fact; r:gives {(2 4 7 8) list:reverse (8 7 4 2)}] - skolem:lemma3326 - skolem:lemma3327 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2748]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2478]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1751 a r:Inference; r:gives { - 2749 :kaprekar 6174 . + 2751 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2751 math:notEqualTo 0}] + skolem:lemma3169 + [ a r:Fact; r:gives {(2 7 5 1) list:quicksort (1 2 5 7)}] + [ a r:Fact; r:gives {(1 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3894 - skolem:lemma3895 - [ a r:Fact; r:gives {(2 4 7 9) list:reverse (9 7 4 2)}] - skolem:lemma3330 - skolem:lemma3331 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2749]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2479]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1752 a r:Inference; r:gives { - 2750 :kaprekar 6174 . + 2752 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2752 math:notEqualTo 0}] + skolem:lemma3170 + [ a r:Fact; r:gives {(2 7 5 2) list:quicksort (2 2 5 7)}] + [ a r:Fact; r:gives {(2 2 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3896 - skolem:lemma3897 - [ a r:Fact; r:gives {(0 2 5 7) list:reverse (7 5 2 0)}] - skolem:lemma2219 - skolem:lemma2220 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2750]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 257]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1753 a r:Inference; r:gives { - 2751 :kaprekar 6174 . + 2753 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2753 math:notEqualTo 0}] + skolem:lemma3171 + [ a r:Fact; r:gives {(2 7 5 3) list:quicksort (2 3 5 7)}] + [ a r:Fact; r:gives {(2 3 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3898 - skolem:lemma3899 - [ a r:Fact; r:gives {(1 2 5 7) list:reverse (7 5 2 1)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2751]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1257]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1754 a r:Inference; r:gives { - 2752 :kaprekar 6174 . + 2754 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2754 math:notEqualTo 0}] + skolem:lemma3172 + [ a r:Fact; r:gives {(2 7 5 4) list:quicksort (2 4 5 7)}] + [ a r:Fact; r:gives {(2 4 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3900 - skolem:lemma3901 - [ a r:Fact; r:gives {(2 2 5 7) list:reverse (7 5 2 2)}] - skolem:lemma2788 - skolem:lemma2789 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2257]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1755 a r:Inference; r:gives { - 2753 :kaprekar 6174 . + 2755 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2755 math:notEqualTo 0}] + skolem:lemma3173 + [ a r:Fact; r:gives {(2 7 5 5) list:quicksort (2 5 5 7)}] + [ a r:Fact; r:gives {(2 5 5 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3902 - skolem:lemma3903 - [ a r:Fact; r:gives {(2 3 5 7) list:reverse (7 5 3 2)}] - skolem:lemma3046 - skolem:lemma3047 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2753]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2357]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1756 a r:Inference; r:gives { - 2754 :kaprekar 6174 . + 2756 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2756 math:notEqualTo 0}] + skolem:lemma3174 + [ a r:Fact; r:gives {(2 7 5 6) list:quicksort (2 5 6 7)}] + [ a r:Fact; r:gives {(2 5 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3904 - skolem:lemma3905 - [ a r:Fact; r:gives {(2 4 5 7) list:reverse (7 5 4 2)}] - skolem:lemma3276 - skolem:lemma3277 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2754]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2457]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1757 a r:Inference; r:gives { - 2755 :kaprekar 6174 . + 2757 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3906 - skolem:lemma3907 - [ a r:Fact; r:gives {(2 5 5 7) list:reverse (7 5 5 2)}] - skolem:lemma3492 - skolem:lemma3493 - [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ a r:Fact; r:gives {2757 math:notEqualTo 0}] + skolem:lemma3175 + [ a r:Fact; r:gives {(2 7 5 7) list:quicksort (2 5 7 7)}] + [ a r:Fact; r:gives {(2 5 7 7) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2755]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2557]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1758 a r:Inference; r:gives { - 2756 :kaprekar 6174 . + 2758 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2758 math:notEqualTo 0}] + skolem:lemma3176 + [ a r:Fact; r:gives {(2 7 5 8) list:quicksort (2 5 7 8)}] + [ a r:Fact; r:gives {(2 5 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3908 - skolem:lemma3909 - [ a r:Fact; r:gives {(2 5 6 7) list:reverse (7 6 5 2)}] - skolem:lemma3520 - skolem:lemma3521 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2756]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2567]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1759 a r:Inference; r:gives { - 2757 :kaprekar 6174 . + 2759 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2759 math:notEqualTo 0}] + skolem:lemma3177 + [ a r:Fact; r:gives {(2 7 5 9) list:quicksort (2 5 7 9)}] + [ a r:Fact; r:gives {(2 5 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3910 - skolem:lemma3911 - [ a r:Fact; r:gives {(2 5 7 7) list:reverse (7 7 5 2)}] - skolem:lemma3546 - skolem:lemma3547 - [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2757]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2577]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1760 a r:Inference; r:gives { - 2758 :kaprekar 6174 . + 2760 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2760 math:notEqualTo 0}] + skolem:lemma3178 + [ a r:Fact; r:gives {(2 7 6 0) list:quicksort (0 2 6 7)}] + [ a r:Fact; r:gives {(0 2 6 7) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2758]; - r:rule skolem:lemma2032. + 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. skolem:lemma1761 a r:Inference; r:gives { - 2759 :kaprekar 6174 . + 2761 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2761 math:notEqualTo 0}] + skolem:lemma3179 + [ a r:Fact; r:gives {(2 7 6 1) list:quicksort (1 2 6 7)}] + [ a r:Fact; r:gives {(1 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3912 - skolem:lemma3913 - [ a r:Fact; r:gives {(2 5 7 9) list:reverse (9 7 5 2)}] - skolem:lemma3550 - skolem:lemma3551 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2759]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2579]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1762 a r:Inference; r:gives { - 2760 :kaprekar 6174 . + 2762 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2762 math:notEqualTo 0}] + skolem:lemma3180 + [ a r:Fact; r:gives {(2 7 6 2) list:quicksort (2 2 6 7)}] + [ a r:Fact; r:gives {(2 2 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3914 - skolem:lemma3915 - [ a r:Fact; r:gives {(0 2 6 7) list:reverse (7 6 2 0)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2760]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 267]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1763 a r:Inference; r:gives { - 2761 :kaprekar 6174 . + 2763 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2763 math:notEqualTo 0}] + skolem:lemma3181 + [ a r:Fact; r:gives {(2 7 6 3) list:quicksort (2 3 6 7)}] + [ a r:Fact; r:gives {(2 3 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3916 - skolem:lemma3917 - [ a r:Fact; r:gives {(1 2 6 7) list:reverse (7 6 2 1)}] - skolem:lemma2546 - skolem:lemma2547 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2761]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1267]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1764 a r:Inference; r:gives { - 2762 :kaprekar 6174 . + 2764 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3918 - skolem:lemma3919 - [ a r:Fact; r:gives {(2 2 6 7) list:reverse (7 6 2 2)}] - skolem:lemma2817 + [ a r:Fact; r:gives {2764 math:notEqualTo 0}] + skolem:lemma3182 + [ a r:Fact; r:gives {(2 7 6 4) list:quicksort (2 4 6 7)}] + [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] skolem:lemma2818 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + 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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2267]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1765 a r:Inference; r:gives { - 2763 :kaprekar 6174 . + 2765 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2765 math:notEqualTo 0}] + skolem:lemma3183 + [ a r:Fact; r:gives {(2 7 6 5) list:quicksort (2 5 6 7)}] + [ a r:Fact; r:gives {(2 5 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3920 - skolem:lemma3921 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2763]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1766 a r:Inference; r:gives { - 2764 :kaprekar 6174 . + 2766 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2766 math:notEqualTo 0}] + skolem:lemma3184 + [ a r:Fact; r:gives {(2 7 6 6) list:quicksort (2 6 6 7)}] + [ a r:Fact; r:gives {(2 6 6 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3922 - skolem:lemma3923 - [ a r:Fact; r:gives {(2 4 6 7) list:reverse (7 6 4 2)}] - skolem:lemma3302 - skolem:lemma3303 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2764]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2467]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1767 a r:Inference; r:gives { - 2765 :kaprekar 6174 . + 2767 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2767 math:notEqualTo 0}] + skolem:lemma3185 + [ a r:Fact; r:gives {(2 7 6 7) list:quicksort (2 6 7 7)}] + [ a r:Fact; r:gives {(2 6 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3924 - skolem:lemma3925 - [ a r:Fact; r:gives {(2 5 6 7) list:reverse (7 6 5 2)}] - skolem:lemma3520 - skolem:lemma3521 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2765]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2567]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1768 a r:Inference; r:gives { - 2766 :kaprekar 6174 . + 2768 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2768 math:notEqualTo 0}] + skolem:lemma3186 + [ a r:Fact; r:gives {(2 7 6 8) list:quicksort (2 6 7 8)}] + [ a r:Fact; r:gives {(2 6 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3926 - skolem:lemma3927 - [ a r:Fact; r:gives {(2 6 6 7) list:reverse (7 6 6 2)}] - skolem:lemma3724 - skolem:lemma3725 - [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2766]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2667]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1769 a r:Inference; r:gives { - 2767 :kaprekar 6174 . + 2769 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2769 math:notEqualTo 0}] + skolem:lemma3187 + [ a r:Fact; r:gives {(2 7 6 9) list:quicksort (2 6 7 9)}] + [ a r:Fact; r:gives {(2 6 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3928 - skolem:lemma3929 - [ a r:Fact; r:gives {(2 6 7 7) list:reverse (7 7 6 2)}] - skolem:lemma3750 - skolem:lemma3751 - [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2767]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2677]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1770 a r:Inference; r:gives { - 2768 :kaprekar 6174 . + 2770 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2770 math:notEqualTo 0}] + skolem:lemma3188 + [ a r:Fact; r:gives {(2 7 7 0) list:quicksort (0 2 7 7)}] + [ a r:Fact; r:gives {(0 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3930 - skolem:lemma3931 - [ a r:Fact; r:gives {(2 6 7 8) list:reverse (8 7 6 2)}] - skolem:lemma3754 - skolem:lemma3755 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2768]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2678]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1771 a r:Inference; r:gives { - 2769 :kaprekar 6174 . + 2771 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2771 math:notEqualTo 0}] + skolem:lemma3189 + [ a r:Fact; r:gives {(2 7 7 1) list:quicksort (1 2 7 7)}] + [ a r:Fact; r:gives {(1 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3932 - skolem:lemma3933 - [ a r:Fact; r:gives {(2 6 7 9) list:reverse (9 7 6 2)}] - skolem:lemma3758 - skolem:lemma3759 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2769]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2679]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1772 a r:Inference; r:gives { - 2770 :kaprekar 6174 . + 2772 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2772 math:notEqualTo 0}] + skolem:lemma3190 + [ a r:Fact; r:gives {(2 7 7 2) list:quicksort (2 2 7 7)}] + [ a r:Fact; r:gives {(2 2 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3934 - skolem:lemma3935 - [ a r:Fact; r:gives {(0 2 7 7) list:reverse (7 7 2 0)}] - skolem:lemma2276 - skolem:lemma2277 - [ a r:Fact; r:gives {(7720 277) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2770]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 277]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1773 a r:Inference; r:gives { - 2771 :kaprekar 6174 . + 2773 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2773 math:notEqualTo 0}] + skolem:lemma3191 + [ a r:Fact; r:gives {(2 7 7 3) list:quicksort (2 3 7 7)}] + [ a r:Fact; r:gives {(2 3 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3936 - skolem:lemma3937 - [ a r:Fact; r:gives {(1 2 7 7) list:reverse (7 7 2 1)}] - skolem:lemma2570 - skolem:lemma2571 - [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2771]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1277]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1774 a r:Inference; r:gives { - 2772 :kaprekar 6174 . + 2774 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2774 math:notEqualTo 0}] + skolem:lemma3192 + [ a r:Fact; r:gives {(2 7 7 4) list:quicksort (2 4 7 7)}] + [ a r:Fact; r:gives {(2 4 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3938 - skolem:lemma3939 - [ a r:Fact; r:gives {(2 2 7 7) list:reverse (7 7 2 2)}] - skolem:lemma2843 - skolem:lemma2844 - [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] - [ a r:Fact; r:gives {5445 math:notEqualTo 6174}] - skolem:lemma2845 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2277]; - 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_8"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1775 a r:Inference; r:gives { - 2773 :kaprekar 6174 . + 2775 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2775 math:notEqualTo 0}] + skolem:lemma3193 + [ a r:Fact; r:gives {(2 7 7 5) list:quicksort (2 5 7 7)}] + [ a r:Fact; r:gives {(2 5 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3940 - skolem:lemma3941 - [ a r:Fact; r:gives {(2 3 7 7) list:reverse (7 7 3 2)}] - skolem:lemma3096 - skolem:lemma3097 - [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2773]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2377]; - 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_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1776 a r:Inference; r:gives { - 2774 :kaprekar 6174 . + 2776 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2776 math:notEqualTo 0}] + skolem:lemma3194 + [ a r:Fact; r:gives {(2 7 7 6) list:quicksort (2 6 7 7)}] + [ a r:Fact; r:gives {(2 6 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3942 - skolem:lemma3943 - [ a r:Fact; r:gives {(2 4 7 7) list:reverse (7 7 4 2)}] - skolem:lemma3322 - skolem:lemma3323 - [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2774]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2477]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1777 a r:Inference; r:gives { - 2775 :kaprekar 6174 . + 2777 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2777 math:notEqualTo 0}] + skolem:lemma3195 + [ a r:Fact; r:gives {(2 7 7 7) list:quicksort (2 7 7 7)}] + [ a r:Fact; r:gives {(2 7 7 7) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3944 - skolem:lemma3945 - [ a r:Fact; r:gives {(2 5 7 7) list:reverse (7 7 5 2)}] - skolem:lemma3546 - skolem:lemma3547 - [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] - [ a r:Fact; r:gives {5175 math:notEqualTo 6174}] - skolem:lemma2031 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2775]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2577]; - 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_8"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1778 a r:Inference; r:gives { - 2776 :kaprekar 6174 . + 2778 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2778 math:notEqualTo 0}] + skolem:lemma3198 + [ a r:Fact; r:gives {(2 7 7 8) list:quicksort (2 7 7 8)}] + [ a r:Fact; r:gives {(2 7 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3946 - skolem:lemma3947 - [ a r:Fact; r:gives {(2 6 7 7) list:reverse (7 7 6 2)}] - skolem:lemma3750 - skolem:lemma3751 - [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] - [ a r:Fact; r:gives {5085 math:notEqualTo 6174}] - skolem:lemma2072 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2776]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2677]; - 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_8"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1779 a r:Inference; r:gives { - 2777 :kaprekar 6174 . + 2779 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2779 math:notEqualTo 0}] + skolem:lemma3201 + [ a r:Fact; r:gives {(2 7 7 9) list:quicksort (2 7 7 9)}] + [ a r:Fact; r:gives {(2 7 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3948 - skolem:lemma3949 - [ a r:Fact; r:gives {(2 7 7 7) list:reverse (7 7 7 2)}] - skolem:lemma3950 - skolem:lemma3951 - [ a r:Fact; r:gives {(7772 2777) math:difference 4995}] - [ a r:Fact; r:gives {4995 math:notEqualTo 6174}] - skolem:lemma2114 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2777]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2777]; - 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_8"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1780 a r:Inference; r:gives { - 2778 :kaprekar 6174 . + 2780 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2780 math:notEqualTo 0}] + skolem:lemma3204 + [ a r:Fact; r:gives {(2 7 8 0) list:quicksort (0 2 7 8)}] + [ a r:Fact; r:gives {(0 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3952 - skolem:lemma3953 - [ a r:Fact; r:gives {(2 7 7 8) list:reverse (8 7 7 2)}] - skolem:lemma3954 - skolem:lemma3955 - [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2778]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2778]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1781 a r:Inference; r:gives { - 2779 :kaprekar 6174 . + 2781 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2781 math:notEqualTo 0}] + skolem:lemma3205 + [ a r:Fact; r:gives {(2 7 8 1) list:quicksort (1 2 7 8)}] + [ a r:Fact; r:gives {(1 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3956 - skolem:lemma3957 - [ a r:Fact; r:gives {(2 7 7 9) list:reverse (9 7 7 2)}] - skolem:lemma3958 - skolem:lemma3959 - [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2779]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2779]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1782 a r:Inference; r:gives { - 2780 :kaprekar 6174 . + 2782 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2782 math:notEqualTo 0}] + skolem:lemma3206 + [ a r:Fact; r:gives {(2 7 8 2) list:quicksort (2 2 7 8)}] + [ a r:Fact; r:gives {(2 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3960 - skolem:lemma3961 - [ a r:Fact; r:gives {(0 2 7 8) list:reverse (8 7 2 0)}] - skolem:lemma2281 - skolem:lemma2282 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2780]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 278]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1783 a r:Inference; r:gives { - 2781 :kaprekar 6174 . + 2783 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2783 math:notEqualTo 0}] + skolem:lemma3207 + [ a r:Fact; r:gives {(2 7 8 3) list:quicksort (2 3 7 8)}] + [ a r:Fact; r:gives {(2 3 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3962 - skolem:lemma3963 - [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2781]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1784 a r:Inference; r:gives { - 2782 :kaprekar 6174 . + 2784 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2784 math:notEqualTo 0}] + skolem:lemma3208 + [ a r:Fact; r:gives {(2 7 8 4) list:quicksort (2 4 7 8)}] + [ a r:Fact; r:gives {(2 4 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3964 - skolem:lemma3965 - [ a r:Fact; r:gives {(2 2 7 8) list:reverse (8 7 2 2)}] - skolem:lemma2848 - skolem:lemma2849 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2782]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2278]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1785 a r:Inference; r:gives { - 2783 :kaprekar 6174 . + 2785 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2785 math:notEqualTo 0}] + skolem:lemma3209 + [ a r:Fact; r:gives {(2 7 8 5) list:quicksort (2 5 7 8)}] + [ a r:Fact; r:gives {(2 5 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3966 - skolem:lemma3967 - [ a r:Fact; r:gives {(2 3 7 8) list:reverse (8 7 3 2)}] - skolem:lemma3100 - skolem:lemma3101 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2783]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2378]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1786 a r:Inference; r:gives { - 2784 :kaprekar 6174 . + 2786 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2786 math:notEqualTo 0}] + skolem:lemma3210 + [ a r:Fact; r:gives {(2 7 8 6) list:quicksort (2 6 7 8)}] + [ a r:Fact; r:gives {(2 6 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3968 - skolem:lemma3969 - [ a r:Fact; r:gives {(2 4 7 8) list:reverse (8 7 4 2)}] - skolem:lemma3326 - skolem:lemma3327 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2784]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2478]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1787 a r:Inference; r:gives { - 2785 :kaprekar 6174 . + 2787 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2787 math:notEqualTo 0}] + skolem:lemma3211 + [ a r:Fact; r:gives {(2 7 8 7) list:quicksort (2 7 7 8)}] + [ a r:Fact; r:gives {(2 7 7 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2785]; - r:rule skolem:lemma2032. + 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. skolem:lemma1788 a r:Inference; r:gives { - 2786 :kaprekar 6174 . + 2788 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2788 math:notEqualTo 0}] + skolem:lemma3212 + [ a r:Fact; r:gives {(2 7 8 8) list:quicksort (2 7 8 8)}] + [ a r:Fact; r:gives {(2 7 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3970 - skolem:lemma3971 - [ a r:Fact; r:gives {(2 6 7 8) list:reverse (8 7 6 2)}] - skolem:lemma3754 - skolem:lemma3755 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2786]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2678]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1789 a r:Inference; r:gives { - 2787 :kaprekar 6174 . + 2789 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2789 math:notEqualTo 0}] + skolem:lemma3215 + [ a r:Fact; r:gives {(2 7 8 9) list:quicksort (2 7 8 9)}] + [ a r:Fact; r:gives {(2 7 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3972 - skolem:lemma3973 - [ a r:Fact; r:gives {(2 7 7 8) list:reverse (8 7 7 2)}] - skolem:lemma3954 - skolem:lemma3955 - [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2787]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2778]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1790 a r:Inference; r:gives { - 2788 :kaprekar 6174 . + 2790 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2790 math:notEqualTo 0}] + skolem:lemma3218 + [ a r:Fact; r:gives {(2 7 9 0) list:quicksort (0 2 7 9)}] + [ a r:Fact; r:gives {(0 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3974 - skolem:lemma3975 - [ a r:Fact; r:gives {(2 7 8 8) list:reverse (8 8 7 2)}] - skolem:lemma3976 - skolem:lemma3977 - [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2788]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2788]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1791 a r:Inference; r:gives { - 2789 :kaprekar 6174 . + 2791 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2791 math:notEqualTo 0}] + skolem:lemma3219 + [ a r:Fact; r:gives {(2 7 9 1) list:quicksort (1 2 7 9)}] + [ a r:Fact; r:gives {(1 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3978 - skolem:lemma3979 - [ a r:Fact; r:gives {(2 7 8 9) list:reverse (9 8 7 2)}] - skolem:lemma3980 - skolem:lemma3981 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2789]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1792 a r:Inference; r:gives { - 2790 :kaprekar 6174 . + 2792 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2792 math:notEqualTo 0}] + skolem:lemma3220 + [ a r:Fact; r:gives {(2 7 9 2) list:quicksort (2 2 7 9)}] + [ a r:Fact; r:gives {(2 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3982 - skolem:lemma3983 - [ a r:Fact; r:gives {(0 2 7 9) list:reverse (9 7 2 0)}] - skolem:lemma2286 - skolem:lemma2287 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {9441 math:notEqualTo 6174}] - skolem:lemma2288 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2790]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 279]; - 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_8"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1793 a r:Inference; r:gives { - 2791 :kaprekar 6174 . + 2793 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2793 math:notEqualTo 0}] + skolem:lemma3221 + [ a r:Fact; r:gives {(2 7 9 3) list:quicksort (2 3 7 9)}] + [ a r:Fact; r:gives {(2 3 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3984 - skolem:lemma3985 - [ a r:Fact; r:gives {(1 2 7 9) list:reverse (9 7 2 1)}] - skolem:lemma2579 - skolem:lemma2580 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2791]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1279]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1794 a r:Inference; r:gives { - 2792 :kaprekar 6174 . + 2794 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2794 math:notEqualTo 0}] + skolem:lemma3222 + [ a r:Fact; r:gives {(2 7 9 4) list:quicksort (2 4 7 9)}] + [ a r:Fact; r:gives {(2 4 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3986 - skolem:lemma3987 - [ a r:Fact; r:gives {(2 2 7 9) list:reverse (9 7 2 2)}] - skolem:lemma2852 - skolem:lemma2853 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2792]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2279]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1795 a r:Inference; r:gives { - 2793 :kaprekar 6174 . + 2795 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2795 math:notEqualTo 0}] + skolem:lemma3223 + [ a r:Fact; r:gives {(2 7 9 5) list:quicksort (2 5 7 9)}] + [ a r:Fact; r:gives {(2 5 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3988 - skolem:lemma3989 - [ a r:Fact; r:gives {(2 3 7 9) list:reverse (9 7 3 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2793]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2379]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1796 a r:Inference; r:gives { - 2794 :kaprekar 6174 . + 2796 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2796 math:notEqualTo 0}] + skolem:lemma3224 + [ a r:Fact; r:gives {(2 7 9 6) list:quicksort (2 6 7 9)}] + [ a r:Fact; r:gives {(2 6 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3990 - skolem:lemma3991 - [ a r:Fact; r:gives {(2 4 7 9) list:reverse (9 7 4 2)}] - skolem:lemma3330 - skolem:lemma3331 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2794]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2479]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1797 a r:Inference; r:gives { - 2795 :kaprekar 6174 . + 2797 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2797 math:notEqualTo 0}] + skolem:lemma3225 + [ a r:Fact; r:gives {(2 7 9 7) list:quicksort (2 7 7 9)}] + [ a r:Fact; r:gives {(2 7 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3992 - skolem:lemma3993 - [ a r:Fact; r:gives {(2 5 7 9) list:reverse (9 7 5 2)}] - skolem:lemma3550 - skolem:lemma3551 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2795]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2579]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1798 a r:Inference; r:gives { - 2796 :kaprekar 6174 . + 2798 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2798 math:notEqualTo 0}] + skolem:lemma3226 + [ a r:Fact; r:gives {(2 7 9 8) list:quicksort (2 7 8 9)}] + [ a r:Fact; r:gives {(2 7 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3994 - skolem:lemma3995 - [ a r:Fact; r:gives {(2 6 7 9) list:reverse (9 7 6 2)}] - skolem:lemma3758 - skolem:lemma3759 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2796]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2679]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1799 a r:Inference; r:gives { - 2797 :kaprekar 6174 . + 2799 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2799 math:notEqualTo 0}] + skolem:lemma3227 + [ a r:Fact; r:gives {(2 7 9 9) list:quicksort (2 7 9 9)}] + [ a r:Fact; r:gives {(2 7 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3996 - skolem:lemma3997 - [ a r:Fact; r:gives {(2 7 7 9) list:reverse (9 7 7 2)}] - skolem:lemma3958 - skolem:lemma3959 - [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2797]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2779]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1800 a r:Inference; r:gives { - 2798 :kaprekar 6174 . + 2800 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2800 math:notEqualTo 0}] + skolem:lemma3230 + [ a r:Fact; r:gives {(2 8 0 0) list:quicksort (0 0 2 8)}] + [ a r:Fact; r:gives {(0 0 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma3998 - skolem:lemma3999 - [ a r:Fact; r:gives {(2 7 8 9) list:reverse (9 8 7 2)}] - skolem:lemma3980 - skolem:lemma3981 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2798]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2789]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1801 a r:Inference; r:gives { - 2799 :kaprekar 6174 . + 2801 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2801 math:notEqualTo 0}] + skolem:lemma3231 + [ a r:Fact; r:gives {(2 8 0 1) list:quicksort (0 1 2 8)}] + [ a r:Fact; r:gives {(0 1 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4000 - skolem:lemma4001 - [ a r:Fact; r:gives {(2 7 9 9) list:reverse (9 9 7 2)}] - skolem:lemma4002 - skolem:lemma4003 - [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2799]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2799]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1802 a r:Inference; r:gives { - 2800 :kaprekar 6174 . + 2802 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2802 math:notEqualTo 0}] + skolem:lemma3232 + [ a r:Fact; r:gives {(2 8 0 2) list:quicksort (0 2 2 8)}] + [ a r:Fact; r:gives {(0 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4004 - skolem:lemma4005 - [ a r:Fact; r:gives {(0 0 2 8) list:reverse (8 2 0 0)}] - skolem:lemma2040 - skolem:lemma2041 - [ a r:Fact; r:gives {(8200 28) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2800]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 28]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1803 a r:Inference; r:gives { - 2801 :kaprekar 6174 . + 2803 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2803 math:notEqualTo 0}] + skolem:lemma3233 + [ a r:Fact; r:gives {(2 8 0 3) list:quicksort (0 2 3 8)}] + [ a r:Fact; r:gives {(0 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4006 - skolem:lemma4007 - [ a r:Fact; r:gives {(0 1 2 8) list:reverse (8 2 1 0)}] - skolem:lemma2085 - skolem:lemma2086 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2801]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1804 a r:Inference; r:gives { - 2802 :kaprekar 6174 . + 2804 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4008 - skolem:lemma4009 - [ a r:Fact; r:gives {(0 2 2 8) list:reverse (8 2 2 0)}] + [ a r:Fact; r:gives {2804 math:notEqualTo 0}] + skolem:lemma3234 + [ a r:Fact; r:gives {(2 8 0 4) list:quicksort (0 2 4 8)}] + [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] + skolem:lemma2126 skolem:lemma2127 - skolem:lemma2128 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2802]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 228]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1805 a r:Inference; r:gives { - 2803 :kaprekar 6174 . + 2805 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2805 math:notEqualTo 0}] + skolem:lemma3235 + [ a r:Fact; r:gives {(2 8 0 5) list:quicksort (0 2 5 8)}] + [ a r:Fact; r:gives {(0 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4010 - skolem:lemma4011 - [ a r:Fact; r:gives {(0 2 3 8) list:reverse (8 3 2 0)}] - skolem:lemma2163 - skolem:lemma2164 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2803]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 238]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1806 a r:Inference; r:gives { - 2804 :kaprekar 6174 . + 2806 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2806 math:notEqualTo 0}] + skolem:lemma3236 + [ a r:Fact; r:gives {(2 8 0 6) list:quicksort (0 2 6 8)}] + [ a r:Fact; r:gives {(0 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4012 - skolem:lemma4013 - [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] - skolem:lemma2191 - skolem:lemma2192 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2804]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 248]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1807 a r:Inference; r:gives { - 2805 :kaprekar 6174 . + 2807 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2807 math:notEqualTo 0}] + skolem:lemma3237 + [ a r:Fact; r:gives {(2 8 0 7) list:quicksort (0 2 7 8)}] + [ a r:Fact; r:gives {(0 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4014 - skolem:lemma4015 - [ a r:Fact; r:gives {(0 2 5 8) list:reverse (8 5 2 0)}] - skolem:lemma2224 - skolem:lemma2225 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2805]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 258]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1808 a r:Inference; r:gives { - 2806 :kaprekar 6174 . + 2808 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2808 math:notEqualTo 0}] + skolem:lemma3238 + [ a r:Fact; r:gives {(2 8 0 8) list:quicksort (0 2 8 8)}] + [ a r:Fact; r:gives {(0 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4016 - skolem:lemma4017 - [ a r:Fact; r:gives {(0 2 6 8) list:reverse (8 6 2 0)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2806]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 268]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1809 a r:Inference; r:gives { - 2807 :kaprekar 6174 . + 2809 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2809 math:notEqualTo 0}] + skolem:lemma3239 + [ a r:Fact; r:gives {(2 8 0 9) list:quicksort (0 2 8 9)}] + [ a r:Fact; r:gives {(0 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4018 - skolem:lemma4019 - [ a r:Fact; r:gives {(0 2 7 8) list:reverse (8 7 2 0)}] - skolem:lemma2281 - skolem:lemma2282 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2807]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 278]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1810 a r:Inference; r:gives { - 2808 :kaprekar 6174 . + 2810 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2810 math:notEqualTo 0}] + skolem:lemma3240 + [ a r:Fact; r:gives {(2 8 1 0) list:quicksort (0 1 2 8)}] + [ a r:Fact; r:gives {(0 1 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4020 - skolem:lemma4021 - [ a r:Fact; r:gives {(0 2 8 8) list:reverse (8 8 2 0)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2808]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 288]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1811 a r:Inference; r:gives { - 2809 :kaprekar 6174 . + 2811 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2811 math:notEqualTo 0}] + skolem:lemma3241 + [ a r:Fact; r:gives {(2 8 1 1) list:quicksort (1 1 2 8)}] + [ a r:Fact; r:gives {(1 1 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4022 - skolem:lemma4023 - [ a r:Fact; r:gives {(0 2 8 9) list:reverse (9 8 2 0)}] - skolem:lemma2312 - skolem:lemma2313 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {9531 math:notEqualTo 6174}] - skolem:lemma2314 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2809]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 289]; - 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_8"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1812 a r:Inference; r:gives { - 2810 :kaprekar 6174 . + 2812 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2812 math:notEqualTo 0}] + skolem:lemma3242 + [ a r:Fact; r:gives {(2 8 1 2) list:quicksort (1 2 2 8)}] + [ a r:Fact; r:gives {(1 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4024 - skolem:lemma4025 - [ a r:Fact; r:gives {(0 1 2 8) list:reverse (8 2 1 0)}] - skolem:lemma2085 - skolem:lemma2086 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2810]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 128]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1813 a r:Inference; r:gives { - 2811 :kaprekar 6174 . + 2813 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2813 math:notEqualTo 0}] + skolem:lemma3243 + [ a r:Fact; r:gives {(2 8 1 3) list:quicksort (1 2 3 8)}] + [ a r:Fact; r:gives {(1 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4026 - skolem:lemma4027 - [ a r:Fact; r:gives {(1 1 2 8) list:reverse (8 2 1 1)}] - skolem:lemma2392 - skolem:lemma2393 - [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2811]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1128]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1814 a r:Inference; r:gives { - 2812 :kaprekar 6174 . + 2814 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2814 math:notEqualTo 0}] + skolem:lemma3244 + [ a r:Fact; r:gives {(2 8 1 4) list:quicksort (1 2 4 8)}] + [ a r:Fact; r:gives {(1 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4028 - skolem:lemma4029 - [ a r:Fact; r:gives {(1 2 2 8) list:reverse (8 2 2 1)}] - skolem:lemma2428 - skolem:lemma2429 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2812]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1228]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1815 a r:Inference; r:gives { - 2813 :kaprekar 6174 . + 2815 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2815 math:notEqualTo 0}] + skolem:lemma3245 + [ a r:Fact; r:gives {(2 8 1 5) list:quicksort (1 2 5 8)}] + [ a r:Fact; r:gives {(1 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4030 - skolem:lemma4031 - [ a r:Fact; r:gives {(1 2 3 8) list:reverse (8 3 2 1)}] - skolem:lemma2462 - skolem:lemma2463 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2813]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1238]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1816 a r:Inference; r:gives { - 2814 :kaprekar 6174 . + 2816 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2816 math:notEqualTo 0}] + skolem:lemma3246 + [ a r:Fact; r:gives {(2 8 1 6) list:quicksort (1 2 6 8)}] + [ a r:Fact; r:gives {(1 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4032 - skolem:lemma4033 - [ a r:Fact; r:gives {(1 2 4 8) list:reverse (8 4 2 1)}] - skolem:lemma2490 - skolem:lemma2491 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2814]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1248]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1817 a r:Inference; r:gives { - 2815 :kaprekar 6174 . + 2817 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2817 math:notEqualTo 0}] + skolem:lemma3247 + [ a r:Fact; r:gives {(2 8 1 7) list:quicksort (1 2 7 8)}] + [ a r:Fact; r:gives {(1 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4034 - skolem:lemma4035 - [ a r:Fact; r:gives {(1 2 5 8) list:reverse (8 5 2 1)}] - skolem:lemma2521 - skolem:lemma2522 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2815]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1258]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1818 a r:Inference; r:gives { - 2816 :kaprekar 6174 . + 2818 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2818 math:notEqualTo 0}] + skolem:lemma3248 + [ a r:Fact; r:gives {(2 8 1 8) list:quicksort (1 2 8 8)}] + [ a r:Fact; r:gives {(1 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4036 - skolem:lemma4037 - [ a r:Fact; r:gives {(1 2 6 8) list:reverse (8 6 2 1)}] - skolem:lemma2550 - skolem:lemma2551 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2816]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1268]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1819 a r:Inference; r:gives { - 2817 :kaprekar 6174 . + 2819 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2819 math:notEqualTo 0}] + skolem:lemma3249 + [ a r:Fact; r:gives {(2 8 1 9) list:quicksort (1 2 8 9)}] + [ a r:Fact; r:gives {(1 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4038 - skolem:lemma4039 - [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2817]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1820 a r:Inference; r:gives { - 2818 :kaprekar 6174 . + 2820 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2820 math:notEqualTo 0}] + skolem:lemma3250 + [ a r:Fact; r:gives {(2 8 2 0) list:quicksort (0 2 2 8)}] + [ a r:Fact; r:gives {(0 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4040 - skolem:lemma4041 - [ a r:Fact; r:gives {(1 2 8 8) list:reverse (8 8 2 1)}] - skolem:lemma2599 - skolem:lemma2600 - [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2818]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1288]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1821 a r:Inference; r:gives { - 2819 :kaprekar 6174 . + 2821 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2821 math:notEqualTo 0}] + skolem:lemma3251 + [ a r:Fact; r:gives {(2 8 2 1) list:quicksort (1 2 2 8)}] + [ a r:Fact; r:gives {(1 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4042 - skolem:lemma4043 - [ a r:Fact; r:gives {(1 2 8 9) list:reverse (9 8 2 1)}] - skolem:lemma2604 - skolem:lemma2605 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2819]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1289]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1822 a r:Inference; r:gives { - 2820 :kaprekar 6174 . + 2822 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2822 math:notEqualTo 0}] + skolem:lemma3252 + [ a r:Fact; r:gives {(2 8 2 2) list:quicksort (2 2 2 8)}] + [ a r:Fact; r:gives {(2 2 2 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4044 - skolem:lemma4045 - [ a r:Fact; r:gives {(0 2 2 8) list:reverse (8 2 2 0)}] - skolem:lemma2127 - skolem:lemma2128 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 228]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1823 a r:Inference; r:gives { - 2821 :kaprekar 6174 . + 2823 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2823 math:notEqualTo 0}] + skolem:lemma3253 + [ a r:Fact; r:gives {(2 8 2 3) list:quicksort (2 2 3 8)}] + [ a r:Fact; r:gives {(2 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4046 - skolem:lemma4047 - [ a r:Fact; r:gives {(1 2 2 8) list:reverse (8 2 2 1)}] - skolem:lemma2428 - skolem:lemma2429 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1228]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1824 a r:Inference; r:gives { - 2822 :kaprekar 6174 . + 2824 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2824 math:notEqualTo 0}] + skolem:lemma3254 + [ a r:Fact; r:gives {(2 8 2 4) list:quicksort (2 2 4 8)}] + [ a r:Fact; r:gives {(2 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4048 - skolem:lemma4049 - [ a r:Fact; r:gives {(2 2 2 8) list:reverse (8 2 2 2)}] - skolem:lemma2699 - skolem:lemma2700 - [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2228]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1825 a r:Inference; r:gives { - 2823 :kaprekar 6174 . + 2825 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2825 math:notEqualTo 0}] + skolem:lemma3255 + [ a r:Fact; r:gives {(2 8 2 5) list:quicksort (2 2 5 8)}] + [ a r:Fact; r:gives {(2 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4050 - skolem:lemma4051 - [ a r:Fact; r:gives {(2 2 3 8) list:reverse (8 3 2 2)}] - skolem:lemma2733 - skolem:lemma2734 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2823]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2238]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1826 a r:Inference; r:gives { - 2824 :kaprekar 6174 . + 2826 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2826 math:notEqualTo 0}] + skolem:lemma3256 + [ a r:Fact; r:gives {(2 8 2 6) list:quicksort (2 2 6 8)}] + [ a r:Fact; r:gives {(2 2 6 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2824]; - r:rule skolem:lemma2032. + 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. skolem:lemma1827 a r:Inference; r:gives { - 2825 :kaprekar 6174 . + 2827 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2827 math:notEqualTo 0}] + skolem:lemma3257 + [ a r:Fact; r:gives {(2 8 2 7) list:quicksort (2 2 7 8)}] + [ a r:Fact; r:gives {(2 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4052 - skolem:lemma4053 - [ a r:Fact; r:gives {(2 2 5 8) list:reverse (8 5 2 2)}] - skolem:lemma2792 - skolem:lemma2793 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2825]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2258]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1828 a r:Inference; r:gives { - 2826 :kaprekar 6174 . + 2828 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2828 math:notEqualTo 0}] + skolem:lemma3258 + [ a r:Fact; r:gives {(2 8 2 8) list:quicksort (2 2 8 8)}] + [ a r:Fact; r:gives {(2 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4054 - skolem:lemma4055 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2826]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1829 a r:Inference; r:gives { - 2827 :kaprekar 6174 . + 2829 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2829 math:notEqualTo 0}] + skolem:lemma3259 + [ a r:Fact; r:gives {(2 8 2 9) list:quicksort (2 2 8 9)}] + [ a r:Fact; r:gives {(2 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4056 - skolem:lemma4057 - [ a r:Fact; r:gives {(2 2 7 8) list:reverse (8 7 2 2)}] - skolem:lemma2848 - skolem:lemma2849 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2827]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2278]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1830 a r:Inference; r:gives { - 2828 :kaprekar 6174 . + 2830 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2830 math:notEqualTo 0}] + skolem:lemma3260 + [ a r:Fact; r:gives {(2 8 3 0) list:quicksort (0 2 3 8)}] + [ a r:Fact; r:gives {(0 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4058 - skolem:lemma4059 - [ a r:Fact; r:gives {(2 2 8 8) list:reverse (8 8 2 2)}] - skolem:lemma2870 - skolem:lemma2871 - [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] - [ a r:Fact; r:gives {6534 math:notEqualTo 6174}] - skolem:lemma2872 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2828]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2288]; - 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_8"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1831 a r:Inference; r:gives { - 2829 :kaprekar 6174 . + 2831 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2831 math:notEqualTo 0}] + skolem:lemma3261 + [ a r:Fact; r:gives {(2 8 3 1) list:quicksort (1 2 3 8)}] + [ a r:Fact; r:gives {(1 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4060 - skolem:lemma4061 - [ a r:Fact; r:gives {(2 2 8 9) list:reverse (9 8 2 2)}] - skolem:lemma2875 - skolem:lemma2876 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2829]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2289]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1832 a r:Inference; r:gives { - 2830 :kaprekar 6174 . + 2832 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2832 math:notEqualTo 0}] + skolem:lemma3262 + [ a r:Fact; r:gives {(2 8 3 2) list:quicksort (2 2 3 8)}] + [ a r:Fact; r:gives {(2 2 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4062 - skolem:lemma4063 - [ a r:Fact; r:gives {(0 2 3 8) list:reverse (8 3 2 0)}] - skolem:lemma2163 - skolem:lemma2164 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2830]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 238]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1833 a r:Inference; r:gives { - 2831 :kaprekar 6174 . + 2833 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2833 math:notEqualTo 0}] + skolem:lemma3263 + [ a r:Fact; r:gives {(2 8 3 3) list:quicksort (2 3 3 8)}] + [ a r:Fact; r:gives {(2 3 3 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4064 - skolem:lemma4065 - [ a r:Fact; r:gives {(1 2 3 8) list:reverse (8 3 2 1)}] - skolem:lemma2462 - skolem:lemma2463 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2831]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1238]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1834 a r:Inference; r:gives { - 2832 :kaprekar 6174 . + 2834 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2834 math:notEqualTo 0}] + skolem:lemma3264 + [ a r:Fact; r:gives {(2 8 3 4) list:quicksort (2 3 4 8)}] + [ a r:Fact; r:gives {(2 3 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4066 - skolem:lemma4067 - [ a r:Fact; r:gives {(2 2 3 8) list:reverse (8 3 2 2)}] - skolem:lemma2733 - skolem:lemma2734 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2238]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1835 a r:Inference; r:gives { - 2833 :kaprekar 6174 . + 2835 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4068 - skolem:lemma4069 - [ a r:Fact; r:gives {(2 3 3 8) list:reverse (8 3 3 2)}] - skolem:lemma2988 - skolem:lemma2989 - [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ a r:Fact; r:gives {2835 math:notEqualTo 0}] + skolem:lemma3265 + [ a r:Fact; r:gives {(2 8 3 5) list:quicksort (2 3 5 8)}] + [ a r:Fact; r:gives {(2 3 5 8) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2833]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2338]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1836 a r:Inference; r:gives { - 2834 :kaprekar 6174 . + 2836 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2836 math:notEqualTo 0}] + skolem:lemma3266 + [ a r:Fact; r:gives {(2 8 3 6) list:quicksort (2 3 6 8)}] + [ a r:Fact; r:gives {(2 3 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4070 - skolem:lemma4071 - [ a r:Fact; r:gives {(2 3 4 8) list:reverse (8 4 3 2)}] - skolem:lemma3020 - skolem:lemma3021 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2834]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2348]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1837 a r:Inference; r:gives { - 2835 :kaprekar 6174 . + 2837 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2837 math:notEqualTo 0}] + skolem:lemma3267 + [ a r:Fact; r:gives {(2 8 3 7) list:quicksort (2 3 7 8)}] + [ a r:Fact; r:gives {(2 3 7 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2835]; - r:rule skolem:lemma2032. + 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. skolem:lemma1838 a r:Inference; r:gives { - 2836 :kaprekar 6174 . + 2838 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2838 math:notEqualTo 0}] + skolem:lemma3268 + [ a r:Fact; r:gives {(2 8 3 8) list:quicksort (2 3 8 8)}] + [ a r:Fact; r:gives {(2 3 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4072 - skolem:lemma4073 - [ a r:Fact; r:gives {(2 3 6 8) list:reverse (8 6 3 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2836]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2368]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1839 a r:Inference; r:gives { - 2837 :kaprekar 6174 . + 2839 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2839 math:notEqualTo 0}] + skolem:lemma3269 + [ a r:Fact; r:gives {(2 8 3 9) list:quicksort (2 3 8 9)}] + [ a r:Fact; r:gives {(2 3 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4074 - skolem:lemma4075 - [ a r:Fact; r:gives {(2 3 7 8) list:reverse (8 7 3 2)}] - skolem:lemma3100 - skolem:lemma3101 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2837]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2378]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1840 a r:Inference; r:gives { - 2838 :kaprekar 6174 . + 2840 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2840 math:notEqualTo 0}] + skolem:lemma3270 + [ a r:Fact; r:gives {(2 8 4 0) list:quicksort (0 2 4 8)}] + [ a r:Fact; r:gives {(0 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4076 - skolem:lemma4077 - [ a r:Fact; r:gives {(2 3 8 8) list:reverse (8 8 3 2)}] - skolem:lemma3122 - skolem:lemma3123 - [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2838]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2388]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1841 a r:Inference; r:gives { - 2839 :kaprekar 6174 . + 2841 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2841 math:notEqualTo 0}] + skolem:lemma3271 + [ a r:Fact; r:gives {(2 8 4 1) list:quicksort (1 2 4 8)}] + [ a r:Fact; r:gives {(1 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4078 - skolem:lemma4079 - [ a r:Fact; r:gives {(2 3 8 9) list:reverse (9 8 3 2)}] - skolem:lemma3126 - skolem:lemma3127 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2839]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2389]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1842 a r:Inference; r:gives { - 2840 :kaprekar 6174 . + 2842 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2842 math:notEqualTo 0}] + skolem:lemma3272 + [ a r:Fact; r:gives {(2 8 4 2) list:quicksort (2 2 4 8)}] + [ a r:Fact; r:gives {(2 2 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4080 - skolem:lemma4081 - [ a r:Fact; r:gives {(0 2 4 8) list:reverse (8 4 2 0)}] - skolem:lemma2191 - skolem:lemma2192 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2840]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 248]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1843 a r:Inference; r:gives { - 2841 :kaprekar 6174 . + 2843 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2843 math:notEqualTo 0}] + skolem:lemma3273 + [ a r:Fact; r:gives {(2 8 4 3) list:quicksort (2 3 4 8)}] + [ a r:Fact; r:gives {(2 3 4 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4082 - skolem:lemma4083 - [ a r:Fact; r:gives {(1 2 4 8) list:reverse (8 4 2 1)}] - skolem:lemma2490 - skolem:lemma2491 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2841]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1248]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1844 a r:Inference; r:gives { - 2842 :kaprekar 6174 . + 2844 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2844 math:notEqualTo 0}] + skolem:lemma3274 + [ a r:Fact; r:gives {(2 8 4 4) list:quicksort (2 4 4 8)}] + [ a r:Fact; r:gives {(2 4 4 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2842]; - r:rule skolem:lemma2032. + 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. skolem:lemma1845 a r:Inference; r:gives { - 2843 :kaprekar 6174 . + 2845 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2845 math:notEqualTo 0}] + skolem:lemma3275 + [ a r:Fact; r:gives {(2 8 4 5) list:quicksort (2 4 5 8)}] + [ a r:Fact; r:gives {(2 4 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4084 - skolem:lemma4085 - [ a r:Fact; r:gives {(2 3 4 8) list:reverse (8 4 3 2)}] - skolem:lemma3020 - skolem:lemma3021 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2843]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2348]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1846 a r:Inference; r:gives { - 2844 :kaprekar 6174 . + 2846 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2846 math:notEqualTo 0}] + skolem:lemma3276 + [ a r:Fact; r:gives {(2 8 4 6) list:quicksort (2 4 6 8)}] + [ a r:Fact; r:gives {(2 4 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4086 - skolem:lemma4087 - [ a r:Fact; r:gives {(2 4 4 8) list:reverse (8 4 4 2)}] - skolem:lemma3250 - skolem:lemma3251 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2844]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2448]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1847 a r:Inference; r:gives { - 2845 :kaprekar 6174 . + 2847 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2847 math:notEqualTo 0}] + skolem:lemma3277 + [ a r:Fact; r:gives {(2 8 4 7) list:quicksort (2 4 7 8)}] + [ a r:Fact; r:gives {(2 4 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4088 - skolem:lemma4089 - [ a r:Fact; r:gives {(2 4 5 8) list:reverse (8 5 4 2)}] - skolem:lemma3280 - skolem:lemma3281 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2845]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2458]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1848 a r:Inference; r:gives { - 2846 :kaprekar 6174 . + 2848 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2848 math:notEqualTo 0}] + skolem:lemma3278 + [ a r:Fact; r:gives {(2 8 4 8) list:quicksort (2 4 8 8)}] + [ a r:Fact; r:gives {(2 4 8 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2846]; - r:rule skolem:lemma2032. + 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. skolem:lemma1849 a r:Inference; r:gives { - 2847 :kaprekar 6174 . + 2849 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2849 math:notEqualTo 0}] + skolem:lemma3279 + [ a r:Fact; r:gives {(2 8 4 9) list:quicksort (2 4 8 9)}] + [ a r:Fact; r:gives {(2 4 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4090 - skolem:lemma4091 - [ a r:Fact; r:gives {(2 4 7 8) list:reverse (8 7 4 2)}] - skolem:lemma3326 - skolem:lemma3327 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2847]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2478]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1850 a r:Inference; r:gives { - 2848 :kaprekar 6174 . + 2850 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2850 math:notEqualTo 0}] + skolem:lemma3280 + [ a r:Fact; r:gives {(2 8 5 0) list:quicksort (0 2 5 8)}] + [ a r:Fact; r:gives {(0 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4092 - skolem:lemma4093 - [ a r:Fact; r:gives {(2 4 8 8) list:reverse (8 8 4 2)}] - skolem:lemma3346 - skolem:lemma3347 - [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2848]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2488]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1851 a r:Inference; r:gives { - 2849 :kaprekar 6174 . + 2851 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2851 math:notEqualTo 0}] + skolem:lemma3281 + [ a r:Fact; r:gives {(2 8 5 1) list:quicksort (1 2 5 8)}] + [ a r:Fact; r:gives {(1 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4094 - skolem:lemma4095 - [ a r:Fact; r:gives {(2 4 8 9) list:reverse (9 8 4 2)}] - skolem:lemma3350 - skolem:lemma3351 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2849]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2489]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1852 a r:Inference; r:gives { - 2850 :kaprekar 6174 . + 2852 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2852 math:notEqualTo 0}] + skolem:lemma3282 + [ a r:Fact; r:gives {(2 8 5 2) list:quicksort (2 2 5 8)}] + [ a r:Fact; r:gives {(2 2 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4096 - skolem:lemma4097 - [ a r:Fact; r:gives {(0 2 5 8) list:reverse (8 5 2 0)}] - skolem:lemma2224 - skolem:lemma2225 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2850]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 258]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1853 a r:Inference; r:gives { - 2851 :kaprekar 6174 . + 2853 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2853 math:notEqualTo 0}] + skolem:lemma3283 + [ a r:Fact; r:gives {(2 8 5 3) list:quicksort (2 3 5 8)}] + [ a r:Fact; r:gives {(2 3 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4098 - skolem:lemma4099 - [ a r:Fact; r:gives {(1 2 5 8) list:reverse (8 5 2 1)}] - skolem:lemma2521 - skolem:lemma2522 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2851]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1258]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1854 a r:Inference; r:gives { - 2852 :kaprekar 6174 . + 2854 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2854 math:notEqualTo 0}] + skolem:lemma3284 + [ a r:Fact; r:gives {(2 8 5 4) list:quicksort (2 4 5 8)}] + [ a r:Fact; r:gives {(2 4 5 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4100 - skolem:lemma4101 - [ a r:Fact; r:gives {(2 2 5 8) list:reverse (8 5 2 2)}] - skolem:lemma2792 - skolem:lemma2793 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2258]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1855 a r:Inference; r:gives { - 2853 :kaprekar 6174 . + 2855 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2855 math:notEqualTo 0}] + skolem:lemma3285 + [ a r:Fact; r:gives {(2 8 5 5) list:quicksort (2 5 5 8)}] + [ a r:Fact; r:gives {(2 5 5 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2853]; - r:rule skolem:lemma2032. + 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. skolem:lemma1856 a r:Inference; r:gives { - 2854 :kaprekar 6174 . + 2856 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2856 math:notEqualTo 0}] + skolem:lemma3286 + [ a r:Fact; r:gives {(2 8 5 6) list:quicksort (2 5 6 8)}] + [ a r:Fact; r:gives {(2 5 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4102 - skolem:lemma4103 - [ a r:Fact; r:gives {(2 4 5 8) list:reverse (8 5 4 2)}] - skolem:lemma3280 - skolem:lemma3281 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2854]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2458]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1857 a r:Inference; r:gives { - 2855 :kaprekar 6174 . + 2857 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2857 math:notEqualTo 0}] + skolem:lemma3287 + [ a r:Fact; r:gives {(2 8 5 7) list:quicksort (2 5 7 8)}] + [ a r:Fact; r:gives {(2 5 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4104 - skolem:lemma4105 - [ a r:Fact; r:gives {(2 5 5 8) list:reverse (8 5 5 2)}] - skolem:lemma3496 - skolem:lemma3497 - [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2855]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2558]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1858 a r:Inference; r:gives { - 2856 :kaprekar 6174 . + 2858 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2858 math:notEqualTo 0}] + skolem:lemma3288 + [ a r:Fact; r:gives {(2 8 5 8) list:quicksort (2 5 8 8)}] + [ a r:Fact; r:gives {(2 5 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4106 - skolem:lemma4107 - [ a r:Fact; r:gives {(2 5 6 8) list:reverse (8 6 5 2)}] - skolem:lemma3524 - skolem:lemma3525 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2856]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2568]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1859 a r:Inference; r:gives { - 2857 :kaprekar 6174 . + 2859 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2859 math:notEqualTo 0}] + skolem:lemma3289 + [ a r:Fact; r:gives {(2 8 5 9) list:quicksort (2 5 8 9)}] + [ a r:Fact; r:gives {(2 5 8 9) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2857]; - r:rule skolem:lemma2032. + 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. skolem:lemma1860 a r:Inference; r:gives { - 2858 :kaprekar 6174 . + 2860 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2860 math:notEqualTo 0}] + skolem:lemma3290 + [ a r:Fact; r:gives {(2 8 6 0) list:quicksort (0 2 6 8)}] + [ a r:Fact; r:gives {(0 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4108 - skolem:lemma4109 - [ a r:Fact; r:gives {(2 5 8 8) list:reverse (8 8 5 2)}] - skolem:lemma3566 - skolem:lemma3567 - [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2858]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2588]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1861 a r:Inference; r:gives { - 2859 :kaprekar 6174 . + 2861 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2861 math:notEqualTo 0}] + skolem:lemma3291 + [ a r:Fact; r:gives {(2 8 6 1) list:quicksort (1 2 6 8)}] + [ a r:Fact; r:gives {(1 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4110 - skolem:lemma4111 - [ a r:Fact; r:gives {(2 5 8 9) list:reverse (9 8 5 2)}] - skolem:lemma3570 - skolem:lemma3571 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2859]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2589]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1862 a r:Inference; r:gives { - 2860 :kaprekar 6174 . + 2862 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2862 math:notEqualTo 0}] + skolem:lemma3292 + [ a r:Fact; r:gives {(2 8 6 2) list:quicksort (2 2 6 8)}] + [ a r:Fact; r:gives {(2 2 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4112 - skolem:lemma4113 - [ a r:Fact; r:gives {(0 2 6 8) list:reverse (8 6 2 0)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2860]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 268]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1863 a r:Inference; r:gives { - 2861 :kaprekar 6174 . + 2863 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2863 math:notEqualTo 0}] + skolem:lemma3293 + [ a r:Fact; r:gives {(2 8 6 3) list:quicksort (2 3 6 8)}] + [ a r:Fact; r:gives {(2 3 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4114 - skolem:lemma4115 - [ a r:Fact; r:gives {(1 2 6 8) list:reverse (8 6 2 1)}] - skolem:lemma2550 - skolem:lemma2551 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2861]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1268]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1864 a r:Inference; r:gives { - 2862 :kaprekar 6174 . + 2864 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4116 - skolem:lemma4117 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] + [ a r:Fact; r:gives {2864 math:notEqualTo 0}] + skolem:lemma3294 + [ a r:Fact; r:gives {(2 8 6 4) list:quicksort (2 4 6 8)}] + [ a r:Fact; r:gives {(2 4 6 8) list:reverse (8 6 4 2)}] skolem:lemma2821 skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1865 a r:Inference; r:gives { - 2863 :kaprekar 6174 . + 2865 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2865 math:notEqualTo 0}] + skolem:lemma3295 + [ a r:Fact; r:gives {(2 8 6 5) list:quicksort (2 5 6 8)}] + [ a r:Fact; r:gives {(2 5 6 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4118 - skolem:lemma4119 - [ a r:Fact; r:gives {(2 3 6 8) list:reverse (8 6 3 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2863]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2368]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1866 a r:Inference; r:gives { - 2864 :kaprekar 6174 . + 2866 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2866 math:notEqualTo 0}] + skolem:lemma3296 + [ a r:Fact; r:gives {(2 8 6 6) list:quicksort (2 6 6 8)}] + [ a r:Fact; r:gives {(2 6 6 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2864]; - r:rule skolem:lemma2032. + 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. skolem:lemma1867 a r:Inference; r:gives { - 2865 :kaprekar 6174 . + 2867 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2867 math:notEqualTo 0}] + skolem:lemma3297 + [ a r:Fact; r:gives {(2 8 6 7) list:quicksort (2 6 7 8)}] + [ a r:Fact; r:gives {(2 6 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4120 - skolem:lemma4121 - [ a r:Fact; r:gives {(2 5 6 8) list:reverse (8 6 5 2)}] - skolem:lemma3524 - skolem:lemma3525 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2865]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2568]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1868 a r:Inference; r:gives { - 2866 :kaprekar 6174 . + 2868 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2868 math:notEqualTo 0}] + skolem:lemma3298 + [ a r:Fact; r:gives {(2 8 6 8) list:quicksort (2 6 8 8)}] + [ a r:Fact; r:gives {(2 6 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4122 - skolem:lemma4123 - [ a r:Fact; r:gives {(2 6 6 8) list:reverse (8 6 6 2)}] - skolem:lemma3728 - skolem:lemma3729 - [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2866]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2668]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1869 a r:Inference; r:gives { - 2867 :kaprekar 6174 . + 2869 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2869 math:notEqualTo 0}] + skolem:lemma3299 + [ a r:Fact; r:gives {(2 8 6 9) list:quicksort (2 6 8 9)}] + [ a r:Fact; r:gives {(2 6 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4124 - skolem:lemma4125 - [ a r:Fact; r:gives {(2 6 7 8) list:reverse (8 7 6 2)}] - skolem:lemma3754 - skolem:lemma3755 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2867]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2678]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1870 a r:Inference; r:gives { - 2868 :kaprekar 6174 . + 2870 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2870 math:notEqualTo 0}] + skolem:lemma3300 + [ a r:Fact; r:gives {(2 8 7 0) list:quicksort (0 2 7 8)}] + [ a r:Fact; r:gives {(0 2 7 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2868]; - r:rule skolem:lemma2032. + 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. skolem:lemma1871 a r:Inference; r:gives { - 2869 :kaprekar 6174 . + 2871 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2871 math:notEqualTo 0}] + skolem:lemma3301 + [ a r:Fact; r:gives {(2 8 7 1) list:quicksort (1 2 7 8)}] + [ a r:Fact; r:gives {(1 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4126 - skolem:lemma4127 - [ a r:Fact; r:gives {(2 6 8 9) list:reverse (9 8 6 2)}] - skolem:lemma3776 - skolem:lemma3777 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2869]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2689]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1872 a r:Inference; r:gives { - 2870 :kaprekar 6174 . + 2872 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2872 math:notEqualTo 0}] + skolem:lemma3302 + [ a r:Fact; r:gives {(2 8 7 2) list:quicksort (2 2 7 8)}] + [ a r:Fact; r:gives {(2 2 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4128 - skolem:lemma4129 - [ a r:Fact; r:gives {(0 2 7 8) list:reverse (8 7 2 0)}] - skolem:lemma2281 - skolem:lemma2282 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2870]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 278]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1873 a r:Inference; r:gives { - 2871 :kaprekar 6174 . + 2873 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2873 math:notEqualTo 0}] + skolem:lemma3303 + [ a r:Fact; r:gives {(2 8 7 3) list:quicksort (2 3 7 8)}] + [ a r:Fact; r:gives {(2 3 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4130 - skolem:lemma4131 - [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2871]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1874 a r:Inference; r:gives { - 2872 :kaprekar 6174 . + 2874 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2874 math:notEqualTo 0}] + skolem:lemma3304 + [ a r:Fact; r:gives {(2 8 7 4) list:quicksort (2 4 7 8)}] + [ a r:Fact; r:gives {(2 4 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4132 - skolem:lemma4133 - [ a r:Fact; r:gives {(2 2 7 8) list:reverse (8 7 2 2)}] - skolem:lemma2848 - skolem:lemma2849 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2278]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1875 a r:Inference; r:gives { - 2873 :kaprekar 6174 . + 2875 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2875 math:notEqualTo 0}] + skolem:lemma3305 + [ a r:Fact; r:gives {(2 8 7 5) list:quicksort (2 5 7 8)}] + [ a r:Fact; r:gives {(2 5 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4134 - skolem:lemma4135 - [ a r:Fact; r:gives {(2 3 7 8) list:reverse (8 7 3 2)}] - skolem:lemma3100 - skolem:lemma3101 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2873]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2378]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1876 a r:Inference; r:gives { - 2874 :kaprekar 6174 . + 2876 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2876 math:notEqualTo 0}] + skolem:lemma3306 + [ a r:Fact; r:gives {(2 8 7 6) list:quicksort (2 6 7 8)}] + [ a r:Fact; r:gives {(2 6 7 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4136 - skolem:lemma4137 - [ a r:Fact; r:gives {(2 4 7 8) list:reverse (8 7 4 2)}] - skolem:lemma3326 - skolem:lemma3327 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2874]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2478]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1877 a r:Inference; r:gives { - 2875 :kaprekar 6174 . + 2877 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2877 math:notEqualTo 0}] + skolem:lemma3307 + [ a r:Fact; r:gives {(2 8 7 7) list:quicksort (2 7 7 8)}] + [ a r:Fact; r:gives {(2 7 7 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2875]; - r:rule skolem:lemma2032. + 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. skolem:lemma1878 a r:Inference; r:gives { - 2876 :kaprekar 6174 . + 2878 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2878 math:notEqualTo 0}] + skolem:lemma3308 + [ a r:Fact; r:gives {(2 8 7 8) list:quicksort (2 7 8 8)}] + [ a r:Fact; r:gives {(2 7 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4138 - skolem:lemma4139 - [ a r:Fact; r:gives {(2 6 7 8) list:reverse (8 7 6 2)}] - skolem:lemma3754 - skolem:lemma3755 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2876]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2678]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1879 a r:Inference; r:gives { - 2877 :kaprekar 6174 . + 2879 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2879 math:notEqualTo 0}] + skolem:lemma3309 + [ a r:Fact; r:gives {(2 8 7 9) list:quicksort (2 7 8 9)}] + [ a r:Fact; r:gives {(2 7 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4140 - skolem:lemma4141 - [ a r:Fact; r:gives {(2 7 7 8) list:reverse (8 7 7 2)}] - skolem:lemma3954 - skolem:lemma3955 - [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2877]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2778]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1880 a r:Inference; r:gives { - 2878 :kaprekar 6174 . + 2880 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2880 math:notEqualTo 0}] + skolem:lemma3310 + [ a r:Fact; r:gives {(2 8 8 0) list:quicksort (0 2 8 8)}] + [ a r:Fact; r:gives {(0 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4142 - skolem:lemma4143 - [ a r:Fact; r:gives {(2 7 8 8) list:reverse (8 8 7 2)}] - skolem:lemma3976 - skolem:lemma3977 - [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2878]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2788]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1881 a r:Inference; r:gives { - 2879 :kaprekar 6174 . + 2881 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2881 math:notEqualTo 0}] + skolem:lemma3311 + [ a r:Fact; r:gives {(2 8 8 1) list:quicksort (1 2 8 8)}] + [ a r:Fact; r:gives {(1 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4144 - skolem:lemma4145 - [ a r:Fact; r:gives {(2 7 8 9) list:reverse (9 8 7 2)}] - skolem:lemma3980 - skolem:lemma3981 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2879]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2789]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1882 a r:Inference; r:gives { - 2880 :kaprekar 6174 . + 2882 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2882 math:notEqualTo 0}] + skolem:lemma3312 + [ a r:Fact; r:gives {(2 8 8 2) list:quicksort (2 2 8 8)}] + [ a r:Fact; r:gives {(2 2 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4146 - skolem:lemma4147 - [ a r:Fact; r:gives {(0 2 8 8) list:reverse (8 8 2 0)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2880]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 288]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1883 a r:Inference; r:gives { - 2881 :kaprekar 6174 . + 2883 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2883 math:notEqualTo 0}] + skolem:lemma3313 + [ a r:Fact; r:gives {(2 8 8 3) list:quicksort (2 3 8 8)}] + [ a r:Fact; r:gives {(2 3 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4148 - skolem:lemma4149 - [ a r:Fact; r:gives {(1 2 8 8) list:reverse (8 8 2 1)}] - skolem:lemma2599 - skolem:lemma2600 - [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2881]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1288]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1884 a r:Inference; r:gives { - 2882 :kaprekar 6174 . + 2884 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2884 math:notEqualTo 0}] + skolem:lemma3314 + [ a r:Fact; r:gives {(2 8 8 4) list:quicksort (2 4 8 8)}] + [ a r:Fact; r:gives {(2 4 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4150 - skolem:lemma4151 - [ a r:Fact; r:gives {(2 2 8 8) list:reverse (8 8 2 2)}] - skolem:lemma2870 - skolem:lemma2871 - [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] - [ a r:Fact; r:gives {6534 math:notEqualTo 6174}] - skolem:lemma2872 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2288]; - 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_8"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1885 a r:Inference; r:gives { - 2883 :kaprekar 6174 . + 2885 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2885 math:notEqualTo 0}] + skolem:lemma3315 + [ a r:Fact; r:gives {(2 8 8 5) list:quicksort (2 5 8 8)}] + [ a r:Fact; r:gives {(2 5 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4152 - skolem:lemma4153 - [ a r:Fact; r:gives {(2 3 8 8) list:reverse (8 8 3 2)}] - skolem:lemma3122 - skolem:lemma3123 - [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] - [ a r:Fact; r:gives {6444 math:notEqualTo 6174}] - skolem:lemma2572 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2883]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2388]; - 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_8"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1886 a r:Inference; r:gives { - 2884 :kaprekar 6174 . + 2886 :kaprekar (0 1). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2886 math:notEqualTo 0}] + skolem:lemma3316 + [ a r:Fact; r:gives {(2 8 8 6) list:quicksort (2 6 8 8)}] + [ a r:Fact; r:gives {(2 6 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4154 - skolem:lemma4155 - [ a r:Fact; r:gives {(2 4 8 8) list:reverse (8 8 4 2)}] - skolem:lemma3346 - skolem:lemma3347 - [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2884]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2488]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1887 a r:Inference; r:gives { - 2885 :kaprekar 6174 . + 2887 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2887 math:notEqualTo 0}] + skolem:lemma3317 + [ a r:Fact; r:gives {(2 8 8 7) list:quicksort (2 7 8 8)}] + [ a r:Fact; r:gives {(2 7 8 8) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4156 - skolem:lemma4157 - [ a r:Fact; r:gives {(2 5 8 8) list:reverse (8 8 5 2)}] - skolem:lemma3566 - skolem:lemma3567 - [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2885]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2588]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1888 a r:Inference; r:gives { - 2886 :kaprekar 6174 . + 2888 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {2888 math:notEqualTo 0}] + skolem:lemma3318 + [ a r:Fact; r:gives {(2 8 8 8) list:quicksort (2 8 8 8)}] + [ a r:Fact; r:gives {(2 8 8 8) list:reverse (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)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2886]; - r:rule skolem:lemma2032. + 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. skolem:lemma1889 a r:Inference; r:gives { - 2887 :kaprekar 6174 . + 2889 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2889 math:notEqualTo 0}] + skolem:lemma3321 + [ a r:Fact; r:gives {(2 8 8 9) list:quicksort (2 8 8 9)}] + [ a r:Fact; r:gives {(2 8 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4158 - skolem:lemma4159 - [ a r:Fact; r:gives {(2 7 8 8) list:reverse (8 8 7 2)}] - skolem:lemma3976 - skolem:lemma3977 - [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] - [ a r:Fact; r:gives {6084 math:notEqualTo 6174}] - skolem:lemma2077 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2887]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2788]; - 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_8"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1890 a r:Inference; r:gives { - 2888 :kaprekar 6174 . + 2890 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2890 math:notEqualTo 0}] + skolem:lemma3324 + [ a r:Fact; r:gives {(2 8 9 0) list:quicksort (0 2 8 9)}] + [ a r:Fact; r:gives {(0 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4160 - skolem:lemma4161 - [ a r:Fact; r:gives {(2 8 8 8) list:reverse (8 8 8 2)}] - skolem:lemma4162 - skolem:lemma4163 - [ a r:Fact; r:gives {(8882 2888) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2888]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2888]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1891 a r:Inference; r:gives { - 2889 :kaprekar 6174 . + 2891 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2891 math:notEqualTo 0}] + skolem:lemma3325 + [ a r:Fact; r:gives {(2 8 9 1) list:quicksort (1 2 8 9)}] + [ a r:Fact; r:gives {(1 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4164 - skolem:lemma4165 - [ a r:Fact; r:gives {(2 8 8 9) list:reverse (9 8 8 2)}] - skolem:lemma4166 - skolem:lemma4167 - [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2889]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2889]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1892 a r:Inference; r:gives { - 2890 :kaprekar 6174 . + 2892 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2892 math:notEqualTo 0}] + skolem:lemma3326 + [ a r:Fact; r:gives {(2 8 9 2) list:quicksort (2 2 8 9)}] + [ a r:Fact; r:gives {(2 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4168 - skolem:lemma4169 - [ a r:Fact; r:gives {(0 2 8 9) list:reverse (9 8 2 0)}] - skolem:lemma2312 - skolem:lemma2313 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {9531 math:notEqualTo 6174}] - skolem:lemma2314 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2890]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 289]; - 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_8"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1893 a r:Inference; r:gives { - 2891 :kaprekar 6174 . + 2893 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2893 math:notEqualTo 0}] + skolem:lemma3327 + [ a r:Fact; r:gives {(2 8 9 3) list:quicksort (2 3 8 9)}] + [ a r:Fact; r:gives {(2 3 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4170 - skolem:lemma4171 - [ a r:Fact; r:gives {(1 2 8 9) list:reverse (9 8 2 1)}] - skolem:lemma2604 - skolem:lemma2605 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2891]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1289]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1894 a r:Inference; r:gives { - 2892 :kaprekar 6174 . + 2894 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2894 math:notEqualTo 0}] + skolem:lemma3328 + [ a r:Fact; r:gives {(2 8 9 4) list:quicksort (2 4 8 9)}] + [ a r:Fact; r:gives {(2 4 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4172 - skolem:lemma4173 - [ a r:Fact; r:gives {(2 2 8 9) list:reverse (9 8 2 2)}] - skolem:lemma2875 - skolem:lemma2876 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2892]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2289]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1895 a r:Inference; r:gives { - 2893 :kaprekar 6174 . + 2895 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2895 math:notEqualTo 0}] + skolem:lemma3329 + [ a r:Fact; r:gives {(2 8 9 5) list:quicksort (2 5 8 9)}] + [ a r:Fact; r:gives {(2 5 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4174 - skolem:lemma4175 - [ a r:Fact; r:gives {(2 3 8 9) list:reverse (9 8 3 2)}] - skolem:lemma3126 - skolem:lemma3127 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2893]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2389]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1896 a r:Inference; r:gives { - 2894 :kaprekar 6174 . + 2896 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2896 math:notEqualTo 0}] + skolem:lemma3330 + [ a r:Fact; r:gives {(2 8 9 6) list:quicksort (2 6 8 9)}] + [ a r:Fact; r:gives {(2 6 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4176 - skolem:lemma4177 - [ a r:Fact; r:gives {(2 4 8 9) list:reverse (9 8 4 2)}] - skolem:lemma3350 - skolem:lemma3351 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2894]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2489]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1897 a r:Inference; r:gives { - 2895 :kaprekar 6174 . + 2897 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2897 math:notEqualTo 0}] + skolem:lemma3331 + [ a r:Fact; r:gives {(2 8 9 7) list:quicksort (2 7 8 9)}] + [ a r:Fact; r:gives {(2 7 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4178 - skolem:lemma4179 - [ a r:Fact; r:gives {(2 5 8 9) list:reverse (9 8 5 2)}] - skolem:lemma3570 - skolem:lemma3571 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2895]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2589]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1898 a r:Inference; r:gives { - 2896 :kaprekar 6174 . + 2898 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2898 math:notEqualTo 0}] + skolem:lemma3332 + [ a r:Fact; r:gives {(2 8 9 8) list:quicksort (2 8 8 9)}] + [ a r:Fact; r:gives {(2 8 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4180 - skolem:lemma4181 - [ a r:Fact; r:gives {(2 6 8 9) list:reverse (9 8 6 2)}] - skolem:lemma3776 - skolem:lemma3777 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2896]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2689]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1899 a r:Inference; r:gives { - 2897 :kaprekar 6174 . + 2899 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2899 math:notEqualTo 0}] + skolem:lemma3333 + [ a r:Fact; r:gives {(2 8 9 9) list:quicksort (2 8 9 9)}] + [ a r:Fact; r:gives {(2 8 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4182 - skolem:lemma4183 - [ a r:Fact; r:gives {(2 7 8 9) list:reverse (9 8 7 2)}] - skolem:lemma3980 - skolem:lemma3981 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2897]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2789]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1900 a r:Inference; r:gives { - 2898 :kaprekar 6174 . + 2900 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2900 math:notEqualTo 0}] + skolem:lemma3336 + [ a r:Fact; r:gives {(2 9 0 0) list:quicksort (0 0 2 9)}] + [ a r:Fact; r:gives {(0 0 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4184 - skolem:lemma4185 - [ a r:Fact; r:gives {(2 8 8 9) list:reverse (9 8 8 2)}] - skolem:lemma4166 - skolem:lemma4167 - [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2898]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2889]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1901 a r:Inference; r:gives { - 2899 :kaprekar 6174 . + 2901 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2901 math:notEqualTo 0}] + skolem:lemma3337 + [ a r:Fact; r:gives {(2 9 0 1) list:quicksort (0 1 2 9)}] + [ a r:Fact; r:gives {(0 1 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4186 - skolem:lemma4187 - [ a r:Fact; r:gives {(2 8 9 9) list:reverse (9 9 8 2)}] - skolem:lemma4188 - skolem:lemma4189 - [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2899]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1902 a r:Inference; r:gives { - 2900 :kaprekar 6174 . + 2902 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2902 math:notEqualTo 0}] + skolem:lemma3338 + [ a r:Fact; r:gives {(2 9 0 2) list:quicksort (0 2 2 9)}] + [ a r:Fact; r:gives {(0 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4190 - skolem:lemma4191 - [ a r:Fact; r:gives {(0 0 2 9) list:reverse (9 2 0 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(9200 29) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2900]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 29]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1903 a r:Inference; r:gives { - 2901 :kaprekar 6174 . + 2903 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2903 math:notEqualTo 0}] + skolem:lemma3339 + [ a r:Fact; r:gives {(2 9 0 3) list:quicksort (0 2 3 9)}] + [ a r:Fact; r:gives {(0 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4192 - skolem:lemma4193 - [ a r:Fact; r:gives {(0 1 2 9) list:reverse (9 2 1 0)}] - skolem:lemma2090 - skolem:lemma2091 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2901]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 129]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1904 a r:Inference; r:gives { - 2902 :kaprekar 6174 . + 2904 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2904 math:notEqualTo 0}] + skolem:lemma3340 + [ a r:Fact; r:gives {(2 9 0 4) list:quicksort (0 2 4 9)}] + [ a r:Fact; r:gives {(0 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4194 - skolem:lemma4195 - [ a r:Fact; r:gives {(0 2 2 9) list:reverse (9 2 2 0)}] - skolem:lemma2132 - skolem:lemma2133 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2902]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 229]; - 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_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1905 a r:Inference; r:gives { - 2903 :kaprekar 6174 . + 2905 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2905 math:notEqualTo 0}] + skolem:lemma3341 + [ a r:Fact; r:gives {(2 9 0 5) list:quicksort (0 2 5 9)}] + [ a r:Fact; r:gives {(0 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4196 - skolem:lemma4197 - [ a r:Fact; r:gives {(0 2 3 9) list:reverse (9 3 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2903]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 239]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1906 a r:Inference; r:gives { - 2904 :kaprekar 6174 . + 2906 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2906 math:notEqualTo 0}] + skolem:lemma3342 + [ a r:Fact; r:gives {(2 9 0 6) list:quicksort (0 2 6 9)}] + [ a r:Fact; r:gives {(0 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4198 - skolem:lemma4199 - [ a r:Fact; r:gives {(0 2 4 9) list:reverse (9 4 2 0)}] - skolem:lemma2195 - skolem:lemma2196 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2904]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 249]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1907 a r:Inference; r:gives { - 2905 :kaprekar 6174 . + 2907 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2907 math:notEqualTo 0}] + skolem:lemma3343 + [ a r:Fact; r:gives {(2 9 0 7) list:quicksort (0 2 7 9)}] + [ a r:Fact; r:gives {(0 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4200 - skolem:lemma4201 - [ a r:Fact; r:gives {(0 2 5 9) list:reverse (9 5 2 0)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {9261 math:notEqualTo 6174}] - skolem:lemma2231 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2905]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 259]; - 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_8"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1908 a r:Inference; r:gives { - 2906 :kaprekar 6174 . + 2908 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2908 math:notEqualTo 0}] + skolem:lemma3344 + [ a r:Fact; r:gives {(2 9 0 8) list:quicksort (0 2 8 9)}] + [ a r:Fact; r:gives {(0 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4202 - skolem:lemma4203 - [ a r:Fact; r:gives {(0 2 6 9) list:reverse (9 6 2 0)}] - skolem:lemma2257 - skolem:lemma2258 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {9351 math:notEqualTo 6174}] - skolem:lemma2259 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2906]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 269]; - 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_8"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1909 a r:Inference; r:gives { - 2907 :kaprekar 6174 . + 2909 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2909 math:notEqualTo 0}] + skolem:lemma3345 + [ a r:Fact; r:gives {(2 9 0 9) list:quicksort (0 2 9 9)}] + [ a r:Fact; r:gives {(0 2 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4204 - skolem:lemma4205 - [ a r:Fact; r:gives {(0 2 7 9) list:reverse (9 7 2 0)}] - skolem:lemma2286 - skolem:lemma2287 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {9441 math:notEqualTo 6174}] - skolem:lemma2288 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2907]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 279]; - 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_8"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1910 a r:Inference; r:gives { - 2908 :kaprekar 6174 . + 2910 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2910 math:notEqualTo 0}] + skolem:lemma3346 + [ a r:Fact; r:gives {(2 9 1 0) list:quicksort (0 1 2 9)}] + [ a r:Fact; r:gives {(0 1 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4206 - skolem:lemma4207 - [ a r:Fact; r:gives {(0 2 8 9) list:reverse (9 8 2 0)}] - skolem:lemma2312 - skolem:lemma2313 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {9531 math:notEqualTo 6174}] - skolem:lemma2314 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2908]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 289]; - 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_8"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1911 a r:Inference; r:gives { - 2909 :kaprekar 6174 . + 2911 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2911 math:notEqualTo 0}] + skolem:lemma3347 + [ a r:Fact; r:gives {(2 9 1 1) list:quicksort (1 1 2 9)}] + [ a r:Fact; r:gives {(1 1 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4208 - skolem:lemma4209 - [ a r:Fact; r:gives {(0 2 9 9) list:reverse (9 9 2 0)}] - skolem:lemma2335 - skolem:lemma2336 - [ a r:Fact; r:gives {(9920 299) math:difference 9621}] - [ a r:Fact; r:gives {9621 math:notEqualTo 6174}] - skolem:lemma2337 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2909]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 299]; - 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_8"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1912 a r:Inference; r:gives { - 2910 :kaprekar 6174 . + 2912 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2912 math:notEqualTo 0}] + skolem:lemma3348 + [ a r:Fact; r:gives {(2 9 1 2) list:quicksort (1 2 2 9)}] + [ a r:Fact; r:gives {(1 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4210 - skolem:lemma4211 - [ a r:Fact; r:gives {(0 1 2 9) list:reverse (9 2 1 0)}] - skolem:lemma2090 - skolem:lemma2091 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2910]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 129]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1913 a r:Inference; r:gives { - 2911 :kaprekar 6174 . + 2913 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2913 math:notEqualTo 0}] + skolem:lemma3349 + [ a r:Fact; r:gives {(2 9 1 3) list:quicksort (1 2 3 9)}] + [ a r:Fact; r:gives {(1 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4212 - skolem:lemma4213 - [ a r:Fact; r:gives {(1 1 2 9) list:reverse (9 2 1 1)}] - skolem:lemma2396 - skolem:lemma2397 - [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2911]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1129]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1914 a r:Inference; r:gives { - 2912 :kaprekar 6174 . + 2914 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2914 math:notEqualTo 0}] + skolem:lemma3350 + [ a r:Fact; r:gives {(2 9 1 4) list:quicksort (1 2 4 9)}] + [ a r:Fact; r:gives {(1 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4214 - skolem:lemma4215 - [ a r:Fact; r:gives {(1 2 2 9) list:reverse (9 2 2 1)}] - skolem:lemma2432 - skolem:lemma2433 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2912]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1229]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1915 a r:Inference; r:gives { - 2913 :kaprekar 6174 . + 2915 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2915 math:notEqualTo 0}] + skolem:lemma3351 + [ a r:Fact; r:gives {(2 9 1 5) list:quicksort (1 2 5 9)}] + [ a r:Fact; r:gives {(1 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4216 - skolem:lemma4217 - [ a r:Fact; r:gives {(1 2 3 9) list:reverse (9 3 2 1)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2913]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1239]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1916 a r:Inference; r:gives { - 2914 :kaprekar 6174 . + 2916 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4218 - skolem:lemma4219 - [ a r:Fact; r:gives {(1 2 4 9) list:reverse (9 4 2 1)}] - skolem:lemma2494 - skolem:lemma2495 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ a r:Fact; r:gives {2916 math:notEqualTo 0}] + skolem:lemma3352 + [ a r:Fact; r:gives {(2 9 1 6) list:quicksort (1 2 6 9)}] + [ a r:Fact; r:gives {(1 2 6 9) list:reverse (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)}] ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2914]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1249]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1917 a r:Inference; r:gives { - 2915 :kaprekar 6174 . + 2917 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2917 math:notEqualTo 0}] + skolem:lemma3353 + [ a r:Fact; r:gives {(2 9 1 7) list:quicksort (1 2 7 9)}] + [ a r:Fact; r:gives {(1 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4220 - skolem:lemma4221 - [ a r:Fact; r:gives {(1 2 5 9) list:reverse (9 5 2 1)}] - skolem:lemma2525 - skolem:lemma2526 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2915]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1259]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1918 a r:Inference; r:gives { - 2916 :kaprekar 6174 . + 2918 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2918 math:notEqualTo 0}] + skolem:lemma3354 + [ a r:Fact; r:gives {(2 9 1 8) list:quicksort (1 2 8 9)}] + [ a r:Fact; r:gives {(1 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4222 - skolem:lemma4223 - [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2916]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1919 a r:Inference; r:gives { - 2917 :kaprekar 6174 . + 2919 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2919 math:notEqualTo 0}] + skolem:lemma3355 + [ a r:Fact; r:gives {(2 9 1 9) list:quicksort (1 2 9 9)}] + [ a r:Fact; r:gives {(1 2 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4224 - skolem:lemma4225 - [ a r:Fact; r:gives {(1 2 7 9) list:reverse (9 7 2 1)}] - skolem:lemma2579 - skolem:lemma2580 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2917]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1279]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1920 a r:Inference; r:gives { - 2918 :kaprekar 6174 . + 2920 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2920 math:notEqualTo 0}] + skolem:lemma3356 + [ a r:Fact; r:gives {(2 9 2 0) list:quicksort (0 2 2 9)}] + [ a r:Fact; r:gives {(0 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4226 - skolem:lemma4227 - [ a r:Fact; r:gives {(1 2 8 9) list:reverse (9 8 2 1)}] - skolem:lemma2604 - skolem:lemma2605 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2918]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1289]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1921 a r:Inference; r:gives { - 2919 :kaprekar 6174 . + 2921 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2921 math:notEqualTo 0}] + skolem:lemma3357 + [ a r:Fact; r:gives {(2 9 2 1) list:quicksort (1 2 2 9)}] + [ a r:Fact; r:gives {(1 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4228 - skolem:lemma4229 - [ a r:Fact; r:gives {(1 2 9 9) list:reverse (9 9 2 1)}] - skolem:lemma2626 - skolem:lemma2627 - [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] - [ a r:Fact; r:gives {8622 math:notEqualTo 6174}] - skolem:lemma2628 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2919]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1299]; - 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_8"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1922 a r:Inference; r:gives { - 2920 :kaprekar 6174 . + 2922 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2922 math:notEqualTo 0}] + skolem:lemma3358 + [ a r:Fact; r:gives {(2 9 2 2) list:quicksort (2 2 2 9)}] + [ a r:Fact; r:gives {(2 2 2 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4230 - skolem:lemma4231 - [ a r:Fact; r:gives {(0 2 2 9) list:reverse (9 2 2 0)}] - skolem:lemma2132 - skolem:lemma2133 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2920]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 229]; - 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_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1923 a r:Inference; r:gives { - 2921 :kaprekar 6174 . + 2923 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2923 math:notEqualTo 0}] + skolem:lemma3359 + [ a r:Fact; r:gives {(2 9 2 3) list:quicksort (2 2 3 9)}] + [ a r:Fact; r:gives {(2 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4232 - skolem:lemma4233 - [ a r:Fact; r:gives {(1 2 2 9) list:reverse (9 2 2 1)}] - skolem:lemma2432 - skolem:lemma2433 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2921]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1229]; - 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_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1924 a r:Inference; r:gives { - 2922 :kaprekar 6174 . + 2924 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2924 math:notEqualTo 0}] + skolem:lemma3360 + [ a r:Fact; r:gives {(2 9 2 4) list:quicksort (2 2 4 9)}] + [ a r:Fact; r:gives {(2 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4234 - skolem:lemma4235 - [ a r:Fact; r:gives {(2 2 2 9) list:reverse (9 2 2 2)}] - skolem:lemma2703 - skolem:lemma2704 - [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2922]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2229]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1925 a r:Inference; r:gives { - 2923 :kaprekar 6174 . + 2925 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2925 math:notEqualTo 0}] + skolem:lemma3361 + [ a r:Fact; r:gives {(2 9 2 5) list:quicksort (2 2 5 9)}] + [ a r:Fact; r:gives {(2 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4236 - skolem:lemma4237 - [ a r:Fact; r:gives {(2 2 3 9) list:reverse (9 3 2 2)}] - skolem:lemma2737 - skolem:lemma2738 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2923]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2239]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1926 a r:Inference; r:gives { - 2924 :kaprekar 6174 . + 2926 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2926 math:notEqualTo 0}] + skolem:lemma3362 + [ a r:Fact; r:gives {(2 9 2 6) list:quicksort (2 2 6 9)}] + [ a r:Fact; r:gives {(2 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4238 - skolem:lemma4239 - [ a r:Fact; r:gives {(2 2 4 9) list:reverse (9 4 2 2)}] - skolem:lemma2765 - skolem:lemma2766 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2924]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2249]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1927 a r:Inference; r:gives { - 2925 :kaprekar 6174 . + 2927 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2927 math:notEqualTo 0}] + skolem:lemma3363 + [ a r:Fact; r:gives {(2 9 2 7) list:quicksort (2 2 7 9)}] + [ a r:Fact; r:gives {(2 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4240 - skolem:lemma4241 - [ a r:Fact; r:gives {(2 2 5 9) list:reverse (9 5 2 2)}] - skolem:lemma2796 - skolem:lemma2797 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2925]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2259]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1928 a r:Inference; r:gives { - 2926 :kaprekar 6174 . + 2928 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2928 math:notEqualTo 0}] + skolem:lemma3364 + [ a r:Fact; r:gives {(2 9 2 8) list:quicksort (2 2 8 9)}] + [ a r:Fact; r:gives {(2 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4242 - skolem:lemma4243 - [ a r:Fact; r:gives {(2 2 6 9) list:reverse (9 6 2 2)}] - skolem:lemma2825 - skolem:lemma2826 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2926]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2269]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1929 a r:Inference; r:gives { - 2927 :kaprekar 6174 . + 2929 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2929 math:notEqualTo 0}] + skolem:lemma3365 + [ a r:Fact; r:gives {(2 9 2 9) list:quicksort (2 2 9 9)}] + [ a r:Fact; r:gives {(2 2 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4244 - skolem:lemma4245 - [ a r:Fact; r:gives {(2 2 7 9) list:reverse (9 7 2 2)}] - skolem:lemma2852 - skolem:lemma2853 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2927]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2279]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1930 a r:Inference; r:gives { - 2928 :kaprekar 6174 . + 2930 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2930 math:notEqualTo 0}] + skolem:lemma3366 + [ a r:Fact; r:gives {(2 9 3 0) list:quicksort (0 2 3 9)}] + [ a r:Fact; r:gives {(0 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4246 - skolem:lemma4247 - [ a r:Fact; r:gives {(2 2 8 9) list:reverse (9 8 2 2)}] - skolem:lemma2875 - skolem:lemma2876 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2928]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2289]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1931 a r:Inference; r:gives { - 2929 :kaprekar 6174 . + 2931 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2931 math:notEqualTo 0}] + skolem:lemma3367 + [ a r:Fact; r:gives {(2 9 3 1) list:quicksort (1 2 3 9)}] + [ a r:Fact; r:gives {(1 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4248 - skolem:lemma4249 - [ a r:Fact; r:gives {(2 2 9 9) list:reverse (9 9 2 2)}] - skolem:lemma2897 - skolem:lemma2898 - [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] - [ a r:Fact; r:gives {7623 math:notEqualTo 6174}] - skolem:lemma2899 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2929]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2299]; - 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_8"]; r:boundTo 7623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1932 a r:Inference; r:gives { - 2930 :kaprekar 6174 . + 2932 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2932 math:notEqualTo 0}] + skolem:lemma3368 + [ a r:Fact; r:gives {(2 9 3 2) list:quicksort (2 2 3 9)}] + [ a r:Fact; r:gives {(2 2 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4250 - skolem:lemma4251 - [ a r:Fact; r:gives {(0 2 3 9) list:reverse (9 3 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {9081 math:notEqualTo 6174}] - skolem:lemma2092 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2930]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 239]; - 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_8"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1933 a r:Inference; r:gives { - 2931 :kaprekar 6174 . + 2933 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2933 math:notEqualTo 0}] + skolem:lemma3369 + [ a r:Fact; r:gives {(2 9 3 3) list:quicksort (2 3 3 9)}] + [ a r:Fact; r:gives {(2 3 3 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4252 - skolem:lemma4253 - [ a r:Fact; r:gives {(1 2 3 9) list:reverse (9 3 2 1)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2931]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1239]; - 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_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1934 a r:Inference; r:gives { - 2932 :kaprekar 6174 . + 2934 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2934 math:notEqualTo 0}] + skolem:lemma3370 + [ a r:Fact; r:gives {(2 9 3 4) list:quicksort (2 3 4 9)}] + [ a r:Fact; r:gives {(2 3 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4254 - skolem:lemma4255 - [ a r:Fact; r:gives {(2 2 3 9) list:reverse (9 3 2 2)}] - skolem:lemma2737 - skolem:lemma2738 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2932]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2239]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1935 a r:Inference; r:gives { - 2933 :kaprekar 6174 . + 2935 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2935 math:notEqualTo 0}] + skolem:lemma3371 + [ a r:Fact; r:gives {(2 9 3 5) list:quicksort (2 3 5 9)}] + [ a r:Fact; r:gives {(2 3 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4256 - skolem:lemma4257 - [ a r:Fact; r:gives {(2 3 3 9) list:reverse (9 3 3 2)}] - skolem:lemma2992 - skolem:lemma2993 - [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2933]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2339]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1936 a r:Inference; r:gives { - 2934 :kaprekar 6174 . + 2936 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2936 math:notEqualTo 0}] + skolem:lemma3372 + [ a r:Fact; r:gives {(2 9 3 6) list:quicksort (2 3 6 9)}] + [ a r:Fact; r:gives {(2 3 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4258 - skolem:lemma4259 - [ a r:Fact; r:gives {(2 3 4 9) list:reverse (9 4 3 2)}] - skolem:lemma3024 - skolem:lemma3025 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2934]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2349]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1937 a r:Inference; r:gives { - 2935 :kaprekar 6174 . + 2937 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2937 math:notEqualTo 0}] + skolem:lemma3373 + [ a r:Fact; r:gives {(2 9 3 7) list:quicksort (2 3 7 9)}] + [ a r:Fact; r:gives {(2 3 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4260 - skolem:lemma4261 - [ a r:Fact; r:gives {(2 3 5 9) list:reverse (9 5 3 2)}] - skolem:lemma3050 - skolem:lemma3051 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2935]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2359]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1938 a r:Inference; r:gives { - 2936 :kaprekar 6174 . + 2938 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2938 math:notEqualTo 0}] + skolem:lemma3374 + [ a r:Fact; r:gives {(2 9 3 8) list:quicksort (2 3 8 9)}] + [ a r:Fact; r:gives {(2 3 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4262 - skolem:lemma4263 - [ a r:Fact; r:gives {(2 3 6 9) list:reverse (9 6 3 2)}] - skolem:lemma3078 - skolem:lemma3079 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2936]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2369]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1939 a r:Inference; r:gives { - 2937 :kaprekar 6174 . + 2939 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2939 math:notEqualTo 0}] + skolem:lemma3375 + [ a r:Fact; r:gives {(2 9 3 9) list:quicksort (2 3 9 9)}] + [ a r:Fact; r:gives {(2 3 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4264 - skolem:lemma4265 - [ a r:Fact; r:gives {(2 3 7 9) list:reverse (9 7 3 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2937]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2379]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1940 a r:Inference; r:gives { - 2938 :kaprekar 6174 . + 2940 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2940 math:notEqualTo 0}] + skolem:lemma3376 + [ a r:Fact; r:gives {(2 9 4 0) list:quicksort (0 2 4 9)}] + [ a r:Fact; r:gives {(0 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4266 - skolem:lemma4267 - [ a r:Fact; r:gives {(2 3 8 9) list:reverse (9 8 3 2)}] - skolem:lemma3126 - skolem:lemma3127 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2938]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2389]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1941 a r:Inference; r:gives { - 2939 :kaprekar 6174 . + 2941 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2941 math:notEqualTo 0}] + skolem:lemma3377 + [ a r:Fact; r:gives {(2 9 4 1) list:quicksort (1 2 4 9)}] + [ a r:Fact; r:gives {(1 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4268 - skolem:lemma4269 - [ a r:Fact; r:gives {(2 3 9 9) list:reverse (9 9 3 2)}] - skolem:lemma3148 - skolem:lemma3149 - [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2939]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2399]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1942 a r:Inference; r:gives { - 2940 :kaprekar 6174 . + 2942 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2942 math:notEqualTo 0}] + skolem:lemma3378 + [ a r:Fact; r:gives {(2 9 4 2) list:quicksort (2 2 4 9)}] + [ a r:Fact; r:gives {(2 2 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4270 - skolem:lemma4271 - [ a r:Fact; r:gives {(0 2 4 9) list:reverse (9 4 2 0)}] - skolem:lemma2195 - skolem:lemma2196 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {9171 math:notEqualTo 6174}] - skolem:lemma2047 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2940]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 249]; - 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_8"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1943 a r:Inference; r:gives { - 2941 :kaprekar 6174 . + 2943 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2943 math:notEqualTo 0}] + skolem:lemma3379 + [ a r:Fact; r:gives {(2 9 4 3) list:quicksort (2 3 4 9)}] + [ a r:Fact; r:gives {(2 3 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4272 - skolem:lemma4273 - [ a r:Fact; r:gives {(1 2 4 9) list:reverse (9 4 2 1)}] - skolem:lemma2494 - skolem:lemma2495 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2941]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1249]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1944 a r:Inference; r:gives { - 2942 :kaprekar 6174 . + 2944 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2944 math:notEqualTo 0}] + skolem:lemma3380 + [ a r:Fact; r:gives {(2 9 4 4) list:quicksort (2 4 4 9)}] + [ a r:Fact; r:gives {(2 4 4 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4274 - skolem:lemma4275 - [ a r:Fact; r:gives {(2 2 4 9) list:reverse (9 4 2 2)}] - skolem:lemma2765 - skolem:lemma2766 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2942]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2249]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1945 a r:Inference; r:gives { - 2943 :kaprekar 6174 . + 2945 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2945 math:notEqualTo 0}] + skolem:lemma3381 + [ a r:Fact; r:gives {(2 9 4 5) list:quicksort (2 4 5 9)}] + [ a r:Fact; r:gives {(2 4 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4276 - skolem:lemma4277 - [ a r:Fact; r:gives {(2 3 4 9) list:reverse (9 4 3 2)}] - skolem:lemma3024 - skolem:lemma3025 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2943]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2349]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1946 a r:Inference; r:gives { - 2944 :kaprekar 6174 . + 2946 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2946 math:notEqualTo 0}] + skolem:lemma3382 + [ a r:Fact; r:gives {(2 9 4 6) list:quicksort (2 4 6 9)}] + [ a r:Fact; r:gives {(2 4 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4278 - skolem:lemma4279 - [ a r:Fact; r:gives {(2 4 4 9) list:reverse (9 4 4 2)}] - skolem:lemma3254 - skolem:lemma3255 - [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2944]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2449]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1947 a r:Inference; r:gives { - 2945 :kaprekar 6174 . + 2947 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2947 math:notEqualTo 0}] + skolem:lemma3383 + [ a r:Fact; r:gives {(2 9 4 7) list:quicksort (2 4 7 9)}] + [ a r:Fact; r:gives {(2 4 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4280 - skolem:lemma4281 - [ a r:Fact; r:gives {(2 4 5 9) list:reverse (9 5 4 2)}] - skolem:lemma3284 - skolem:lemma3285 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2945]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2459]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1948 a r:Inference; r:gives { - 2946 :kaprekar 6174 . + 2948 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2948 math:notEqualTo 0}] + skolem:lemma3384 + [ a r:Fact; r:gives {(2 9 4 8) list:quicksort (2 4 8 9)}] + [ a r:Fact; r:gives {(2 4 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4282 - skolem:lemma4283 - [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] - skolem:lemma3306 - skolem:lemma3307 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2946]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2469]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1949 a r:Inference; r:gives { - 2947 :kaprekar 6174 . + 2949 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2949 math:notEqualTo 0}] + skolem:lemma3385 + [ a r:Fact; r:gives {(2 9 4 9) list:quicksort (2 4 9 9)}] + [ a r:Fact; r:gives {(2 4 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4284 - skolem:lemma4285 - [ a r:Fact; r:gives {(2 4 7 9) list:reverse (9 7 4 2)}] - skolem:lemma3330 - skolem:lemma3331 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2947]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2479]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1950 a r:Inference; r:gives { - 2948 :kaprekar 6174 . + 2950 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2950 math:notEqualTo 0}] + skolem:lemma3386 + [ a r:Fact; r:gives {(2 9 5 0) list:quicksort (0 2 5 9)}] + [ a r:Fact; r:gives {(0 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4286 - skolem:lemma4287 - [ a r:Fact; r:gives {(2 4 8 9) list:reverse (9 8 4 2)}] - skolem:lemma3350 - skolem:lemma3351 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2948]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2489]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1951 a r:Inference; r:gives { - 2949 :kaprekar 6174 . + 2951 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2951 math:notEqualTo 0}] + skolem:lemma3387 + [ a r:Fact; r:gives {(2 9 5 1) list:quicksort (1 2 5 9)}] + [ a r:Fact; r:gives {(1 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4288 - skolem:lemma4289 - [ a r:Fact; r:gives {(2 4 9 9) list:reverse (9 9 4 2)}] - skolem:lemma3372 - skolem:lemma3373 - [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2949]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2499]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1952 a r:Inference; r:gives { - 2950 :kaprekar 6174 . + 2952 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2952 math:notEqualTo 0}] + skolem:lemma3388 + [ a r:Fact; r:gives {(2 9 5 2) list:quicksort (2 2 5 9)}] + [ a r:Fact; r:gives {(2 2 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4290 - skolem:lemma4291 - [ a r:Fact; r:gives {(0 2 5 9) list:reverse (9 5 2 0)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {9261 math:notEqualTo 6174}] - skolem:lemma2231 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2950]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 259]; - 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_8"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1953 a r:Inference; r:gives { - 2951 :kaprekar 6174 . + 2953 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2953 math:notEqualTo 0}] + skolem:lemma3389 + [ a r:Fact; r:gives {(2 9 5 3) list:quicksort (2 3 5 9)}] + [ a r:Fact; r:gives {(2 3 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4292 - skolem:lemma4293 - [ a r:Fact; r:gives {(1 2 5 9) list:reverse (9 5 2 1)}] - skolem:lemma2525 - skolem:lemma2526 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {8262 math:notEqualTo 6174}] - skolem:lemma2226 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2951]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1259]; - 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_8"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1954 a r:Inference; r:gives { - 2952 :kaprekar 6174 . + 2954 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2954 math:notEqualTo 0}] + skolem:lemma3390 + [ a r:Fact; r:gives {(2 9 5 4) list:quicksort (2 4 5 9)}] + [ a r:Fact; r:gives {(2 4 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4294 - skolem:lemma4295 - [ a r:Fact; r:gives {(2 2 5 9) list:reverse (9 5 2 2)}] - skolem:lemma2796 - skolem:lemma2797 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2952]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2259]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1955 a r:Inference; r:gives { - 2953 :kaprekar 6174 . + 2955 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2955 math:notEqualTo 0}] + skolem:lemma3391 + [ a r:Fact; r:gives {(2 9 5 5) list:quicksort (2 5 5 9)}] + [ a r:Fact; r:gives {(2 5 5 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4296 - skolem:lemma4297 - [ a r:Fact; r:gives {(2 3 5 9) list:reverse (9 5 3 2)}] - skolem:lemma3050 - skolem:lemma3051 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2953]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2359]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1956 a r:Inference; r:gives { - 2954 :kaprekar 6174 . + 2956 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2956 math:notEqualTo 0}] + skolem:lemma3392 + [ a r:Fact; r:gives {(2 9 5 6) list:quicksort (2 5 6 9)}] + [ a r:Fact; r:gives {(2 5 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4298 - skolem:lemma4299 - [ a r:Fact; r:gives {(2 4 5 9) list:reverse (9 5 4 2)}] - skolem:lemma3284 - skolem:lemma3285 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2954]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2459]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1957 a r:Inference; r:gives { - 2955 :kaprekar 6174 . + 2957 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2957 math:notEqualTo 0}] + skolem:lemma3393 + [ a r:Fact; r:gives {(2 9 5 7) list:quicksort (2 5 7 9)}] + [ a r:Fact; r:gives {(2 5 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4300 - skolem:lemma4301 - [ a r:Fact; r:gives {(2 5 5 9) list:reverse (9 5 5 2)}] - skolem:lemma3500 - skolem:lemma3501 - [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2955]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2559]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1958 a r:Inference; r:gives { - 2956 :kaprekar 6174 . + 2958 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2958 math:notEqualTo 0}] + skolem:lemma3394 + [ a r:Fact; r:gives {(2 9 5 8) list:quicksort (2 5 8 9)}] + [ a r:Fact; r:gives {(2 5 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4302 - skolem:lemma4303 - [ a r:Fact; r:gives {(2 5 6 9) list:reverse (9 6 5 2)}] - skolem:lemma3528 - skolem:lemma3529 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2956]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2569]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1959 a r:Inference; r:gives { - 2957 :kaprekar 6174 . + 2959 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2959 math:notEqualTo 0}] + skolem:lemma3395 + [ a r:Fact; r:gives {(2 9 5 9) list:quicksort (2 5 9 9)}] + [ a r:Fact; r:gives {(2 5 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4304 - skolem:lemma4305 - [ a r:Fact; r:gives {(2 5 7 9) list:reverse (9 7 5 2)}] - skolem:lemma3550 - skolem:lemma3551 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2957]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2579]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1960 a r:Inference; r:gives { - 2958 :kaprekar 6174 . + 2960 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2960 math:notEqualTo 0}] + skolem:lemma3396 + [ a r:Fact; r:gives {(2 9 6 0) list:quicksort (0 2 6 9)}] + [ a r:Fact; r:gives {(0 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4306 - skolem:lemma4307 - [ a r:Fact; r:gives {(2 5 8 9) list:reverse (9 8 5 2)}] - skolem:lemma3570 - skolem:lemma3571 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2958]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2589]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1961 a r:Inference; r:gives { - 2959 :kaprekar 6174 . + 2961 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2961 math:notEqualTo 0}] + skolem:lemma3397 + [ a r:Fact; r:gives {(2 9 6 1) list:quicksort (1 2 6 9)}] + [ a r:Fact; r:gives {(1 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4308 - skolem:lemma4309 - [ a r:Fact; r:gives {(2 5 9 9) list:reverse (9 9 5 2)}] - skolem:lemma3592 - skolem:lemma3593 - [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2959]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2599]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1962 a r:Inference; r:gives { - 2960 :kaprekar 6174 . + 2962 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2962 math:notEqualTo 0}] + skolem:lemma3398 + [ a r:Fact; r:gives {(2 9 6 2) list:quicksort (2 2 6 9)}] + [ a r:Fact; r:gives {(2 2 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4310 - skolem:lemma4311 - [ a r:Fact; r:gives {(0 2 6 9) list:reverse (9 6 2 0)}] - skolem:lemma2257 - skolem:lemma2258 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {9351 math:notEqualTo 6174}] - skolem:lemma2259 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2960]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 269]; - 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_8"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1963 a r:Inference; r:gives { - 2961 :kaprekar 6174 . + 2963 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2963 math:notEqualTo 0}] + skolem:lemma3399 + [ a r:Fact; r:gives {(2 9 6 3) list:quicksort (2 3 6 9)}] + [ a r:Fact; r:gives {(2 3 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4312 - skolem:lemma4313 - [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2961]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1964 a r:Inference; r:gives { - 2962 :kaprekar 6174 . + 2964 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4314 - skolem:lemma4315 - [ a r:Fact; r:gives {(2 2 6 9) list:reverse (9 6 2 2)}] + [ a r:Fact; r:gives {2964 math:notEqualTo 0}] + skolem:lemma3400 + [ a r:Fact; r:gives {(2 9 6 4) list:quicksort (2 4 6 9)}] + [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] + skolem:lemma2824 skolem:lemma2825 - skolem:lemma2826 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2962]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2269]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1965 a r:Inference; r:gives { - 2963 :kaprekar 6174 . + 2965 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2965 math:notEqualTo 0}] + skolem:lemma3401 + [ a r:Fact; r:gives {(2 9 6 5) list:quicksort (2 5 6 9)}] + [ a r:Fact; r:gives {(2 5 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4316 - skolem:lemma4317 - [ a r:Fact; r:gives {(2 3 6 9) list:reverse (9 6 3 2)}] - skolem:lemma3078 - skolem:lemma3079 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2963]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2369]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1966 a r:Inference; r:gives { - 2964 :kaprekar 6174 . + 2966 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2966 math:notEqualTo 0}] + skolem:lemma3402 + [ a r:Fact; r:gives {(2 9 6 6) list:quicksort (2 6 6 9)}] + [ a r:Fact; r:gives {(2 6 6 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4318 - skolem:lemma4319 - [ a r:Fact; r:gives {(2 4 6 9) list:reverse (9 6 4 2)}] - skolem:lemma3306 - skolem:lemma3307 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2964]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2469]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1967 a r:Inference; r:gives { - 2965 :kaprekar 6174 . + 2967 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2967 math:notEqualTo 0}] + skolem:lemma3403 + [ a r:Fact; r:gives {(2 9 6 7) list:quicksort (2 6 7 9)}] + [ a r:Fact; r:gives {(2 6 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4320 - skolem:lemma4321 - [ a r:Fact; r:gives {(2 5 6 9) list:reverse (9 6 5 2)}] - skolem:lemma3528 - skolem:lemma3529 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2965]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2569]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1968 a r:Inference; r:gives { - 2966 :kaprekar 6174 . + 2968 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2968 math:notEqualTo 0}] + skolem:lemma3404 + [ a r:Fact; r:gives {(2 9 6 8) list:quicksort (2 6 8 9)}] + [ a r:Fact; r:gives {(2 6 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4322 - skolem:lemma4323 - [ a r:Fact; r:gives {(2 6 6 9) list:reverse (9 6 6 2)}] - skolem:lemma3732 - skolem:lemma3733 - [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2966]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2669]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1969 a r:Inference; r:gives { - 2967 :kaprekar 6174 . + 2969 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2969 math:notEqualTo 0}] + skolem:lemma3405 + [ a r:Fact; r:gives {(2 9 6 9) list:quicksort (2 6 9 9)}] + [ a r:Fact; r:gives {(2 6 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4324 - skolem:lemma4325 - [ a r:Fact; r:gives {(2 6 7 9) list:reverse (9 7 6 2)}] - skolem:lemma3758 - skolem:lemma3759 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2967]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2679]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1970 a r:Inference; r:gives { - 2968 :kaprekar 6174 . + 2970 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2970 math:notEqualTo 0}] + skolem:lemma3406 + [ a r:Fact; r:gives {(2 9 7 0) list:quicksort (0 2 7 9)}] + [ a r:Fact; r:gives {(0 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4326 - skolem:lemma4327 - [ a r:Fact; r:gives {(2 6 8 9) list:reverse (9 8 6 2)}] - skolem:lemma3776 - skolem:lemma3777 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2968]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2689]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1971 a r:Inference; r:gives { - 2969 :kaprekar 6174 . + 2971 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2971 math:notEqualTo 0}] + skolem:lemma3407 + [ a r:Fact; r:gives {(2 9 7 1) list:quicksort (1 2 7 9)}] + [ a r:Fact; r:gives {(1 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4328 - skolem:lemma4329 - [ a r:Fact; r:gives {(2 6 9 9) list:reverse (9 9 6 2)}] - skolem:lemma3798 - skolem:lemma3799 - [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2969]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2699]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1972 a r:Inference; r:gives { - 2970 :kaprekar 6174 . + 2972 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2972 math:notEqualTo 0}] + skolem:lemma3408 + [ a r:Fact; r:gives {(2 9 7 2) list:quicksort (2 2 7 9)}] + [ a r:Fact; r:gives {(2 2 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4330 - skolem:lemma4331 - [ a r:Fact; r:gives {(0 2 7 9) list:reverse (9 7 2 0)}] - skolem:lemma2286 - skolem:lemma2287 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {9441 math:notEqualTo 6174}] - skolem:lemma2288 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2970]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 279]; - 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_8"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. skolem:lemma1973 a r:Inference; r:gives { - 2971 :kaprekar 6174 . + 2973 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2973 math:notEqualTo 0}] + skolem:lemma3409 + [ a r:Fact; r:gives {(2 9 7 3) list:quicksort (2 3 7 9)}] + [ a r:Fact; r:gives {(2 3 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4332 - skolem:lemma4333 - [ a r:Fact; r:gives {(1 2 7 9) list:reverse (9 7 2 1)}] - skolem:lemma2579 - skolem:lemma2580 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {8442 math:notEqualTo 6174}] - skolem:lemma2283 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2971]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1279]; - 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_8"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1974 a r:Inference; r:gives { - 2972 :kaprekar 6174 . + 2974 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2974 math:notEqualTo 0}] + skolem:lemma3410 + [ a r:Fact; r:gives {(2 9 7 4) list:quicksort (2 4 7 9)}] + [ a r:Fact; r:gives {(2 4 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4334 - skolem:lemma4335 - [ a r:Fact; r:gives {(2 2 7 9) list:reverse (9 7 2 2)}] - skolem:lemma2852 - skolem:lemma2853 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2972]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2279]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1975 a r:Inference; r:gives { - 2973 :kaprekar 6174 . + 2975 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2975 math:notEqualTo 0}] + skolem:lemma3411 + [ a r:Fact; r:gives {(2 9 7 5) list:quicksort (2 5 7 9)}] + [ a r:Fact; r:gives {(2 5 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4336 - skolem:lemma4337 - [ a r:Fact; r:gives {(2 3 7 9) list:reverse (9 7 3 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2973]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2379]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1976 a r:Inference; r:gives { - 2974 :kaprekar 6174 . + 2976 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2976 math:notEqualTo 0}] + skolem:lemma3412 + [ a r:Fact; r:gives {(2 9 7 6) list:quicksort (2 6 7 9)}] + [ a r:Fact; r:gives {(2 6 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4338 - skolem:lemma4339 - [ a r:Fact; r:gives {(2 4 7 9) list:reverse (9 7 4 2)}] - skolem:lemma3330 - skolem:lemma3331 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2974]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2479]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1977 a r:Inference; r:gives { - 2975 :kaprekar 6174 . + 2977 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2977 math:notEqualTo 0}] + skolem:lemma3413 + [ a r:Fact; r:gives {(2 9 7 7) list:quicksort (2 7 7 9)}] + [ a r:Fact; r:gives {(2 7 7 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4340 - skolem:lemma4341 - [ a r:Fact; r:gives {(2 5 7 9) list:reverse (9 7 5 2)}] - skolem:lemma3550 - skolem:lemma3551 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2975]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2579]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1978 a r:Inference; r:gives { - 2976 :kaprekar 6174 . + 2978 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2978 math:notEqualTo 0}] + skolem:lemma3414 + [ a r:Fact; r:gives {(2 9 7 8) list:quicksort (2 7 8 9)}] + [ a r:Fact; r:gives {(2 7 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4342 - skolem:lemma4343 - [ a r:Fact; r:gives {(2 6 7 9) list:reverse (9 7 6 2)}] - skolem:lemma3758 - skolem:lemma3759 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2976]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2679]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1979 a r:Inference; r:gives { - 2977 :kaprekar 6174 . + 2979 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2979 math:notEqualTo 0}] + skolem:lemma3415 + [ a r:Fact; r:gives {(2 9 7 9) list:quicksort (2 7 9 9)}] + [ a r:Fact; r:gives {(2 7 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4344 - skolem:lemma4345 - [ a r:Fact; r:gives {(2 7 7 9) list:reverse (9 7 7 2)}] - skolem:lemma3958 - skolem:lemma3959 - [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2977]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2779]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1980 a r:Inference; r:gives { - 2978 :kaprekar 6174 . + 2980 :kaprekar (0 7). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2980 math:notEqualTo 0}] + skolem:lemma3416 + [ a r:Fact; r:gives {(2 9 8 0) list:quicksort (0 2 8 9)}] + [ a r:Fact; r:gives {(0 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4346 - skolem:lemma4347 - [ a r:Fact; r:gives {(2 7 8 9) list:reverse (9 8 7 2)}] - skolem:lemma3980 - skolem:lemma3981 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2978]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2789]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1981 a r:Inference; r:gives { - 2979 :kaprekar 6174 . + 2981 :kaprekar (0 2). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2981 math:notEqualTo 0}] + skolem:lemma3417 + [ a r:Fact; r:gives {(2 9 8 1) list:quicksort (1 2 8 9)}] + [ a r:Fact; r:gives {(1 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4348 - skolem:lemma4349 - [ a r:Fact; r:gives {(2 7 9 9) list:reverse (9 9 7 2)}] - skolem:lemma4002 - skolem:lemma4003 - [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2979]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2799]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1982 a r:Inference; r:gives { - 2980 :kaprekar 6174 . + 2982 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2982 math:notEqualTo 0}] + skolem:lemma3418 + [ a r:Fact; r:gives {(2 9 8 2) list:quicksort (2 2 8 9)}] + [ a r:Fact; r:gives {(2 2 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4350 - skolem:lemma4351 - [ a r:Fact; r:gives {(0 2 8 9) list:reverse (9 8 2 0)}] - skolem:lemma2312 - skolem:lemma2313 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {9531 math:notEqualTo 6174}] - skolem:lemma2314 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2980]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 289]; - 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_8"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1983 a r:Inference; r:gives { - 2981 :kaprekar 6174 . + 2983 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2983 math:notEqualTo 0}] + skolem:lemma3419 + [ a r:Fact; r:gives {(2 9 8 3) list:quicksort (2 3 8 9)}] + [ a r:Fact; r:gives {(2 3 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4352 - skolem:lemma4353 - [ a r:Fact; r:gives {(1 2 8 9) list:reverse (9 8 2 1)}] - skolem:lemma2604 - skolem:lemma2605 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2981]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1289]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1984 a r:Inference; r:gives { - 2982 :kaprekar 6174 . + 2984 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2984 math:notEqualTo 0}] + skolem:lemma3420 + [ a r:Fact; r:gives {(2 9 8 4) list:quicksort (2 4 8 9)}] + [ a r:Fact; r:gives {(2 4 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4354 - skolem:lemma4355 - [ a r:Fact; r:gives {(2 2 8 9) list:reverse (9 8 2 2)}] - skolem:lemma2875 - skolem:lemma2876 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2982]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2289]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1985 a r:Inference; r:gives { - 2983 :kaprekar 6174 . + 2985 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2985 math:notEqualTo 0}] + skolem:lemma3421 + [ a r:Fact; r:gives {(2 9 8 5) list:quicksort (2 5 8 9)}] + [ a r:Fact; r:gives {(2 5 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4356 - skolem:lemma4357 - [ a r:Fact; r:gives {(2 3 8 9) list:reverse (9 8 3 2)}] - skolem:lemma3126 - skolem:lemma3127 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2983]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2389]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1986 a r:Inference; r:gives { - 2984 :kaprekar 6174 . + 2986 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2986 math:notEqualTo 0}] + skolem:lemma3422 + [ a r:Fact; r:gives {(2 9 8 6) list:quicksort (2 6 8 9)}] + [ a r:Fact; r:gives {(2 6 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4358 - skolem:lemma4359 - [ a r:Fact; r:gives {(2 4 8 9) list:reverse (9 8 4 2)}] - skolem:lemma3350 - skolem:lemma3351 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2984]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2489]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1987 a r:Inference; r:gives { - 2985 :kaprekar 6174 . + 2987 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2987 math:notEqualTo 0}] + skolem:lemma3423 + [ a r:Fact; r:gives {(2 9 8 7) list:quicksort (2 7 8 9)}] + [ a r:Fact; r:gives {(2 7 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4360 - skolem:lemma4361 - [ a r:Fact; r:gives {(2 5 8 9) list:reverse (9 8 5 2)}] - skolem:lemma3570 - skolem:lemma3571 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2985]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2589]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1988 a r:Inference; r:gives { - 2986 :kaprekar 6174 . + 2988 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2988 math:notEqualTo 0}] + skolem:lemma3424 + [ a r:Fact; r:gives {(2 9 8 8) list:quicksort (2 8 8 9)}] + [ a r:Fact; r:gives {(2 8 8 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4362 - skolem:lemma4363 - [ a r:Fact; r:gives {(2 6 8 9) list:reverse (9 8 6 2)}] - skolem:lemma3776 - skolem:lemma3777 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2986]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2689]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1989 a r:Inference; r:gives { - 2987 :kaprekar 6174 . + 2989 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2989 math:notEqualTo 0}] + skolem:lemma3425 + [ a r:Fact; r:gives {(2 9 8 9) list:quicksort (2 8 9 9)}] + [ a r:Fact; r:gives {(2 8 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4364 - skolem:lemma4365 - [ a r:Fact; r:gives {(2 7 8 9) list:reverse (9 8 7 2)}] - skolem:lemma3980 - skolem:lemma3981 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2987]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2789]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1990 a r:Inference; r:gives { - 2988 :kaprekar 6174 . + 2990 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2990 math:notEqualTo 0}] + skolem:lemma3426 + [ a r:Fact; r:gives {(2 9 9 0) list:quicksort (0 2 9 9)}] + [ a r:Fact; r:gives {(0 2 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4366 - skolem:lemma4367 - [ a r:Fact; r:gives {(2 8 8 9) list:reverse (9 8 8 2)}] - skolem:lemma4166 - skolem:lemma4167 - [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2988]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2889]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1991 a r:Inference; r:gives { - 2989 :kaprekar 6174 . + 2991 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 + [ a r:Fact; r:gives {2991 math:notEqualTo 0}] + skolem:lemma3427 + [ a r:Fact; r:gives {(2 9 9 1) list:quicksort (1 2 9 9)}] + [ a r:Fact; r:gives {(1 2 9 9) list:reverse (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 {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4368 - skolem:lemma4369 - [ a r:Fact; r:gives {(2 8 9 9) list:reverse (9 9 8 2)}] - skolem:lemma4188 - skolem:lemma4189 - [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2989]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2899]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. skolem:lemma1992 a r:Inference; r:gives { - 2990 :kaprekar 6174 . + 2992 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4370 - skolem:lemma4371 - [ a r:Fact; r:gives {(0 2 9 9) list:reverse (9 9 2 0)}] - skolem:lemma2335 - skolem:lemma2336 - [ a r:Fact; r:gives {(9920 299) math:difference 9621}] - [ a r:Fact; r:gives {9621 math:notEqualTo 6174}] - skolem:lemma2337 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2990]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 299]; - 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_8"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma1993 a r:Inference; - r:gives { - 2991 :kaprekar 6174 . - }; - r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4372 - skolem:lemma4373 - [ a r:Fact; r:gives {(1 2 9 9) list:reverse (9 9 2 1)}] - skolem:lemma2626 - skolem:lemma2627 - [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] - [ a r:Fact; r:gives {8622 math:notEqualTo 6174}] - skolem:lemma2628 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1299]; - 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_8"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma1994 a r:Inference; - r:gives { - 2992 :kaprekar 6174 . - }; - r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4374 - skolem:lemma4375 + [ a r:Fact; r:gives {2992 math:notEqualTo 0}] + skolem:lemma3428 + [ a r:Fact; r:gives {(2 9 9 2) list:quicksort (2 2 9 9)}] [ a r:Fact; r:gives {(2 2 9 9) list:reverse (9 9 2 2)}] - skolem:lemma2897 - skolem:lemma2898 + skolem:lemma2568 + skolem:lemma2569 [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] - [ a r:Fact; r:gives {7623 math:notEqualTo 6174}] - skolem:lemma2899 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2299]; - 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_8"]; r:boundTo 7623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. -skolem:lemma1995 a r:Inference; +skolem:lemma1993 a r:Inference; r:gives { - 2993 :kaprekar 6174 . + 2993 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4376 - skolem:lemma4377 + [ a r:Fact; r:gives {2993 math:notEqualTo 0}] + skolem:lemma3429 + [ a r:Fact; r:gives {(2 9 9 3) list:quicksort (2 3 9 9)}] [ a r:Fact; r:gives {(2 3 9 9) list:reverse (9 9 3 2)}] - skolem:lemma3148 - skolem:lemma3149 + skolem:lemma2724 + skolem:lemma2725 [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] - [ a r:Fact; r:gives {7533 math:notEqualTo 6174}] - skolem:lemma2601 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2399]; - 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_8"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. -skolem:lemma1996 a r:Inference; +skolem:lemma1994 a r:Inference; r:gives { - 2994 :kaprekar 6174 . + 2994 :kaprekar (0 5). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4378 - skolem:lemma4379 + [ a r:Fact; r:gives {2994 math:notEqualTo 0}] + skolem:lemma3430 + [ a r:Fact; r:gives {(2 9 9 4) list:quicksort (2 4 9 9)}] [ a r:Fact; r:gives {(2 4 9 9) list:reverse (9 9 4 2)}] - skolem:lemma3372 - skolem:lemma3373 + skolem:lemma2866 + skolem:lemma2867 [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2499]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. -skolem:lemma1997 a r:Inference; +skolem:lemma1995 a r:Inference; r:gives { - 2995 :kaprekar 6174 . + 2995 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4380 - skolem:lemma4381 + [ a r:Fact; r:gives {2995 math:notEqualTo 0}] + skolem:lemma3431 + [ a r:Fact; r:gives {(2 9 9 5) list:quicksort (2 5 9 9)}] [ a r:Fact; r:gives {(2 5 9 9) list:reverse (9 9 5 2)}] - skolem:lemma3592 - skolem:lemma3593 + skolem:lemma2996 + skolem:lemma2997 [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] - [ a r:Fact; r:gives {7353 math:notEqualTo 6174}] - skolem:lemma2249 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2599]; - 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_8"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. -skolem:lemma1998 a r:Inference; +skolem:lemma1996 a r:Inference; r:gives { - 2996 :kaprekar 6174 . + 2996 :kaprekar (0 6). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4382 - skolem:lemma4383 + [ a r:Fact; r:gives {2996 math:notEqualTo 0}] + skolem:lemma3432 + [ a r:Fact; r:gives {(2 9 9 6) list:quicksort (2 6 9 9)}] [ a r:Fact; r:gives {(2 6 9 9) list:reverse (9 9 6 2)}] - skolem:lemma3798 - skolem:lemma3799 + skolem:lemma3116 + skolem:lemma3117 [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] - [ a r:Fact; r:gives {7263 math:notEqualTo 6174}] - skolem:lemma2221 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2699]; - 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_8"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. -skolem:lemma1999 a r:Inference; +skolem:lemma1997 a r:Inference; r:gives { - 2997 :kaprekar 6174 . + 2997 :kaprekar (0 5). }; r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4384 - skolem:lemma4385 + [ a r:Fact; r:gives {2997 math:notEqualTo 0}] + skolem:lemma3433 + [ a r:Fact; r:gives {(2 9 9 7) list:quicksort (2 7 9 9)}] [ a r:Fact; r:gives {(2 7 9 9) list:reverse (9 9 7 2)}] - skolem:lemma4002 - skolem:lemma4003 + skolem:lemma3228 + skolem:lemma3229 [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 + [ 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 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_2"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2799]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma2003. -skolem:lemma2000 a r:Inference; +skolem:lemma1998 a r:Inference; r:gives { - 2998 :kaprekar 6174 . + 2998 :kaprekar (0 3). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4386 - skolem:lemma4387 + [ a r:Fact; r:gives {2998 math:notEqualTo 0}] + skolem:lemma3434 + [ a r:Fact; r:gives {(2 9 9 8) list:quicksort (2 8 9 9)}] [ a r:Fact; r:gives {(2 8 9 9) list:reverse (9 9 8 2)}] - skolem:lemma4188 - skolem:lemma4189 + skolem:lemma3334 + skolem:lemma3335 [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] - [ a r:Fact; r:gives {7083 math:notEqualTo 6174}] - skolem:lemma2082 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2899]; - 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_8"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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. -skolem:lemma2001 a r:Inference; +skolem:lemma1999 a r:Inference; r:gives { - 2999 :kaprekar 6174 . + 2999 :kaprekar (0 4). }; r:evidence ( - skolem:lemma2002 - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {{ - :recursion :count 0. - } log:becomes { - :recursion :count 1. - }}] - skolem:lemma4388 - skolem:lemma4389 + [ a r:Fact; r:gives {2999 math:notEqualTo 0}] + skolem:lemma3435 + [ a r:Fact; r:gives {(2 9 9 9) list:quicksort (2 9 9 9)}] [ a r:Fact; r:gives {(2 9 9 9) list:reverse (9 9 9 2)}] - skolem:lemma4390 - skolem:lemma4391 + skolem:lemma3436 + skolem:lemma3437 [ a r:Fact; r:gives {(9992 2999) math:difference 6993}] - [ a r:Fact; r:gives {6993 math:notEqualTo 6174}] - skolem:lemma2124 + [ 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2999]; - 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_8"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma2002 a r:Extraction; - r:gives { - :recursion :count 0 . - }; - r:because [ a r:Parsing; r:source ]. + 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. -skolem:lemma2003 a r:Inference; +skolem:lemma2000 a r:Inference; r:gives { 2000 :numberToDigits (2 0 0 0). }; @@ -54087,32 +49992,9 @@ skolem:lemma2003 a r:Inference; 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:lemma4392. - -skolem:lemma2004 a r:Inference; - r:gives { - (2 0 0 0) :sort (0 0 0 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 0) list:firstRest (2 (0 0 0))}] - skolem:lemma4393 - skolem:lemma4394 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 0) (2)) list:append (0 0 0 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 0 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2005 a r:Inference; +skolem:lemma2001 a r:Inference; r:gives { (0 0 0 2) :digitsToNumber 2 . }; @@ -54130,9 +50012,9 @@ skolem:lemma2005 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2006 a r:Inference; +skolem:lemma2002 a r:Inference; r:gives { (2 0 0 0) :digitsToNumber 2000 . }; @@ -54150,66 +50032,33 @@ skolem:lemma2006 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2007 a r:Inference; - r:gives { - 1998 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4398 - skolem:lemma4399 - [ a r:Fact; r:gives {(1 8 9 9) list:reverse (9 9 8 1)}] - skolem:lemma4400 - skolem:lemma4401 - [ a r:Fact; r:gives {(9981 1899) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9981]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma2008 a r:Extraction; +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_2 :kaprekar var:x_9. + @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). } <= { - :recursion :count var:x_0. - (var:x_0 1) math:sum var:x_1. - { - :recursion :count var:x_0. - } log:becomes { - :recursion :count var:x_1. - }. - var:x_2 :numberToDigits var:x_3. - var:x_3 :sort var:x_4. - var:x_4 list:reverse var:x_5. - var:x_4 :digitsToNumber var:x_6. - var:x_5 :digitsToNumber var:x_7. - (var:x_7 var:x_6) math:difference var:x_8. - var:x_8 math:notEqualTo 6174 . - var:x_8 :kaprekar var:x_9. + var:x_0 math:notEqualTo 0 . + var:x_0 :numberToDigits var:x_1. + var:x_1 list:quicksort var:x_2. + var:x_2 list:reverse 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:lemma2009 a r:Inference; +skolem:lemma2004 a r:Inference; r:gives { 2001 :numberToDigits (2 0 0 1). }; @@ -54228,32 +50077,9 @@ skolem:lemma2009 a r:Inference; 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:lemma4392. - -skolem:lemma2010 a r:Inference; - r:gives { - (2 0 0 1) :sort (0 0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 1) list:firstRest (2 (0 0 1))}] - skolem:lemma4402 - skolem:lemma4403 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 1) (2)) list:append (0 0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 1 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2011 a r:Inference; +skolem:lemma2005 a r:Inference; r:gives { (0 0 1 2) :digitsToNumber 12 . }; @@ -54271,9 +50097,9 @@ skolem:lemma2011 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2012 a r:Inference; +skolem:lemma2006 a r:Inference; r:gives { (2 1 0 0) :digitsToNumber 2100 . }; @@ -54291,9 +50117,9 @@ skolem:lemma2012 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2013 a r:Inference; +skolem:lemma2007 a r:Inference; r:gives { 2002 :numberToDigits (2 0 0 2). }; @@ -54312,32 +50138,9 @@ skolem:lemma2013 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma2014 a r:Inference; - r:gives { - (2 0 0 2) :sort (0 0 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 2) list:firstRest (2 (0 0 2))}] - skolem:lemma4404 - skolem:lemma4405 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 2) (2)) list:append (0 0 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2015 a r:Inference; +skolem:lemma2008 a r:Inference; r:gives { (0 0 2 2) :digitsToNumber 22 . }; @@ -54355,9 +50158,9 @@ skolem:lemma2015 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2016 a r:Inference; +skolem:lemma2009 a r:Inference; r:gives { (2 2 0 0) :digitsToNumber 2200 . }; @@ -54375,9 +50178,9 @@ skolem:lemma2016 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2017 a r:Inference; +skolem:lemma2010 a r:Inference; r:gives { 2003 :numberToDigits (2 0 0 3). }; @@ -54396,32 +50199,9 @@ skolem:lemma2017 a r:Inference; 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:lemma4392. - -skolem:lemma2018 a r:Inference; - r:gives { - (2 0 0 3) :sort (0 0 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 3) list:firstRest (2 (0 0 3))}] - skolem:lemma4406 - skolem:lemma4407 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 0) (2 3)) list:append (0 0 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (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 (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2019 a r:Inference; +skolem:lemma2011 a r:Inference; r:gives { (0 0 2 3) :digitsToNumber 23 . }; @@ -54439,9 +50219,9 @@ skolem:lemma2019 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2020 a r:Inference; +skolem:lemma2012 a r:Inference; r:gives { (3 2 0 0) :digitsToNumber 3200 . }; @@ -54459,42 +50239,9 @@ skolem:lemma2020 a r:Inference; 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:lemma4397. - -skolem:lemma2021 a r:Inference; - r:gives { - 3177 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4409 - skolem:lemma4410 - [ a r:Fact; r:gives {(1 3 7 7) list:reverse (7 7 3 1)}] - skolem:lemma4411 - skolem:lemma4412 - [ a r:Fact; r:gives {(7731 1377) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1377]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2022 a r:Inference; +skolem:lemma2013 a r:Inference; r:gives { 2004 :numberToDigits (2 0 0 4). }; @@ -54513,32 +50260,9 @@ skolem:lemma2022 a r:Inference; 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:lemma4392. - -skolem:lemma2023 a r:Inference; - r:gives { - (2 0 0 4) :sort (0 0 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 4) list:firstRest (2 (0 0 4))}] - skolem:lemma4413 - skolem:lemma4407 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 0) (2 4)) list:append (0 0 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2024 a r:Inference; +skolem:lemma2014 a r:Inference; r:gives { (0 0 2 4) :digitsToNumber 24 . }; @@ -54556,9 +50280,9 @@ skolem:lemma2024 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2025 a r:Inference; +skolem:lemma2015 a r:Inference; r:gives { (4 2 0 0) :digitsToNumber 4200 . }; @@ -54576,19 +50300,9 @@ skolem:lemma2025 a r:Inference; 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:lemma4397. - -skolem:lemma2026 a r:Inference; - r:gives { - 4176 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4176]; - r:rule skolem:lemma2032. + r:rule skolem:lemma3439. -skolem:lemma2027 a r:Inference; +skolem:lemma2016 a r:Inference; r:gives { 2005 :numberToDigits (2 0 0 5). }; @@ -54607,32 +50321,9 @@ skolem:lemma2027 a r:Inference; 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:lemma4392. - -skolem:lemma2028 a r:Inference; - r:gives { - (2 0 0 5) :sort (0 0 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 5) list:firstRest (2 (0 0 5))}] - skolem:lemma4415 - skolem:lemma4407 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 0) (2 5)) list:append (0 0 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2029 a r:Inference; +skolem:lemma2017 a r:Inference; r:gives { (0 0 2 5) :digitsToNumber 25 . }; @@ -54650,9 +50341,9 @@ skolem:lemma2029 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2030 a r:Inference; +skolem:lemma2018 a r:Inference; r:gives { (5 2 0 0) :digitsToNumber 5200 . }; @@ -54670,50 +50361,70 @@ skolem:lemma2030 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2031 a r:Inference; +skolem:lemma2019 a r:Inference; r:gives { - 5175 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4417 - skolem:lemma4418 - [ a r:Fact; r:gives {(1 5 5 7) list:reverse (7 5 5 1)}] - skolem:lemma4419 - skolem:lemma4420 - [ a r:Fact; r:gives {(7551 1557) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 + 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_0"]; r:boundTo 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_2"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7551]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma3438. -skolem:lemma2032 a r:Extraction; +skolem:lemma2020 a r:Inference; r:gives { - @forSome var:x_0. { - var:x_0 :kaprekar 6174. - } <= true. + (0 0 2 6) :digitsToNumber 26 . }; - r:because [ a r:Parsing; r:source ]. + 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:lemma3439. -skolem:lemma2033 a r:Inference; +skolem:lemma2021 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:lemma3439. + +skolem:lemma2022 a r:Inference; r:gives { 2007 :numberToDigits (2 0 0 7). }; @@ -54732,32 +50443,9 @@ skolem:lemma2033 a r:Inference; 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:lemma4392. - -skolem:lemma2034 a r:Inference; - r:gives { - (2 0 0 7) :sort (0 0 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 7) list:firstRest (2 (0 0 7))}] - skolem:lemma4421 - skolem:lemma4407 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 0) (2 7)) list:append (0 0 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2035 a r:Inference; +skolem:lemma2023 a r:Inference; r:gives { (0 0 2 7) :digitsToNumber 27 . }; @@ -54775,9 +50463,9 @@ skolem:lemma2035 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2036 a r:Inference; +skolem:lemma2024 a r:Inference; r:gives { (7 2 0 0) :digitsToNumber 7200 . }; @@ -54795,42 +50483,9 @@ skolem:lemma2036 a r:Inference; 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:lemma4397. - -skolem:lemma2037 a r:Inference; - r:gives { - 7173 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4423 - skolem:lemma4424 - [ a r:Fact; r:gives {(1 3 7 7) list:reverse (7 7 3 1)}] - skolem:lemma4411 - skolem:lemma4412 - [ a r:Fact; r:gives {(7731 1377) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1377]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2038 a r:Inference; +skolem:lemma2025 a r:Inference; r:gives { 2008 :numberToDigits (2 0 0 8). }; @@ -54849,32 +50504,9 @@ skolem:lemma2038 a r:Inference; 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:lemma4392. - -skolem:lemma2039 a r:Inference; - r:gives { - (2 0 0 8) :sort (0 0 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 8) list:firstRest (2 (0 0 8))}] - skolem:lemma4425 - skolem:lemma4407 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 0) (2 8)) list:append (0 0 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2040 a r:Inference; +skolem:lemma2026 a r:Inference; r:gives { (0 0 2 8) :digitsToNumber 28 . }; @@ -54892,9 +50524,9 @@ skolem:lemma2040 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2041 a r:Inference; +skolem:lemma2027 a r:Inference; r:gives { (8 2 0 0) :digitsToNumber 8200 . }; @@ -54912,42 +50544,9 @@ skolem:lemma2041 a r:Inference; 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:lemma4397. - -skolem:lemma2042 a r:Inference; - r:gives { - 8172 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4427 - skolem:lemma4428 - [ a r:Fact; r:gives {(1 2 7 8) list:reverse (8 7 2 1)}] - skolem:lemma2575 - skolem:lemma2576 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {7443 math:notEqualTo 6174}] - skolem:lemma2278 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1278]; - 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_8"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2043 a r:Inference; +skolem:lemma2028 a r:Inference; r:gives { 2009 :numberToDigits (2 0 0 9). }; @@ -54966,32 +50565,9 @@ skolem:lemma2043 a r:Inference; 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:lemma4392. - -skolem:lemma2044 a r:Inference; - r:gives { - (2 0 0 9) :sort (0 0 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0 9) list:firstRest (2 (0 0 9))}] - skolem:lemma4429 - skolem:lemma4407 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 0) (2 9)) list:append (0 0 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 0 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_2"]; r:boundTo (0 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2045 a r:Inference; +skolem:lemma2029 a r:Inference; r:gives { (0 0 2 9) :digitsToNumber 29 . }; @@ -55009,9 +50585,9 @@ skolem:lemma2045 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2046 a r:Inference; +skolem:lemma2030 a r:Inference; r:gives { (9 2 0 0) :digitsToNumber 9200 . }; @@ -55029,42 +50605,9 @@ skolem:lemma2046 a r:Inference; 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:lemma4397. - -skolem:lemma2047 a r:Inference; - r:gives { - 9171 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4431 - skolem:lemma4432 - [ a r:Fact; r:gives {(1 1 7 9) list:reverse (9 7 1 1)}] - skolem:lemma4433 - skolem:lemma4434 - [ a r:Fact; r:gives {(9711 1179) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 7 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1179]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9711]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2048 a r:Inference; +skolem:lemma2031 a r:Inference; r:gives { 2010 :numberToDigits (2 0 1 0). }; @@ -55083,32 +50626,9 @@ skolem:lemma2048 a r:Inference; 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:lemma4392. - -skolem:lemma2049 a r:Inference; - r:gives { - (2 0 1 0) :sort (0 0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 0) list:firstRest (2 (0 1 0))}] - skolem:lemma4435 - skolem:lemma4436 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 1) (2)) list:append (0 0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 1 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2050 a r:Inference; +skolem:lemma2032 a r:Inference; r:gives { 2011 :numberToDigits (2 0 1 1). }; @@ -55127,32 +50647,9 @@ skolem:lemma2050 a r:Inference; 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:lemma4392. - -skolem:lemma2051 a r:Inference; - r:gives { - (2 0 1 1) :sort (0 1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 1) list:firstRest (2 (0 1 1))}] - skolem:lemma4437 - skolem:lemma4438 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 1) (2)) list:append (0 1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 1 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2052 a r:Inference; +skolem:lemma2033 a r:Inference; r:gives { (0 1 1 2) :digitsToNumber 112 . }; @@ -55170,9 +50667,9 @@ skolem:lemma2052 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2053 a r:Inference; +skolem:lemma2034 a r:Inference; r:gives { (2 1 1 0) :digitsToNumber 2110 . }; @@ -55190,9 +50687,9 @@ skolem:lemma2053 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2054 a r:Inference; +skolem:lemma2035 a r:Inference; r:gives { 2012 :numberToDigits (2 0 1 2). }; @@ -55211,32 +50708,9 @@ skolem:lemma2054 a r:Inference; 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:lemma4392. - -skolem:lemma2055 a r:Inference; - r:gives { - (2 0 1 2) :sort (0 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 2) list:firstRest (2 (0 1 2))}] - skolem:lemma4439 - skolem:lemma4440 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 2) (2)) list:append (0 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2056 a r:Inference; +skolem:lemma2036 a r:Inference; r:gives { (0 1 2 2) :digitsToNumber 122 . }; @@ -55254,9 +50728,9 @@ skolem:lemma2056 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2057 a r:Inference; +skolem:lemma2037 a r:Inference; r:gives { (2 2 1 0) :digitsToNumber 2210 . }; @@ -55274,9 +50748,9 @@ skolem:lemma2057 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2058 a r:Inference; +skolem:lemma2038 a r:Inference; r:gives { 2013 :numberToDigits (2 0 1 3). }; @@ -55295,32 +50769,9 @@ skolem:lemma2058 a r:Inference; 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:lemma4392. - -skolem:lemma2059 a r:Inference; - r:gives { - (2 0 1 3) :sort (0 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 3) list:firstRest (2 (0 1 3))}] - skolem:lemma4441 - skolem:lemma4442 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 1) (2 3)) list:append (0 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2060 a r:Inference; +skolem:lemma2039 a r:Inference; r:gives { (0 1 2 3) :digitsToNumber 123 . }; @@ -55338,9 +50789,9 @@ skolem:lemma2060 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2061 a r:Inference; +skolem:lemma2040 a r:Inference; r:gives { (3 2 1 0) :digitsToNumber 3210 . }; @@ -55358,42 +50809,9 @@ skolem:lemma2061 a r:Inference; 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:lemma4397. - -skolem:lemma2062 a r:Inference; - r:gives { - 3087 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 3}] - [ a r:Fact; r:gives {(3 1) math:sum 4}] - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 4. - }}] - skolem:lemma4443 - skolem:lemma4444 - [ a r:Fact; r:gives {(0 3 7 8) list:reverse (8 7 3 0)}] - skolem:lemma4445 - skolem:lemma4446 - [ a r:Fact; r:gives {(8730 378) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 0 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 378]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2063 a r:Inference; +skolem:lemma2041 a r:Inference; r:gives { 2014 :numberToDigits (2 0 1 4). }; @@ -55412,32 +50830,9 @@ skolem:lemma2063 a r:Inference; 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:lemma4392. - -skolem:lemma2064 a r:Inference; - r:gives { - (2 0 1 4) :sort (0 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 4) list:firstRest (2 (0 1 4))}] - skolem:lemma4447 - skolem:lemma4442 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 1) (2 4)) list:append (0 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2065 a r:Inference; +skolem:lemma2042 a r:Inference; r:gives { (0 1 2 4) :digitsToNumber 124 . }; @@ -55455,9 +50850,9 @@ skolem:lemma2065 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2066 a r:Inference; +skolem:lemma2043 a r:Inference; r:gives { (4 2 1 0) :digitsToNumber 4210 . }; @@ -55475,42 +50870,9 @@ skolem:lemma2066 a r:Inference; 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:lemma4397. - -skolem:lemma2067 a r:Inference; - r:gives { - 4086 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4448 - skolem:lemma4449 - [ a r:Fact; r:gives {(0 4 6 8) list:reverse (8 6 4 0)}] - skolem:lemma4450 - skolem:lemma4451 - [ a r:Fact; r:gives {(8640 468) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 0 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8640]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2068 a r:Inference; +skolem:lemma2044 a r:Inference; r:gives { 2015 :numberToDigits (2 0 1 5). }; @@ -55529,32 +50891,9 @@ skolem:lemma2068 a r:Inference; 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:lemma4392. - -skolem:lemma2069 a r:Inference; - r:gives { - (2 0 1 5) :sort (0 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 5) list:firstRest (2 (0 1 5))}] - skolem:lemma4452 - skolem:lemma4442 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 1) (2 5)) list:append (0 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2070 a r:Inference; +skolem:lemma2045 a r:Inference; r:gives { (0 1 2 5) :digitsToNumber 125 . }; @@ -55572,9 +50911,9 @@ skolem:lemma2070 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2071 a r:Inference; +skolem:lemma2046 a r:Inference; r:gives { (5 2 1 0) :digitsToNumber 5210 . }; @@ -55592,42 +50931,9 @@ skolem:lemma2071 a r:Inference; 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:lemma4397. - -skolem:lemma2072 a r:Inference; - r:gives { - 5085 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4453 - skolem:lemma4454 - [ a r:Fact; r:gives {(0 5 5 8) list:reverse (8 5 5 0)}] - skolem:lemma4455 - skolem:lemma4456 - [ a r:Fact; r:gives {(8550 558) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 0 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 5 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8550]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2073 a r:Inference; +skolem:lemma2047 a r:Inference; r:gives { 2016 :numberToDigits (2 0 1 6). }; @@ -55646,32 +50952,9 @@ skolem:lemma2073 a r:Inference; 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:lemma4392. - -skolem:lemma2074 a r:Inference; - r:gives { - (2 0 1 6) :sort (0 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 6) list:firstRest (2 (0 1 6))}] - skolem:lemma4457 - skolem:lemma4442 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 1) (2 6)) list:append (0 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2075 a r:Inference; +skolem:lemma2048 a r:Inference; r:gives { (0 1 2 6) :digitsToNumber 126 . }; @@ -55689,9 +50972,9 @@ skolem:lemma2075 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2076 a r:Inference; +skolem:lemma2049 a r:Inference; r:gives { (6 2 1 0) :digitsToNumber 6210 . }; @@ -55709,42 +50992,9 @@ skolem:lemma2076 a r:Inference; 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:lemma4397. - -skolem:lemma2077 a r:Inference; - r:gives { - 6084 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4459 - skolem:lemma4460 - [ a r:Fact; r:gives {(0 4 6 8) list:reverse (8 6 4 0)}] - skolem:lemma4450 - skolem:lemma4451 - [ a r:Fact; r:gives {(8640 468) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 0 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8640]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2078 a r:Inference; +skolem:lemma2050 a r:Inference; r:gives { 2017 :numberToDigits (2 0 1 7). }; @@ -55763,32 +51013,9 @@ skolem:lemma2078 a r:Inference; 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:lemma4392. - -skolem:lemma2079 a r:Inference; - r:gives { - (2 0 1 7) :sort (0 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 7) list:firstRest (2 (0 1 7))}] - skolem:lemma4461 - skolem:lemma4442 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 1) (2 7)) list:append (0 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2080 a r:Inference; +skolem:lemma2051 a r:Inference; r:gives { (0 1 2 7) :digitsToNumber 127 . }; @@ -55806,9 +51033,9 @@ skolem:lemma2080 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2081 a r:Inference; +skolem:lemma2052 a r:Inference; r:gives { (7 2 1 0) :digitsToNumber 7210 . }; @@ -55826,42 +51053,9 @@ skolem:lemma2081 a r:Inference; 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:lemma4397. - -skolem:lemma2082 a r:Inference; - r:gives { - 7083 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4462 - skolem:lemma4463 - [ a r:Fact; r:gives {(0 3 7 8) list:reverse (8 7 3 0)}] - skolem:lemma4445 - skolem:lemma4446 - [ a r:Fact; r:gives {(8730 378) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 0 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 7 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 378]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2083 a r:Inference; +skolem:lemma2053 a r:Inference; r:gives { 2018 :numberToDigits (2 0 1 8). }; @@ -55880,32 +51074,9 @@ skolem:lemma2083 a r:Inference; 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:lemma4392. - -skolem:lemma2084 a r:Inference; - r:gives { - (2 0 1 8) :sort (0 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 8) list:firstRest (2 (0 1 8))}] - skolem:lemma4464 - skolem:lemma4442 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 1) (2 8)) list:append (0 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2085 a r:Inference; +skolem:lemma2054 a r:Inference; r:gives { (0 1 2 8) :digitsToNumber 128 . }; @@ -55923,9 +51094,9 @@ skolem:lemma2085 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2086 a r:Inference; +skolem:lemma2055 a r:Inference; r:gives { (8 2 1 0) :digitsToNumber 8210 . }; @@ -55943,42 +51114,9 @@ skolem:lemma2086 a r:Inference; 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:lemma4397. - -skolem:lemma2087 a r:Inference; - r:gives { - 8082 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 2}] - [ a r:Fact; r:gives {(2 1) math:sum 3}] - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 3. - }}] - skolem:lemma4465 - skolem:lemma4466 - [ a r:Fact; r:gives {(0 2 8 8) list:reverse (8 8 2 0)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {8532 math:notEqualTo 6174}] - skolem:lemma2309 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 288]; - 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_8"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2088 a r:Inference; +skolem:lemma2056 a r:Inference; r:gives { 2019 :numberToDigits (2 0 1 9). }; @@ -55997,32 +51135,9 @@ skolem:lemma2088 a r:Inference; 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:lemma4392. - -skolem:lemma2089 a r:Inference; - r:gives { - (2 0 1 9) :sort (0 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1 9) list:firstRest (2 (0 1 9))}] - skolem:lemma4467 - skolem:lemma4442 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 1) (2 9)) list:append (0 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 1 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_2"]; r:boundTo (0 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2090 a r:Inference; +skolem:lemma2057 a r:Inference; r:gives { (0 1 2 9) :digitsToNumber 129 . }; @@ -56040,9 +51155,9 @@ skolem:lemma2090 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2091 a r:Inference; +skolem:lemma2058 a r:Inference; r:gives { (9 2 1 0) :digitsToNumber 9210 . }; @@ -56060,42 +51175,9 @@ skolem:lemma2091 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2092 a r:Inference; - r:gives { - 9081 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4468 - skolem:lemma4469 - [ a r:Fact; r:gives {(0 1 8 9) list:reverse (9 8 1 0)}] - skolem:lemma4470 - skolem:lemma4471 - [ a r:Fact; r:gives {(9810 189) math:difference 9621}] - [ a r:Fact; r:gives {9621 math:notEqualTo 6174}] - skolem:lemma2337 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 189]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9810]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma2093 a r:Inference; +skolem:lemma2059 a r:Inference; r:gives { 2020 :numberToDigits (2 0 2 0). }; @@ -56114,32 +51196,9 @@ skolem:lemma2093 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2094 a r:Inference; - r:gives { - (2 0 2 0) :sort (0 0 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 0) list:firstRest (2 (0 2 0))}] - skolem:lemma4472 - skolem:lemma4473 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 2) (2)) list:append (0 0 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma2095 a r:Inference; +skolem:lemma2060 a r:Inference; r:gives { 2021 :numberToDigits (2 0 2 1). }; @@ -56158,32 +51217,9 @@ skolem:lemma2095 a r:Inference; 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:lemma4392. - -skolem:lemma2096 a r:Inference; - r:gives { - (2 0 2 1) :sort (0 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 1) list:firstRest (2 (0 2 1))}] - skolem:lemma4474 - skolem:lemma4475 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 2) (2)) list:append (0 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2097 a r:Inference; +skolem:lemma2061 a r:Inference; r:gives { 2022 :numberToDigits (2 0 2 2). }; @@ -56202,32 +51238,9 @@ skolem:lemma2097 a r:Inference; 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:lemma4392. - -skolem:lemma2098 a r:Inference; - r:gives { - (2 0 2 2) :sort (0 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 2) list:firstRest (2 (0 2 2))}] - skolem:lemma4476 - skolem:lemma4477 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 2 2) (2)) list:append (0 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 2 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2099 a r:Inference; +skolem:lemma2062 a r:Inference; r:gives { (0 2 2 2) :digitsToNumber 222 . }; @@ -56245,9 +51258,9 @@ skolem:lemma2099 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2100 a r:Inference; +skolem:lemma2063 a r:Inference; r:gives { (2 2 2 0) :digitsToNumber 2220 . }; @@ -56265,9 +51278,9 @@ skolem:lemma2100 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2101 a r:Inference; +skolem:lemma2064 a r:Inference; r:gives { 2023 :numberToDigits (2 0 2 3). }; @@ -56286,32 +51299,9 @@ skolem:lemma2101 a r:Inference; 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:lemma4392. - -skolem:lemma2102 a r:Inference; - r:gives { - (2 0 2 3) :sort (0 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 3) list:firstRest (2 (0 2 3))}] - skolem:lemma4478 - skolem:lemma4479 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 2) (2 3)) list:append (0 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2103 a r:Inference; +skolem:lemma2065 a r:Inference; r:gives { (0 2 2 3) :digitsToNumber 223 . }; @@ -56329,9 +51319,9 @@ skolem:lemma2103 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2104 a r:Inference; +skolem:lemma2066 a r:Inference; r:gives { (3 2 2 0) :digitsToNumber 3220 . }; @@ -56349,9 +51339,9 @@ skolem:lemma2104 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2105 a r:Inference; +skolem:lemma2067 a r:Inference; r:gives { 2024 :numberToDigits (2 0 2 4). }; @@ -56370,32 +51360,9 @@ skolem:lemma2105 a r:Inference; 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:lemma4392. - -skolem:lemma2106 a r:Inference; - r:gives { - (2 0 2 4) :sort (0 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 4) list:firstRest (2 (0 2 4))}] - skolem:lemma4480 - skolem:lemma4479 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 2) (2 4)) list:append (0 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2107 a r:Inference; +skolem:lemma2068 a r:Inference; r:gives { (0 2 2 4) :digitsToNumber 224 . }; @@ -56413,9 +51380,9 @@ skolem:lemma2107 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2108 a r:Inference; +skolem:lemma2069 a r:Inference; r:gives { (4 2 2 0) :digitsToNumber 4220 . }; @@ -56433,42 +51400,9 @@ skolem:lemma2108 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2109 a r:Inference; - r:gives { - 3996 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 3}] - [ a r:Fact; r:gives {(3 1) math:sum 4}] - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 4. - }}] - skolem:lemma4481 - skolem:lemma4482 - [ a r:Fact; r:gives {(3 6 9 9) list:reverse (9 9 6 3)}] - skolem:lemma4483 - skolem:lemma4484 - [ a r:Fact; r:gives {(9963 3699) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3699]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2110 a r:Inference; +skolem:lemma2070 a r:Inference; r:gives { 2025 :numberToDigits (2 0 2 5). }; @@ -56487,32 +51421,9 @@ skolem:lemma2110 a r:Inference; 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:lemma4392. - -skolem:lemma2111 a r:Inference; - r:gives { - (2 0 2 5) :sort (0 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 5) list:firstRest (2 (0 2 5))}] - skolem:lemma4485 - skolem:lemma4479 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 2) (2 5)) list:append (0 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2112 a r:Inference; +skolem:lemma2071 a r:Inference; r:gives { (0 2 2 5) :digitsToNumber 225 . }; @@ -56530,9 +51441,9 @@ skolem:lemma2112 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2113 a r:Inference; +skolem:lemma2072 a r:Inference; r:gives { (5 2 2 0) :digitsToNumber 5220 . }; @@ -56550,42 +51461,9 @@ skolem:lemma2113 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2114 a r:Inference; - r:gives { - 4995 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4486 - skolem:lemma4487 - [ a r:Fact; r:gives {(4 5 9 9) list:reverse (9 9 5 4)}] - skolem:lemma4488 - skolem:lemma4489 - [ a r:Fact; r:gives {(9954 4599) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9954]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2115 a r:Inference; +skolem:lemma2073 a r:Inference; r:gives { 2026 :numberToDigits (2 0 2 6). }; @@ -56604,32 +51482,9 @@ skolem:lemma2115 a r:Inference; 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:lemma4392. - -skolem:lemma2116 a r:Inference; - r:gives { - (2 0 2 6) :sort (0 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 6) list:firstRest (2 (0 2 6))}] - skolem:lemma4490 - skolem:lemma4479 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 2) (2 6)) list:append (0 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2117 a r:Inference; +skolem:lemma2074 a r:Inference; r:gives { (0 2 2 6) :digitsToNumber 226 . }; @@ -56647,9 +51502,9 @@ skolem:lemma2117 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2118 a r:Inference; +skolem:lemma2075 a r:Inference; r:gives { (6 2 2 0) :digitsToNumber 6220 . }; @@ -56667,42 +51522,9 @@ skolem:lemma2118 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2119 a r:Inference; - r:gives { - 5994 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 2}] - [ a r:Fact; r:gives {(2 1) math:sum 3}] - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 3. - }}] - skolem:lemma4491 - skolem:lemma4492 - [ a r:Fact; r:gives {(4 5 9 9) list:reverse (9 9 5 4)}] - skolem:lemma4488 - skolem:lemma4489 - [ a r:Fact; r:gives {(9954 4599) math:difference 5355}] - [ a r:Fact; r:gives {5355 math:notEqualTo 6174}] - skolem:lemma2543 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9954]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2120 a r:Inference; +skolem:lemma2076 a r:Inference; r:gives { 2027 :numberToDigits (2 0 2 7). }; @@ -56721,32 +51543,9 @@ skolem:lemma2120 a r:Inference; 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:lemma4392. - -skolem:lemma2121 a r:Inference; - r:gives { - (2 0 2 7) :sort (0 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 7) list:firstRest (2 (0 2 7))}] - skolem:lemma4493 - skolem:lemma4479 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 2) (2 7)) list:append (0 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2122 a r:Inference; +skolem:lemma2077 a r:Inference; r:gives { (0 2 2 7) :digitsToNumber 227 . }; @@ -56764,9 +51563,9 @@ skolem:lemma2122 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2123 a r:Inference; +skolem:lemma2078 a r:Inference; r:gives { (7 2 2 0) :digitsToNumber 7220 . }; @@ -56784,42 +51583,9 @@ skolem:lemma2123 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2124 a r:Inference; - r:gives { - 6993 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4494 - skolem:lemma4495 - [ a r:Fact; r:gives {(3 6 9 9) list:reverse (9 9 6 3)}] - skolem:lemma4483 - skolem:lemma4484 - [ a r:Fact; r:gives {(9963 3699) math:difference 6264}] - [ a r:Fact; r:gives {6264 math:notEqualTo 6174}] - skolem:lemma2216 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3699]; - 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_8"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2125 a r:Inference; +skolem:lemma2079 a r:Inference; r:gives { 2028 :numberToDigits (2 0 2 8). }; @@ -56838,32 +51604,9 @@ skolem:lemma2125 a r:Inference; 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:lemma4392. - -skolem:lemma2126 a r:Inference; - r:gives { - (2 0 2 8) :sort (0 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 8) list:firstRest (2 (0 2 8))}] - skolem:lemma4496 - skolem:lemma4479 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 2) (2 8)) list:append (0 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2127 a r:Inference; +skolem:lemma2080 a r:Inference; r:gives { (0 2 2 8) :digitsToNumber 228 . }; @@ -56881,9 +51624,9 @@ skolem:lemma2127 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2128 a r:Inference; +skolem:lemma2081 a r:Inference; r:gives { (8 2 2 0) :digitsToNumber 8220 . }; @@ -56901,42 +51644,9 @@ skolem:lemma2128 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2129 a r:Inference; - r:gives { - 7992 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 2}] - [ a r:Fact; r:gives {(2 1) math:sum 3}] - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 3. - }}] - skolem:lemma4497 - skolem:lemma4498 - [ a r:Fact; r:gives {(2 7 9 9) list:reverse (9 9 7 2)}] - skolem:lemma4002 - skolem:lemma4003 - [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] - [ a r:Fact; r:gives {7173 math:notEqualTo 6174}] - skolem:lemma2037 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2799]; - 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_8"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2130 a r:Inference; +skolem:lemma2082 a r:Inference; r:gives { 2029 :numberToDigits (2 0 2 9). }; @@ -56955,32 +51665,9 @@ skolem:lemma2130 a r:Inference; 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:lemma4392. - -skolem:lemma2131 a r:Inference; - r:gives { - (2 0 2 9) :sort (0 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2 9) list:firstRest (2 (0 2 9))}] - skolem:lemma4499 - skolem:lemma4479 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 2) (2 9)) list:append (0 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 2 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_2"]; r:boundTo (0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2132 a r:Inference; +skolem:lemma2083 a r:Inference; r:gives { (0 2 2 9) :digitsToNumber 229 . }; @@ -56998,9 +51685,9 @@ skolem:lemma2132 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2133 a r:Inference; +skolem:lemma2084 a r:Inference; r:gives { (9 2 2 0) :digitsToNumber 9220 . }; @@ -57018,42 +51705,9 @@ skolem:lemma2133 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2134 a r:Inference; - r:gives { - 8991 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4500 - skolem:lemma4501 - [ a r:Fact; r:gives {(1 8 9 9) list:reverse (9 9 8 1)}] - skolem:lemma4400 - skolem:lemma4401 - [ a r:Fact; r:gives {(9981 1899) math:difference 8082}] - [ a r:Fact; r:gives {8082 math:notEqualTo 6174}] - skolem:lemma2087 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9981]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2135 a r:Inference; +skolem:lemma2085 a r:Inference; r:gives { 2030 :numberToDigits (2 0 3 0). }; @@ -57072,32 +51726,9 @@ skolem:lemma2135 a r:Inference; 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:lemma4392. - -skolem:lemma2136 a r:Inference; - r:gives { - (2 0 3 0) :sort (0 0 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 0) list:firstRest (2 (0 3 0))}] - skolem:lemma4502 - skolem:lemma4407 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 0) (2 3)) list:append (0 0 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (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 (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2137 a r:Inference; +skolem:lemma2086 a r:Inference; r:gives { 2031 :numberToDigits (2 0 3 1). }; @@ -57116,32 +51747,9 @@ skolem:lemma2137 a r:Inference; 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:lemma4392. - -skolem:lemma2138 a r:Inference; - r:gives { - (2 0 3 1) :sort (0 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 1) list:firstRest (2 (0 3 1))}] - skolem:lemma4503 - skolem:lemma4442 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 1) (2 3)) list:append (0 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2139 a r:Inference; +skolem:lemma2087 a r:Inference; r:gives { 2032 :numberToDigits (2 0 3 2). }; @@ -57160,32 +51768,9 @@ skolem:lemma2139 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2140 a r:Inference; - r:gives { - (2 0 3 2) :sort (0 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 2) list:firstRest (2 (0 3 2))}] - skolem:lemma4504 - skolem:lemma4479 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 2) (2 3)) list:append (0 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 3)]; - r:rule skolem:lemma4396. - -skolem:lemma2141 a r:Inference; +skolem:lemma2088 a r:Inference; r:gives { 2033 :numberToDigits (2 0 3 3). }; @@ -57204,32 +51789,9 @@ skolem:lemma2141 a r:Inference; 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:lemma4392. - -skolem:lemma2142 a r:Inference; - r:gives { - (2 0 3 3) :sort (0 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 3) list:firstRest (2 (0 3 3))}] - skolem:lemma4505 - skolem:lemma4506 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((0) (2 3 3)) list:append (0 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2143 a r:Inference; +skolem:lemma2089 a r:Inference; r:gives { (0 2 3 3) :digitsToNumber 233 . }; @@ -57247,9 +51809,9 @@ skolem:lemma2143 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2144 a r:Inference; +skolem:lemma2090 a r:Inference; r:gives { (3 3 2 0) :digitsToNumber 3320 . }; @@ -57267,9 +51829,9 @@ skolem:lemma2144 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2145 a r:Inference; +skolem:lemma2091 a r:Inference; r:gives { 2034 :numberToDigits (2 0 3 4). }; @@ -57288,32 +51850,9 @@ skolem:lemma2145 a r:Inference; 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:lemma4392. - -skolem:lemma2146 a r:Inference; - r:gives { - (2 0 3 4) :sort (0 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 4) list:firstRest (2 (0 3 4))}] - skolem:lemma4508 - skolem:lemma4506 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((0) (2 3 4)) list:append (0 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 (3 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 (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2147 a r:Inference; +skolem:lemma2092 a r:Inference; r:gives { (0 2 3 4) :digitsToNumber 234 . }; @@ -57331,9 +51870,9 @@ skolem:lemma2147 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2148 a r:Inference; +skolem:lemma2093 a r:Inference; r:gives { (4 3 2 0) :digitsToNumber 4320 . }; @@ -57351,9 +51890,9 @@ skolem:lemma2148 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2149 a r:Inference; +skolem:lemma2094 a r:Inference; r:gives { 2035 :numberToDigits (2 0 3 5). }; @@ -57372,32 +51911,9 @@ skolem:lemma2149 a r:Inference; 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:lemma4392. - -skolem:lemma2150 a r:Inference; - r:gives { - (2 0 3 5) :sort (0 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 5) list:firstRest (2 (0 3 5))}] - skolem:lemma4510 - skolem:lemma4506 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((0) (2 3 5)) list:append (0 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 (3 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 (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2151 a r:Inference; +skolem:lemma2095 a r:Inference; r:gives { (0 2 3 5) :digitsToNumber 235 . }; @@ -57415,9 +51931,9 @@ skolem:lemma2151 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2152 a r:Inference; +skolem:lemma2096 a r:Inference; r:gives { (5 3 2 0) :digitsToNumber 5320 . }; @@ -57435,9 +51951,9 @@ skolem:lemma2152 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2153 a r:Inference; +skolem:lemma2097 a r:Inference; r:gives { 2036 :numberToDigits (2 0 3 6). }; @@ -57456,32 +51972,9 @@ skolem:lemma2153 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2154 a r:Inference; - r:gives { - (2 0 3 6) :sort (0 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 6) list:firstRest (2 (0 3 6))}] - skolem:lemma4512 - skolem:lemma4506 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((0) (2 3 6)) list:append (0 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 (3 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 (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma2155 a r:Inference; +skolem:lemma2098 a r:Inference; r:gives { (0 2 3 6) :digitsToNumber 236 . }; @@ -57499,9 +51992,9 @@ skolem:lemma2155 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2156 a r:Inference; +skolem:lemma2099 a r:Inference; r:gives { (6 3 2 0) :digitsToNumber 6320 . }; @@ -57519,9 +52012,9 @@ skolem:lemma2156 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2157 a r:Inference; +skolem:lemma2100 a r:Inference; r:gives { 2037 :numberToDigits (2 0 3 7). }; @@ -57540,32 +52033,9 @@ skolem:lemma2157 a r:Inference; 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:lemma4392. - -skolem:lemma2158 a r:Inference; - r:gives { - (2 0 3 7) :sort (0 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 7) list:firstRest (2 (0 3 7))}] - skolem:lemma4514 - skolem:lemma4506 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((0) (2 3 7)) list:append (0 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 (3 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 (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2159 a r:Inference; +skolem:lemma2101 a r:Inference; r:gives { (0 2 3 7) :digitsToNumber 237 . }; @@ -57583,9 +52053,9 @@ skolem:lemma2159 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2160 a r:Inference; +skolem:lemma2102 a r:Inference; r:gives { (7 3 2 0) :digitsToNumber 7320 . }; @@ -57603,9 +52073,9 @@ skolem:lemma2160 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2161 a r:Inference; +skolem:lemma2103 a r:Inference; r:gives { 2038 :numberToDigits (2 0 3 8). }; @@ -57624,32 +52094,9 @@ skolem:lemma2161 a r:Inference; 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:lemma4392. - -skolem:lemma2162 a r:Inference; - r:gives { - (2 0 3 8) :sort (0 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 8) list:firstRest (2 (0 3 8))}] - skolem:lemma4516 - skolem:lemma4506 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((0) (2 3 8)) list:append (0 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 (3 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 (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2163 a r:Inference; +skolem:lemma2104 a r:Inference; r:gives { (0 2 3 8) :digitsToNumber 238 . }; @@ -57667,9 +52114,9 @@ skolem:lemma2163 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2164 a r:Inference; +skolem:lemma2105 a r:Inference; r:gives { (8 3 2 0) :digitsToNumber 8320 . }; @@ -57687,9 +52134,9 @@ skolem:lemma2164 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2165 a r:Inference; +skolem:lemma2106 a r:Inference; r:gives { 2039 :numberToDigits (2 0 3 9). }; @@ -57708,32 +52155,9 @@ skolem:lemma2165 a r:Inference; 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:lemma4392. - -skolem:lemma2166 a r:Inference; - r:gives { - (2 0 3 9) :sort (0 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3 9) list:firstRest (2 (0 3 9))}] - skolem:lemma4518 - skolem:lemma4506 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((0) (2 3 9)) list:append (0 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 3 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_2"]; r:boundTo (0 3 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 (3 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 (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2167 a r:Inference; +skolem:lemma2107 a r:Inference; r:gives { (0 2 3 9) :digitsToNumber 239 . }; @@ -57751,9 +52175,9 @@ skolem:lemma2167 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2168 a r:Inference; +skolem:lemma2108 a r:Inference; r:gives { (9 3 2 0) :digitsToNumber 9320 . }; @@ -57771,9 +52195,9 @@ skolem:lemma2168 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2169 a r:Inference; +skolem:lemma2109 a r:Inference; r:gives { 2040 :numberToDigits (2 0 4 0). }; @@ -57792,32 +52216,9 @@ skolem:lemma2169 a r:Inference; 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:lemma4392. - -skolem:lemma2170 a r:Inference; - r:gives { - (2 0 4 0) :sort (0 0 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 0) list:firstRest (2 (0 4 0))}] - skolem:lemma4520 - skolem:lemma4407 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 0) (2 4)) list:append (0 0 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2171 a r:Inference; +skolem:lemma2110 a r:Inference; r:gives { 2041 :numberToDigits (2 0 4 1). }; @@ -57836,32 +52237,9 @@ skolem:lemma2171 a r:Inference; 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:lemma4392. - -skolem:lemma2172 a r:Inference; - r:gives { - (2 0 4 1) :sort (0 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 1) list:firstRest (2 (0 4 1))}] - skolem:lemma4521 - skolem:lemma4442 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 1) (2 4)) list:append (0 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2173 a r:Inference; +skolem:lemma2111 a r:Inference; r:gives { 2042 :numberToDigits (2 0 4 2). }; @@ -57880,32 +52258,9 @@ skolem:lemma2173 a r:Inference; 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:lemma4392. - -skolem:lemma2174 a r:Inference; - r:gives { - (2 0 4 2) :sort (0 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 2) list:firstRest (2 (0 4 2))}] - skolem:lemma4522 - skolem:lemma4479 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 2) (2 4)) list:append (0 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2175 a r:Inference; +skolem:lemma2112 a r:Inference; r:gives { 2043 :numberToDigits (2 0 4 3). }; @@ -57924,32 +52279,9 @@ skolem:lemma2175 a r:Inference; 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:lemma4392. - -skolem:lemma2176 a r:Inference; - r:gives { - (2 0 4 3) :sort (0 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 3) list:firstRest (2 (0 4 3))}] - skolem:lemma4523 - skolem:lemma4506 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((0) (2 3 4)) list:append (0 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 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 (4 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2177 a r:Inference; +skolem:lemma2113 a r:Inference; r:gives { 2044 :numberToDigits (2 0 4 4). }; @@ -57968,32 +52300,9 @@ skolem:lemma2177 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2178 a r:Inference; - r:gives { - (2 0 4 4) :sort (0 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 4) list:firstRest (2 (0 4 4))}] - skolem:lemma4525 - skolem:lemma4506 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((0) (2 4 4)) list:append (0 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 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 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma2179 a r:Inference; +skolem:lemma2114 a r:Inference; r:gives { (0 2 4 4) :digitsToNumber 244 . }; @@ -58011,9 +52320,9 @@ skolem:lemma2179 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2180 a r:Inference; +skolem:lemma2115 a r:Inference; r:gives { (4 4 2 0) :digitsToNumber 4420 . }; @@ -58031,9 +52340,9 @@ skolem:lemma2180 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2181 a r:Inference; +skolem:lemma2116 a r:Inference; r:gives { 2045 :numberToDigits (2 0 4 5). }; @@ -58052,32 +52361,9 @@ skolem:lemma2181 a r:Inference; 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:lemma4392. - -skolem:lemma2182 a r:Inference; - r:gives { - (2 0 4 5) :sort (0 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 5) list:firstRest (2 (0 4 5))}] - skolem:lemma4527 - skolem:lemma4506 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((0) (2 4 5)) list:append (0 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 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 (4 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 (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2183 a r:Inference; +skolem:lemma2117 a r:Inference; r:gives { (0 2 4 5) :digitsToNumber 245 . }; @@ -58095,9 +52381,9 @@ skolem:lemma2183 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2184 a r:Inference; +skolem:lemma2118 a r:Inference; r:gives { (5 4 2 0) :digitsToNumber 5420 . }; @@ -58115,9 +52401,70 @@ skolem:lemma2184 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2185 a r:Inference; +skolem:lemma2119 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:lemma3438. + +skolem:lemma2120 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:lemma3439. + +skolem:lemma2121 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:lemma3439. + +skolem:lemma2122 a r:Inference; r:gives { 2047 :numberToDigits (2 0 4 7). }; @@ -58136,32 +52483,9 @@ skolem:lemma2185 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2186 a r:Inference; - r:gives { - (2 0 4 7) :sort (0 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 7) list:firstRest (2 (0 4 7))}] - skolem:lemma4529 - skolem:lemma4506 - skolem:lemma4530 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((0) (2 4 7)) list:append (0 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 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 (4 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 (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2187 a r:Inference; +skolem:lemma2123 a r:Inference; r:gives { (0 2 4 7) :digitsToNumber 247 . }; @@ -58179,9 +52503,9 @@ skolem:lemma2187 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2188 a r:Inference; +skolem:lemma2124 a r:Inference; r:gives { (7 4 2 0) :digitsToNumber 7420 . }; @@ -58199,9 +52523,9 @@ skolem:lemma2188 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2189 a r:Inference; +skolem:lemma2125 a r:Inference; r:gives { 2048 :numberToDigits (2 0 4 8). }; @@ -58220,32 +52544,9 @@ skolem:lemma2189 a r:Inference; 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:lemma4392. - -skolem:lemma2190 a r:Inference; - r:gives { - (2 0 4 8) :sort (0 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 8) list:firstRest (2 (0 4 8))}] - skolem:lemma4531 - skolem:lemma4506 - skolem:lemma4532 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((0) (2 4 8)) list:append (0 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 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 (4 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 (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2191 a r:Inference; +skolem:lemma2126 a r:Inference; r:gives { (0 2 4 8) :digitsToNumber 248 . }; @@ -58263,9 +52564,9 @@ skolem:lemma2191 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2192 a r:Inference; +skolem:lemma2127 a r:Inference; r:gives { (8 4 2 0) :digitsToNumber 8420 . }; @@ -58283,9 +52584,9 @@ skolem:lemma2192 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2193 a r:Inference; +skolem:lemma2128 a r:Inference; r:gives { 2049 :numberToDigits (2 0 4 9). }; @@ -58304,32 +52605,9 @@ skolem:lemma2193 a r:Inference; 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:lemma4392. - -skolem:lemma2194 a r:Inference; - r:gives { - (2 0 4 9) :sort (0 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4 9) list:firstRest (2 (0 4 9))}] - skolem:lemma4533 - skolem:lemma4506 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((0) (2 4 9)) list:append (0 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 4 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_2"]; r:boundTo (0 4 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 (4 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 (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2195 a r:Inference; +skolem:lemma2129 a r:Inference; r:gives { (0 2 4 9) :digitsToNumber 249 . }; @@ -58347,9 +52625,9 @@ skolem:lemma2195 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2196 a r:Inference; +skolem:lemma2130 a r:Inference; r:gives { (9 4 2 0) :digitsToNumber 9420 . }; @@ -58367,9 +52645,9 @@ skolem:lemma2196 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2197 a r:Inference; +skolem:lemma2131 a r:Inference; r:gives { 2050 :numberToDigits (2 0 5 0). }; @@ -58388,32 +52666,9 @@ skolem:lemma2197 a r:Inference; 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:lemma4392. - -skolem:lemma2198 a r:Inference; - r:gives { - (2 0 5 0) :sort (0 0 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 0) list:firstRest (2 (0 5 0))}] - skolem:lemma4535 - skolem:lemma4407 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 0) (2 5)) list:append (0 0 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2199 a r:Inference; +skolem:lemma2132 a r:Inference; r:gives { 2051 :numberToDigits (2 0 5 1). }; @@ -58432,32 +52687,9 @@ skolem:lemma2199 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2200 a r:Inference; - r:gives { - (2 0 5 1) :sort (0 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 1) list:firstRest (2 (0 5 1))}] - skolem:lemma4536 - skolem:lemma4442 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 1) (2 5)) list:append (0 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 5)]; - r:rule skolem:lemma4396. - -skolem:lemma2201 a r:Inference; +skolem:lemma2133 a r:Inference; r:gives { 2052 :numberToDigits (2 0 5 2). }; @@ -58476,32 +52708,9 @@ skolem:lemma2201 a r:Inference; 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:lemma4392. - -skolem:lemma2202 a r:Inference; - r:gives { - (2 0 5 2) :sort (0 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 2) list:firstRest (2 (0 5 2))}] - skolem:lemma4537 - skolem:lemma4479 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 2) (2 5)) list:append (0 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2203 a r:Inference; +skolem:lemma2134 a r:Inference; r:gives { 2053 :numberToDigits (2 0 5 3). }; @@ -58520,32 +52729,9 @@ skolem:lemma2203 a r:Inference; 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:lemma4392. - -skolem:lemma2204 a r:Inference; - r:gives { - (2 0 5 3) :sort (0 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 3) list:firstRest (2 (0 5 3))}] - skolem:lemma4538 - skolem:lemma4506 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((0) (2 3 5)) list:append (0 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2205 a r:Inference; +skolem:lemma2135 a r:Inference; r:gives { 2054 :numberToDigits (2 0 5 4). }; @@ -58564,32 +52750,9 @@ skolem:lemma2205 a r:Inference; 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:lemma4392. - -skolem:lemma2206 a r:Inference; - r:gives { - (2 0 5 4) :sort (0 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 4) list:firstRest (2 (0 5 4))}] - skolem:lemma4540 - skolem:lemma4506 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((0) (2 4 5)) list:append (0 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2207 a r:Inference; +skolem:lemma2136 a r:Inference; r:gives { 2055 :numberToDigits (2 0 5 5). }; @@ -58608,32 +52771,9 @@ skolem:lemma2207 a r:Inference; 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:lemma4392. - -skolem:lemma2208 a r:Inference; - r:gives { - (2 0 5 5) :sort (0 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 5) list:firstRest (2 (0 5 5))}] - skolem:lemma4542 - skolem:lemma4506 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((0) (2 5 5)) list:append (0 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2209 a r:Inference; +skolem:lemma2137 a r:Inference; r:gives { (0 2 5 5) :digitsToNumber 255 . }; @@ -58651,9 +52791,9 @@ skolem:lemma2209 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2210 a r:Inference; +skolem:lemma2138 a r:Inference; r:gives { (5 5 2 0) :digitsToNumber 5520 . }; @@ -58671,42 +52811,9 @@ skolem:lemma2210 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2211 a r:Inference; - r:gives { - 5265 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4544 - skolem:lemma4545 - [ a r:Fact; r:gives {(2 5 5 6) list:reverse (6 5 5 2)}] - skolem:lemma3488 - skolem:lemma3489 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2556]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2212 a r:Inference; +skolem:lemma2139 a r:Inference; r:gives { 2056 :numberToDigits (2 0 5 6). }; @@ -58725,34 +52832,11 @@ skolem:lemma2212 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2213 a r:Inference; +skolem:lemma2140 a r:Inference; r:gives { - (2 0 5 6) :sort (0 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 6) list:firstRest (2 (0 5 6))}] - skolem:lemma4546 - skolem:lemma4506 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((0) (2 5 6)) list:append (0 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 (5 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 (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma2214 a r:Inference; - r:gives { - (0 2 5 6) :digitsToNumber 256 . + (0 2 5 6) :digitsToNumber 256 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] @@ -58768,9 +52852,9 @@ skolem:lemma2214 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2215 a r:Inference; +skolem:lemma2141 a r:Inference; r:gives { (6 5 2 0) :digitsToNumber 6520 . }; @@ -58788,42 +52872,9 @@ skolem:lemma2215 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2216 a r:Inference; - r:gives { - 6264 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 4}] - [ a r:Fact; r:gives {(4 1) math:sum 5}] - [ a r:Fact; r:gives {{ - :recursion :count 4. - } log:becomes { - :recursion :count 5. - }}] - skolem:lemma4548 - skolem:lemma4549 - [ a r:Fact; r:gives {(2 4 6 6) list:reverse (6 6 4 2)}] - skolem:lemma3298 - skolem:lemma3299 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2466]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2217 a r:Inference; +skolem:lemma2142 a r:Inference; r:gives { 2057 :numberToDigits (2 0 5 7). }; @@ -58842,32 +52893,9 @@ skolem:lemma2217 a r:Inference; 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:lemma4392. - -skolem:lemma2218 a r:Inference; - r:gives { - (2 0 5 7) :sort (0 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 7) list:firstRest (2 (0 5 7))}] - skolem:lemma4550 - skolem:lemma4506 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((0) (2 5 7)) list:append (0 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 (5 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 (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2219 a r:Inference; +skolem:lemma2143 a r:Inference; r:gives { (0 2 5 7) :digitsToNumber 257 . }; @@ -58885,9 +52913,9 @@ skolem:lemma2219 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2220 a r:Inference; +skolem:lemma2144 a r:Inference; r:gives { (7 5 2 0) :digitsToNumber 7520 . }; @@ -58905,42 +52933,9 @@ skolem:lemma2220 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2221 a r:Inference; - r:gives { - 7263 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4552 - skolem:lemma4553 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2222 a r:Inference; +skolem:lemma2145 a r:Inference; r:gives { 2058 :numberToDigits (2 0 5 8). }; @@ -58959,32 +52954,9 @@ skolem:lemma2222 a r:Inference; 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:lemma4392. - -skolem:lemma2223 a r:Inference; - r:gives { - (2 0 5 8) :sort (0 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 8) list:firstRest (2 (0 5 8))}] - skolem:lemma4554 - skolem:lemma4506 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((0) (2 5 8)) list:append (0 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 (5 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 (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2224 a r:Inference; +skolem:lemma2146 a r:Inference; r:gives { (0 2 5 8) :digitsToNumber 258 . }; @@ -59002,9 +52974,9 @@ skolem:lemma2224 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2225 a r:Inference; +skolem:lemma2147 a r:Inference; r:gives { (8 5 2 0) :digitsToNumber 8520 . }; @@ -59022,42 +52994,9 @@ skolem:lemma2225 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2226 a r:Inference; - r:gives { - 8262 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4556 - skolem:lemma4557 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2227 a r:Inference; +skolem:lemma2148 a r:Inference; r:gives { 2059 :numberToDigits (2 0 5 9). }; @@ -59076,32 +53015,9 @@ skolem:lemma2227 a r:Inference; 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:lemma4392. - -skolem:lemma2228 a r:Inference; - r:gives { - (2 0 5 9) :sort (0 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5 9) list:firstRest (2 (0 5 9))}] - skolem:lemma4558 - skolem:lemma4506 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((0) (2 5 9)) list:append (0 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 5 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_2"]; r:boundTo (0 5 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 (5 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 (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2229 a r:Inference; +skolem:lemma2149 a r:Inference; r:gives { (0 2 5 9) :digitsToNumber 259 . }; @@ -59119,9 +53035,9 @@ skolem:lemma2229 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2230 a r:Inference; +skolem:lemma2150 a r:Inference; r:gives { (9 5 2 0) :digitsToNumber 9520 . }; @@ -59139,42 +53055,30 @@ skolem:lemma2230 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2231 a r:Inference; +skolem:lemma2151 a r:Inference; r:gives { - 9261 :kaprekar 6174 . + 2060 :numberToDigits (2 0 6 0). }; r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4560 - skolem:lemma4561 - [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 + [ 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_0"]; r:boundTo 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_2"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + 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:lemma3438. -skolem:lemma2232 a r:Inference; +skolem:lemma2152 a r:Inference; r:gives { 2061 :numberToDigits (2 0 6 1). }; @@ -59193,32 +53097,9 @@ skolem:lemma2232 a r:Inference; 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:lemma4392. - -skolem:lemma2233 a r:Inference; - r:gives { - (2 0 6 1) :sort (0 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 1) list:firstRest (2 (0 6 1))}] - skolem:lemma4562 - skolem:lemma4442 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 1) (2 6)) list:append (0 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2234 a r:Inference; +skolem:lemma2153 a r:Inference; r:gives { 2062 :numberToDigits (2 0 6 2). }; @@ -59237,32 +53118,9 @@ skolem:lemma2234 a r:Inference; 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:lemma4392. - -skolem:lemma2235 a r:Inference; - r:gives { - (2 0 6 2) :sort (0 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 2) list:firstRest (2 (0 6 2))}] - skolem:lemma4563 - skolem:lemma4479 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 2) (2 6)) list:append (0 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2236 a r:Inference; +skolem:lemma2154 a r:Inference; r:gives { 2063 :numberToDigits (2 0 6 3). }; @@ -59281,32 +53139,30 @@ skolem:lemma2236 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2237 a r:Inference; +skolem:lemma2155 a r:Inference; r:gives { - (2 0 6 3) :sort (0 2 3 6). + 2064 :numberToDigits (2 0 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 0 6 3) list:firstRest (2 (0 6 3))}] - skolem:lemma4564 - skolem:lemma4506 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((0) (2 3 6)) list:append (0 2 3 6)}] + [ 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_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 6)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma2238 a r:Inference; +skolem:lemma2156 a r:Inference; r:gives { 2065 :numberToDigits (2 0 6 5). }; @@ -59325,32 +53181,9 @@ skolem:lemma2238 a r:Inference; 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:lemma4392. - -skolem:lemma2239 a r:Inference; - r:gives { - (2 0 6 5) :sort (0 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 5) list:firstRest (2 (0 6 5))}] - skolem:lemma4566 - skolem:lemma4506 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((0) (2 5 6)) list:append (0 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2240 a r:Inference; +skolem:lemma2157 a r:Inference; r:gives { 2066 :numberToDigits (2 0 6 6). }; @@ -59369,32 +53202,9 @@ skolem:lemma2240 a r:Inference; 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:lemma4392. - -skolem:lemma2241 a r:Inference; - r:gives { - (2 0 6 6) :sort (0 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 6) list:firstRest (2 (0 6 6))}] - skolem:lemma4568 - skolem:lemma4506 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((0) (2 6 6)) list:append (0 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 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 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2242 a r:Inference; +skolem:lemma2158 a r:Inference; r:gives { (0 2 6 6) :digitsToNumber 266 . }; @@ -59412,9 +53222,9 @@ skolem:lemma2242 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2243 a r:Inference; +skolem:lemma2159 a r:Inference; r:gives { (6 6 2 0) :digitsToNumber 6620 . }; @@ -59432,42 +53242,9 @@ skolem:lemma2243 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2244 a r:Inference; - r:gives { - 6354 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 2}] - [ a r:Fact; r:gives {(2 1) math:sum 3}] - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 3. - }}] - skolem:lemma4570 - skolem:lemma4571 - [ a r:Fact; r:gives {(3 4 5 6) list:reverse (6 5 4 3)}] - skolem:lemma4572 - skolem:lemma4573 - [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3456]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2245 a r:Inference; +skolem:lemma2160 a r:Inference; r:gives { 2067 :numberToDigits (2 0 6 7). }; @@ -59486,32 +53263,9 @@ skolem:lemma2245 a r:Inference; 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:lemma4392. - -skolem:lemma2246 a r:Inference; - r:gives { - (2 0 6 7) :sort (0 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 7) list:firstRest (2 (0 6 7))}] - skolem:lemma4574 - skolem:lemma4506 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((0) (2 6 7)) list:append (0 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 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 (6 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 (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2247 a r:Inference; +skolem:lemma2161 a r:Inference; r:gives { (0 2 6 7) :digitsToNumber 267 . }; @@ -59529,9 +53283,9 @@ skolem:lemma2247 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2248 a r:Inference; +skolem:lemma2162 a r:Inference; r:gives { (7 6 2 0) :digitsToNumber 7620 . }; @@ -59549,42 +53303,9 @@ skolem:lemma2248 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2249 a r:Inference; - r:gives { - 7353 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4576 - skolem:lemma4577 - [ a r:Fact; r:gives {(3 3 5 7) list:reverse (7 5 3 3)}] - skolem:lemma4578 - skolem:lemma4579 - [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3357]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma2250 a r:Inference; +skolem:lemma2163 a r:Inference; r:gives { 2068 :numberToDigits (2 0 6 8). }; @@ -59603,32 +53324,9 @@ skolem:lemma2250 a r:Inference; 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:lemma4392. - -skolem:lemma2251 a r:Inference; - r:gives { - (2 0 6 8) :sort (0 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 8) list:firstRest (2 (0 6 8))}] - skolem:lemma4580 - skolem:lemma4506 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((0) (2 6 8)) list:append (0 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 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 (6 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 (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2252 a r:Inference; +skolem:lemma2164 a r:Inference; r:gives { (0 2 6 8) :digitsToNumber 268 . }; @@ -59646,9 +53344,9 @@ skolem:lemma2252 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2253 a r:Inference; +skolem:lemma2165 a r:Inference; r:gives { (8 6 2 0) :digitsToNumber 8620 . }; @@ -59666,19 +53364,9 @@ skolem:lemma2253 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2254 a r:Inference; - r:gives { - 8352 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8352]; - r:rule skolem:lemma2032. + r:rule skolem:lemma3439. -skolem:lemma2255 a r:Inference; +skolem:lemma2166 a r:Inference; r:gives { 2069 :numberToDigits (2 0 6 9). }; @@ -59697,32 +53385,9 @@ skolem:lemma2255 a r:Inference; 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:lemma4392. - -skolem:lemma2256 a r:Inference; - r:gives { - (2 0 6 9) :sort (0 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6 9) list:firstRest (2 (0 6 9))}] - skolem:lemma4582 - skolem:lemma4506 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((0) (2 6 9)) list:append (0 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 6 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_2"]; r:boundTo (0 6 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 (6 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 (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2257 a r:Inference; +skolem:lemma2167 a r:Inference; r:gives { (0 2 6 9) :digitsToNumber 269 . }; @@ -59740,9 +53405,9 @@ skolem:lemma2257 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2258 a r:Inference; +skolem:lemma2168 a r:Inference; r:gives { (9 6 2 0) :digitsToNumber 9620 . }; @@ -59760,42 +53425,9 @@ skolem:lemma2258 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2259 a r:Inference; - r:gives { - 9351 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4584 - skolem:lemma4585 - [ a r:Fact; r:gives {(1 3 5 9) list:reverse (9 5 3 1)}] - skolem:lemma4586 - skolem:lemma4587 - [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1359]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2260 a r:Inference; +skolem:lemma2169 a r:Inference; r:gives { 2070 :numberToDigits (2 0 7 0). }; @@ -59814,32 +53446,9 @@ skolem:lemma2260 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2261 a r:Inference; - r:gives { - (2 0 7 0) :sort (0 0 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 0) list:firstRest (2 (0 7 0))}] - skolem:lemma4588 - skolem:lemma4407 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 0) (2 7)) list:append (0 0 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2262 a r:Inference; +skolem:lemma2170 a r:Inference; r:gives { 2071 :numberToDigits (2 0 7 1). }; @@ -59858,32 +53467,9 @@ skolem:lemma2262 a r:Inference; 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:lemma4392. - -skolem:lemma2263 a r:Inference; - r:gives { - (2 0 7 1) :sort (0 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 1) list:firstRest (2 (0 7 1))}] - skolem:lemma4589 - skolem:lemma4442 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 1) (2 7)) list:append (0 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2264 a r:Inference; +skolem:lemma2171 a r:Inference; r:gives { 2072 :numberToDigits (2 0 7 2). }; @@ -59902,32 +53488,9 @@ skolem:lemma2264 a r:Inference; 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:lemma4392. - -skolem:lemma2265 a r:Inference; - r:gives { - (2 0 7 2) :sort (0 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 2) list:firstRest (2 (0 7 2))}] - skolem:lemma4590 - skolem:lemma4479 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 2) (2 7)) list:append (0 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2266 a r:Inference; +skolem:lemma2172 a r:Inference; r:gives { 2073 :numberToDigits (2 0 7 3). }; @@ -59946,32 +53509,9 @@ skolem:lemma2266 a r:Inference; 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:lemma4392. - -skolem:lemma2267 a r:Inference; - r:gives { - (2 0 7 3) :sort (0 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 3) list:firstRest (2 (0 7 3))}] - skolem:lemma4591 - skolem:lemma4506 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((0) (2 3 7)) list:append (0 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2268 a r:Inference; +skolem:lemma2173 a r:Inference; r:gives { 2074 :numberToDigits (2 0 7 4). }; @@ -59990,32 +53530,9 @@ skolem:lemma2268 a r:Inference; 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:lemma4392. - -skolem:lemma2269 a r:Inference; - r:gives { - (2 0 7 4) :sort (0 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 4) list:firstRest (2 (0 7 4))}] - skolem:lemma4593 - skolem:lemma4506 - skolem:lemma4594 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((0) (2 4 7)) list:append (0 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2270 a r:Inference; +skolem:lemma2174 a r:Inference; r:gives { 2075 :numberToDigits (2 0 7 5). }; @@ -60034,32 +53551,9 @@ skolem:lemma2270 a r:Inference; 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:lemma4392. - -skolem:lemma2271 a r:Inference; - r:gives { - (2 0 7 5) :sort (0 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 5) list:firstRest (2 (0 7 5))}] - skolem:lemma4595 - skolem:lemma4506 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((0) (2 5 7)) list:append (0 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2272 a r:Inference; +skolem:lemma2175 a r:Inference; r:gives { 2076 :numberToDigits (2 0 7 6). }; @@ -60078,32 +53572,9 @@ skolem:lemma2272 a r:Inference; 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:lemma4392. - -skolem:lemma2273 a r:Inference; - r:gives { - (2 0 7 6) :sort (0 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 6) list:firstRest (2 (0 7 6))}] - skolem:lemma4597 - skolem:lemma4506 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((0) (2 6 7)) list:append (0 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2274 a r:Inference; +skolem:lemma2176 a r:Inference; r:gives { 2077 :numberToDigits (2 0 7 7). }; @@ -60122,32 +53593,9 @@ skolem:lemma2274 a r:Inference; 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:lemma4392. - -skolem:lemma2275 a r:Inference; - r:gives { - (2 0 7 7) :sort (0 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 7) list:firstRest (2 (0 7 7))}] - skolem:lemma4599 - skolem:lemma4506 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((0) (2 7 7)) list:append (0 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2276 a r:Inference; +skolem:lemma2177 a r:Inference; r:gives { (0 2 7 7) :digitsToNumber 277 . }; @@ -60165,9 +53613,9 @@ skolem:lemma2276 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2277 a r:Inference; +skolem:lemma2178 a r:Inference; r:gives { (7 7 2 0) :digitsToNumber 7720 . }; @@ -60185,42 +53633,9 @@ skolem:lemma2277 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2278 a r:Inference; - r:gives { - 7443 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 2}] - [ a r:Fact; r:gives {(2 1) math:sum 3}] - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 3. - }}] - skolem:lemma4601 - skolem:lemma4602 - [ a r:Fact; r:gives {(3 4 4 7) list:reverse (7 4 4 3)}] - skolem:lemma4603 - skolem:lemma4604 - [ a r:Fact; r:gives {(7443 3447) math:difference 3996}] - [ a r:Fact; r:gives {3996 math:notEqualTo 6174}] - skolem:lemma2109 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7443]; - 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 (3 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3447]; - 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_8"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2279 a r:Inference; +skolem:lemma2179 a r:Inference; r:gives { 2078 :numberToDigits (2 0 7 8). }; @@ -60239,32 +53654,9 @@ skolem:lemma2279 a r:Inference; 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:lemma4392. - -skolem:lemma2280 a r:Inference; - r:gives { - (2 0 7 8) :sort (0 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 8) list:firstRest (2 (0 7 8))}] - skolem:lemma4605 - skolem:lemma4506 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((0) (2 7 8)) list:append (0 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 (7 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 (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2281 a r:Inference; +skolem:lemma2180 a r:Inference; r:gives { (0 2 7 8) :digitsToNumber 278 . }; @@ -60282,9 +53674,9 @@ skolem:lemma2281 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2282 a r:Inference; +skolem:lemma2181 a r:Inference; r:gives { (8 7 2 0) :digitsToNumber 8720 . }; @@ -60302,42 +53694,9 @@ skolem:lemma2282 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2283 a r:Inference; - r:gives { - 8442 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4607 - skolem:lemma4608 - [ a r:Fact; r:gives {(2 4 4 8) list:reverse (8 4 4 2)}] - skolem:lemma3250 - skolem:lemma3251 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {5994 math:notEqualTo 6174}] - skolem:lemma2119 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8442]; - 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 (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2448]; - 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_8"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2284 a r:Inference; +skolem:lemma2182 a r:Inference; r:gives { 2079 :numberToDigits (2 0 7 9). }; @@ -60356,32 +53715,9 @@ skolem:lemma2284 a r:Inference; 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:lemma4392. - -skolem:lemma2285 a r:Inference; - r:gives { - (2 0 7 9) :sort (0 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7 9) list:firstRest (2 (0 7 9))}] - skolem:lemma4609 - skolem:lemma4506 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((0) (2 7 9)) list:append (0 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 7 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_2"]; r:boundTo (0 7 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 (7 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 (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2286 a r:Inference; +skolem:lemma2183 a r:Inference; r:gives { (0 2 7 9) :digitsToNumber 279 . }; @@ -60399,9 +53735,9 @@ skolem:lemma2286 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2287 a r:Inference; +skolem:lemma2184 a r:Inference; r:gives { (9 7 2 0) :digitsToNumber 9720 . }; @@ -60419,42 +53755,9 @@ skolem:lemma2287 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2288 a r:Inference; - r:gives { - 9441 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4611 - skolem:lemma4612 - [ a r:Fact; r:gives {(1 4 4 9) list:reverse (9 4 4 1)}] - skolem:lemma4613 - skolem:lemma4614 - [ a r:Fact; r:gives {(9441 1449) math:difference 7992}] - [ a r:Fact; r:gives {7992 math:notEqualTo 6174}] - skolem:lemma2129 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2289 a r:Inference; +skolem:lemma2185 a r:Inference; r:gives { 2080 :numberToDigits (2 0 8 0). }; @@ -60473,32 +53776,9 @@ skolem:lemma2289 a r:Inference; 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:lemma4392. - -skolem:lemma2290 a r:Inference; - r:gives { - (2 0 8 0) :sort (0 0 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 0) list:firstRest (2 (0 8 0))}] - skolem:lemma4615 - skolem:lemma4407 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 0) (2 8)) list:append (0 0 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2291 a r:Inference; +skolem:lemma2186 a r:Inference; r:gives { 2081 :numberToDigits (2 0 8 1). }; @@ -60517,32 +53797,9 @@ skolem:lemma2291 a r:Inference; 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:lemma4392. - -skolem:lemma2292 a r:Inference; - r:gives { - (2 0 8 1) :sort (0 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 1) list:firstRest (2 (0 8 1))}] - skolem:lemma4616 - skolem:lemma4442 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 1) (2 8)) list:append (0 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2293 a r:Inference; +skolem:lemma2187 a r:Inference; r:gives { 2082 :numberToDigits (2 0 8 2). }; @@ -60561,32 +53818,9 @@ skolem:lemma2293 a r:Inference; 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:lemma4392. - -skolem:lemma2294 a r:Inference; - r:gives { - (2 0 8 2) :sort (0 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 2) list:firstRest (2 (0 8 2))}] - skolem:lemma4617 - skolem:lemma4479 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 2) (2 8)) list:append (0 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2295 a r:Inference; +skolem:lemma2188 a r:Inference; r:gives { 2083 :numberToDigits (2 0 8 3). }; @@ -60605,32 +53839,9 @@ skolem:lemma2295 a r:Inference; 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:lemma4392. - -skolem:lemma2296 a r:Inference; - r:gives { - (2 0 8 3) :sort (0 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 3) list:firstRest (2 (0 8 3))}] - skolem:lemma4618 - skolem:lemma4506 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((0) (2 3 8)) list:append (0 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2297 a r:Inference; +skolem:lemma2189 a r:Inference; r:gives { 2084 :numberToDigits (2 0 8 4). }; @@ -60649,32 +53860,9 @@ skolem:lemma2297 a r:Inference; 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:lemma4392. - -skolem:lemma2298 a r:Inference; - r:gives { - (2 0 8 4) :sort (0 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 4) list:firstRest (2 (0 8 4))}] - skolem:lemma4620 - skolem:lemma4506 - skolem:lemma4621 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((0) (2 4 8)) list:append (0 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2299 a r:Inference; +skolem:lemma2190 a r:Inference; r:gives { 2085 :numberToDigits (2 0 8 5). }; @@ -60693,32 +53881,9 @@ skolem:lemma2299 a r:Inference; 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:lemma4392. - -skolem:lemma2300 a r:Inference; - r:gives { - (2 0 8 5) :sort (0 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 5) list:firstRest (2 (0 8 5))}] - skolem:lemma4622 - skolem:lemma4506 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((0) (2 5 8)) list:append (0 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2301 a r:Inference; +skolem:lemma2191 a r:Inference; r:gives { 2086 :numberToDigits (2 0 8 6). }; @@ -60737,32 +53902,9 @@ skolem:lemma2301 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2302 a r:Inference; - r:gives { - (2 0 8 6) :sort (0 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 6) list:firstRest (2 (0 8 6))}] - skolem:lemma4624 - skolem:lemma4506 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((0) (2 6 8)) list:append (0 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2303 a r:Inference; +skolem:lemma2192 a r:Inference; r:gives { 2087 :numberToDigits (2 0 8 7). }; @@ -60781,32 +53923,9 @@ skolem:lemma2303 a r:Inference; 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:lemma4392. - -skolem:lemma2304 a r:Inference; - r:gives { - (2 0 8 7) :sort (0 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 7) list:firstRest (2 (0 8 7))}] - skolem:lemma4626 - skolem:lemma4506 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((0) (2 7 8)) list:append (0 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2305 a r:Inference; +skolem:lemma2193 a r:Inference; r:gives { 2088 :numberToDigits (2 0 8 8). }; @@ -60825,32 +53944,9 @@ skolem:lemma2305 a r:Inference; 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:lemma4392. - -skolem:lemma2306 a r:Inference; - r:gives { - (2 0 8 8) :sort (0 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 8) list:firstRest (2 (0 8 8))}] - skolem:lemma4628 - skolem:lemma4506 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((0) (2 8 8)) list:append (0 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2307 a r:Inference; +skolem:lemma2194 a r:Inference; r:gives { (0 2 8 8) :digitsToNumber 288 . }; @@ -60868,9 +53964,9 @@ skolem:lemma2307 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2308 a r:Inference; +skolem:lemma2195 a r:Inference; r:gives { (8 8 2 0) :digitsToNumber 8820 . }; @@ -60888,19 +53984,9 @@ skolem:lemma2308 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2309 a r:Inference; - r:gives { - 8532 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8532]; - r:rule skolem:lemma2032. + r:rule skolem:lemma3439. -skolem:lemma2310 a r:Inference; +skolem:lemma2196 a r:Inference; r:gives { 2089 :numberToDigits (2 0 8 9). }; @@ -60919,32 +54005,9 @@ skolem:lemma2310 a r:Inference; 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:lemma4392. - -skolem:lemma2311 a r:Inference; - r:gives { - (2 0 8 9) :sort (0 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8 9) list:firstRest (2 (0 8 9))}] - skolem:lemma4630 - skolem:lemma4506 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((0) (2 8 9)) list:append (0 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 8 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_2"]; r:boundTo (0 8 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 (8 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 (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2312 a r:Inference; +skolem:lemma2197 a r:Inference; r:gives { (0 2 8 9) :digitsToNumber 289 . }; @@ -60962,9 +54025,9 @@ skolem:lemma2312 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2313 a r:Inference; +skolem:lemma2198 a r:Inference; r:gives { (9 8 2 0) :digitsToNumber 9820 . }; @@ -60982,42 +54045,9 @@ skolem:lemma2313 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2314 a r:Inference; - r:gives { - 9531 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4632 - skolem:lemma4633 - [ a r:Fact; r:gives {(1 3 5 9) list:reverse (9 5 3 1)}] - skolem:lemma4586 - skolem:lemma4587 - [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] - [ a r:Fact; r:gives {8172 math:notEqualTo 6174}] - skolem:lemma2042 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9531]; - 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 (1 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1359]; - 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_8"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. - -skolem:lemma2315 a r:Inference; +skolem:lemma2199 a r:Inference; r:gives { 2090 :numberToDigits (2 0 9 0). }; @@ -61036,32 +54066,9 @@ skolem:lemma2315 a r:Inference; 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:lemma4392. - -skolem:lemma2316 a r:Inference; - r:gives { - (2 0 9 0) :sort (0 0 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 0) list:firstRest (2 (0 9 0))}] - skolem:lemma4634 - skolem:lemma4407 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 0) (2 9)) list:append (0 0 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2317 a r:Inference; +skolem:lemma2200 a r:Inference; r:gives { 2091 :numberToDigits (2 0 9 1). }; @@ -61080,32 +54087,9 @@ skolem:lemma2317 a r:Inference; 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:lemma4392. - -skolem:lemma2318 a r:Inference; - r:gives { - (2 0 9 1) :sort (0 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 1) list:firstRest (2 (0 9 1))}] - skolem:lemma4635 - skolem:lemma4442 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 1) (2 9)) list:append (0 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2319 a r:Inference; +skolem:lemma2201 a r:Inference; r:gives { 2092 :numberToDigits (2 0 9 2). }; @@ -61124,32 +54108,9 @@ skolem:lemma2319 a r:Inference; 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:lemma4392. - -skolem:lemma2320 a r:Inference; - r:gives { - (2 0 9 2) :sort (0 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 2) list:firstRest (2 (0 9 2))}] - skolem:lemma4636 - skolem:lemma4479 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 2) (2 9)) list:append (0 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2321 a r:Inference; +skolem:lemma2202 a r:Inference; r:gives { 2093 :numberToDigits (2 0 9 3). }; @@ -61168,32 +54129,9 @@ skolem:lemma2321 a r:Inference; 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:lemma4392. - -skolem:lemma2322 a r:Inference; - r:gives { - (2 0 9 3) :sort (0 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 3) list:firstRest (2 (0 9 3))}] - skolem:lemma4637 - skolem:lemma4506 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((0) (2 3 9)) list:append (0 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2323 a r:Inference; +skolem:lemma2203 a r:Inference; r:gives { 2094 :numberToDigits (2 0 9 4). }; @@ -61212,32 +54150,9 @@ skolem:lemma2323 a r:Inference; 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:lemma4392. - -skolem:lemma2324 a r:Inference; - r:gives { - (2 0 9 4) :sort (0 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 4) list:firstRest (2 (0 9 4))}] - skolem:lemma4639 - skolem:lemma4506 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((0) (2 4 9)) list:append (0 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2325 a r:Inference; +skolem:lemma2204 a r:Inference; r:gives { 2095 :numberToDigits (2 0 9 5). }; @@ -61256,32 +54171,9 @@ skolem:lemma2325 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2326 a r:Inference; - r:gives { - (2 0 9 5) :sort (0 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 5) list:firstRest (2 (0 9 5))}] - skolem:lemma4641 - skolem:lemma4506 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((0) (2 5 9)) list:append (0 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2327 a r:Inference; +skolem:lemma2205 a r:Inference; r:gives { 2096 :numberToDigits (2 0 9 6). }; @@ -61300,32 +54192,9 @@ skolem:lemma2327 a r:Inference; 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:lemma4392. - -skolem:lemma2328 a r:Inference; - r:gives { - (2 0 9 6) :sort (0 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 6) list:firstRest (2 (0 9 6))}] - skolem:lemma4643 - skolem:lemma4506 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((0) (2 6 9)) list:append (0 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2329 a r:Inference; +skolem:lemma2206 a r:Inference; r:gives { 2097 :numberToDigits (2 0 9 7). }; @@ -61344,32 +54213,9 @@ skolem:lemma2329 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2330 a r:Inference; - r:gives { - (2 0 9 7) :sort (0 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 7) list:firstRest (2 (0 9 7))}] - skolem:lemma4645 - skolem:lemma4506 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((0) (2 7 9)) list:append (0 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2331 a r:Inference; +skolem:lemma2207 a r:Inference; r:gives { 2098 :numberToDigits (2 0 9 8). }; @@ -61388,32 +54234,9 @@ skolem:lemma2331 a r:Inference; 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:lemma4392. - -skolem:lemma2332 a r:Inference; - r:gives { - (2 0 9 8) :sort (0 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 8) list:firstRest (2 (0 9 8))}] - skolem:lemma4647 - skolem:lemma4506 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((0) (2 8 9)) list:append (0 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2333 a r:Inference; +skolem:lemma2208 a r:Inference; r:gives { 2099 :numberToDigits (2 0 9 9). }; @@ -61432,32 +54255,9 @@ skolem:lemma2333 a r:Inference; 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:lemma4392. - -skolem:lemma2334 a r:Inference; - r:gives { - (2 0 9 9) :sort (0 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9 9) list:firstRest (2 (0 9 9))}] - skolem:lemma4649 - skolem:lemma4506 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((0) (2 9 9)) list:append (0 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 9 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_2"]; r:boundTo (0 9 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 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2335 a r:Inference; +skolem:lemma2209 a r:Inference; r:gives { (0 2 9 9) :digitsToNumber 299 . }; @@ -61475,9 +54275,9 @@ skolem:lemma2335 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2336 a r:Inference; +skolem:lemma2210 a r:Inference; r:gives { (9 9 2 0) :digitsToNumber 9920 . }; @@ -61495,42 +54295,9 @@ skolem:lemma2336 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2337 a r:Inference; - r:gives { - 9621 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 2}] - [ a r:Fact; r:gives {(2 1) math:sum 3}] - [ a r:Fact; r:gives {{ - :recursion :count 2. - } log:becomes { - :recursion :count 3. - }}] - skolem:lemma4651 - skolem:lemma4652 - [ a r:Fact; r:gives {(1 2 6 9) list:reverse (9 6 2 1)}] - skolem:lemma2554 - skolem:lemma2555 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {8352 math:notEqualTo 6174}] - skolem:lemma2254 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9621]; - 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 (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1269]; - 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_8"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2338 a r:Inference; +skolem:lemma2211 a r:Inference; r:gives { 2100 :numberToDigits (2 1 0 0). }; @@ -61549,32 +54316,9 @@ skolem:lemma2338 a r:Inference; 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:lemma4392. - -skolem:lemma2339 a r:Inference; - r:gives { - (2 1 0 0) :sort (0 0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 0) list:firstRest (2 (1 0 0))}] - skolem:lemma4653 - skolem:lemma4654 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 1) (2)) list:append (0 0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 1 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2340 a r:Inference; +skolem:lemma2212 a r:Inference; r:gives { 2101 :numberToDigits (2 1 0 1). }; @@ -61593,32 +54337,9 @@ skolem:lemma2340 a r:Inference; 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:lemma4392. - -skolem:lemma2341 a r:Inference; - r:gives { - (2 1 0 1) :sort (0 1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 1) list:firstRest (2 (1 0 1))}] - skolem:lemma4655 - skolem:lemma4656 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 1) (2)) list:append (0 1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 1 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2342 a r:Inference; +skolem:lemma2213 a r:Inference; r:gives { 2102 :numberToDigits (2 1 0 2). }; @@ -61637,32 +54358,9 @@ skolem:lemma2342 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma2343 a r:Inference; - r:gives { - (2 1 0 2) :sort (0 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 2) list:firstRest (2 (1 0 2))}] - skolem:lemma4657 - skolem:lemma4658 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 2) (2)) list:append (0 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2344 a r:Inference; +skolem:lemma2214 a r:Inference; r:gives { 2103 :numberToDigits (2 1 0 3). }; @@ -61681,32 +54379,9 @@ skolem:lemma2344 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2345 a r:Inference; - r:gives { - (2 1 0 3) :sort (0 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 3) list:firstRest (2 (1 0 3))}] - skolem:lemma4659 - skolem:lemma4660 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 1) (2 3)) list:append (0 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 3)]; - r:rule skolem:lemma4396. - -skolem:lemma2346 a r:Inference; +skolem:lemma2215 a r:Inference; r:gives { 2104 :numberToDigits (2 1 0 4). }; @@ -61725,32 +54400,9 @@ skolem:lemma2346 a r:Inference; 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:lemma4392. - -skolem:lemma2347 a r:Inference; - r:gives { - (2 1 0 4) :sort (0 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 4) list:firstRest (2 (1 0 4))}] - skolem:lemma4661 - skolem:lemma4660 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 1) (2 4)) list:append (0 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2348 a r:Inference; +skolem:lemma2216 a r:Inference; r:gives { 2105 :numberToDigits (2 1 0 5). }; @@ -61769,32 +54421,9 @@ skolem:lemma2348 a r:Inference; 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:lemma4392. - -skolem:lemma2349 a r:Inference; - r:gives { - (2 1 0 5) :sort (0 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 5) list:firstRest (2 (1 0 5))}] - skolem:lemma4662 - skolem:lemma4660 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 1) (2 5)) list:append (0 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2350 a r:Inference; +skolem:lemma2217 a r:Inference; r:gives { 2106 :numberToDigits (2 1 0 6). }; @@ -61813,32 +54442,9 @@ skolem:lemma2350 a r:Inference; 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:lemma4392. - -skolem:lemma2351 a r:Inference; - r:gives { - (2 1 0 6) :sort (0 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 6) list:firstRest (2 (1 0 6))}] - skolem:lemma4663 - skolem:lemma4660 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 1) (2 6)) list:append (0 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2352 a r:Inference; +skolem:lemma2218 a r:Inference; r:gives { 2107 :numberToDigits (2 1 0 7). }; @@ -61857,32 +54463,9 @@ skolem:lemma2352 a r:Inference; 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:lemma4392. - -skolem:lemma2353 a r:Inference; - r:gives { - (2 1 0 7) :sort (0 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 7) list:firstRest (2 (1 0 7))}] - skolem:lemma4664 - skolem:lemma4660 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 1) (2 7)) list:append (0 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2354 a r:Inference; +skolem:lemma2219 a r:Inference; r:gives { 2108 :numberToDigits (2 1 0 8). }; @@ -61901,32 +54484,9 @@ skolem:lemma2354 a r:Inference; 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:lemma4392. - -skolem:lemma2355 a r:Inference; - r:gives { - (2 1 0 8) :sort (0 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 8) list:firstRest (2 (1 0 8))}] - skolem:lemma4665 - skolem:lemma4660 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 1) (2 8)) list:append (0 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2356 a r:Inference; +skolem:lemma2220 a r:Inference; r:gives { 2109 :numberToDigits (2 1 0 9). }; @@ -61945,32 +54505,9 @@ skolem:lemma2356 a r:Inference; 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:lemma4392. - -skolem:lemma2357 a r:Inference; - r:gives { - (2 1 0 9) :sort (0 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0 9) list:firstRest (2 (1 0 9))}] - skolem:lemma4666 - skolem:lemma4660 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 1) (2 9)) list:append (0 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 0 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_2"]; r:boundTo (1 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2358 a r:Inference; +skolem:lemma2221 a r:Inference; r:gives { 2110 :numberToDigits (2 1 1 0). }; @@ -61989,32 +54526,9 @@ skolem:lemma2358 a r:Inference; 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:lemma4392. - -skolem:lemma2359 a r:Inference; - r:gives { - (2 1 1 0) :sort (0 1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 0) list:firstRest (2 (1 1 0))}] - skolem:lemma4667 - skolem:lemma4668 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 1) (2)) list:append (0 1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 1 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2360 a r:Inference; +skolem:lemma2222 a r:Inference; r:gives { 2111 :numberToDigits (2 1 1 1). }; @@ -62033,32 +54547,9 @@ skolem:lemma2360 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2361 a r:Inference; - r:gives { - (2 1 1 1) :sort (1 1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 1) list:firstRest (2 (1 1 1))}] - skolem:lemma4669 - skolem:lemma4670 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 1 1) (2)) list:append (1 1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 1 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma2362 a r:Inference; +skolem:lemma2223 a r:Inference; r:gives { (1 1 1 2) :digitsToNumber 1112 . }; @@ -62076,9 +54567,9 @@ skolem:lemma2362 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2363 a r:Inference; +skolem:lemma2224 a r:Inference; r:gives { (2 1 1 1) :digitsToNumber 2111 . }; @@ -62096,42 +54587,9 @@ skolem:lemma2363 a r:Inference; 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:lemma4397. - -skolem:lemma2364 a r:Inference; - r:gives { - 999 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4671 - skolem:lemma4672 - [ a r:Fact; r:gives {(0 9 9 9) list:reverse (9 9 9 0)}] - skolem:lemma4673 - skolem:lemma4674 - [ a r:Fact; r:gives {(9990 999) math:difference 8991}] - [ a r:Fact; r:gives {8991 math:notEqualTo 6174}] - skolem:lemma2134 - ); - 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 2]; - 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 (0 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9 9 0)]; - 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_7"]; r:boundTo 9990]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2365 a r:Inference; +skolem:lemma2225 a r:Inference; r:gives { 2112 :numberToDigits (2 1 1 2). }; @@ -62150,32 +54608,9 @@ skolem:lemma2365 a r:Inference; 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:lemma4392. - -skolem:lemma2366 a r:Inference; - r:gives { - (2 1 1 2) :sort (1 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 2) list:firstRest (2 (1 1 2))}] - skolem:lemma4675 - skolem:lemma4676 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 1 2) (2)) list:append (1 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2367 a r:Inference; +skolem:lemma2226 a r:Inference; r:gives { (1 1 2 2) :digitsToNumber 1122 . }; @@ -62193,9 +54628,9 @@ skolem:lemma2367 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2368 a r:Inference; +skolem:lemma2227 a r:Inference; r:gives { (2 2 1 1) :digitsToNumber 2211 . }; @@ -62213,42 +54648,9 @@ skolem:lemma2368 a r:Inference; 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:lemma4397. - -skolem:lemma2369 a r:Inference; - r:gives { - 1089 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4677 - skolem:lemma4678 - [ a r:Fact; r:gives {(0 1 8 9) list:reverse (9 8 1 0)}] - skolem:lemma4470 - skolem:lemma4471 - [ a r:Fact; r:gives {(9810 189) math:difference 9621}] - [ a r:Fact; r:gives {9621 math:notEqualTo 6174}] - skolem:lemma2337 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 8 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 189]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9810]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2370 a r:Inference; +skolem:lemma2228 a r:Inference; r:gives { 2113 :numberToDigits (2 1 1 3). }; @@ -62267,32 +54669,9 @@ skolem:lemma2370 a r:Inference; 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:lemma4392. - -skolem:lemma2371 a r:Inference; - r:gives { - (2 1 1 3) :sort (1 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 3) list:firstRest (2 (1 1 3))}] - skolem:lemma4679 - skolem:lemma4680 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 1) (2 3)) list:append (1 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2372 a r:Inference; +skolem:lemma2229 a r:Inference; r:gives { (1 1 2 3) :digitsToNumber 1123 . }; @@ -62310,9 +54689,9 @@ skolem:lemma2372 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2373 a r:Inference; +skolem:lemma2230 a r:Inference; r:gives { (3 2 1 1) :digitsToNumber 3211 . }; @@ -62330,9 +54709,9 @@ skolem:lemma2373 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2374 a r:Inference; +skolem:lemma2231 a r:Inference; r:gives { 2114 :numberToDigits (2 1 1 4). }; @@ -62351,32 +54730,9 @@ skolem:lemma2374 a r:Inference; 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:lemma4392. - -skolem:lemma2375 a r:Inference; - r:gives { - (2 1 1 4) :sort (1 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 4) list:firstRest (2 (1 1 4))}] - skolem:lemma4681 - skolem:lemma4680 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 1) (2 4)) list:append (1 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2376 a r:Inference; +skolem:lemma2232 a r:Inference; r:gives { (1 1 2 4) :digitsToNumber 1124 . }; @@ -62394,9 +54750,9 @@ skolem:lemma2376 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2377 a r:Inference; +skolem:lemma2233 a r:Inference; r:gives { (4 2 1 1) :digitsToNumber 4211 . }; @@ -62414,9 +54770,9 @@ skolem:lemma2377 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2378 a r:Inference; +skolem:lemma2234 a r:Inference; r:gives { 2115 :numberToDigits (2 1 1 5). }; @@ -62435,32 +54791,9 @@ skolem:lemma2378 a r:Inference; 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:lemma4392. - -skolem:lemma2379 a r:Inference; - r:gives { - (2 1 1 5) :sort (1 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 5) list:firstRest (2 (1 1 5))}] - skolem:lemma4682 - skolem:lemma4680 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 1) (2 5)) list:append (1 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2380 a r:Inference; +skolem:lemma2235 a r:Inference; r:gives { (1 1 2 5) :digitsToNumber 1125 . }; @@ -62478,9 +54811,9 @@ skolem:lemma2380 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2381 a r:Inference; +skolem:lemma2236 a r:Inference; r:gives { (5 2 1 1) :digitsToNumber 5211 . }; @@ -62498,9 +54831,9 @@ skolem:lemma2381 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2382 a r:Inference; +skolem:lemma2237 a r:Inference; r:gives { 2116 :numberToDigits (2 1 1 6). }; @@ -62519,32 +54852,9 @@ skolem:lemma2382 a r:Inference; 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:lemma4392. - -skolem:lemma2383 a r:Inference; - r:gives { - (2 1 1 6) :sort (1 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 6) list:firstRest (2 (1 1 6))}] - skolem:lemma4683 - skolem:lemma4680 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 1) (2 6)) list:append (1 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2384 a r:Inference; +skolem:lemma2238 a r:Inference; r:gives { (1 1 2 6) :digitsToNumber 1126 . }; @@ -62562,9 +54872,9 @@ skolem:lemma2384 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2385 a r:Inference; +skolem:lemma2239 a r:Inference; r:gives { (6 2 1 1) :digitsToNumber 6211 . }; @@ -62582,9 +54892,9 @@ skolem:lemma2385 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2386 a r:Inference; +skolem:lemma2240 a r:Inference; r:gives { 2117 :numberToDigits (2 1 1 7). }; @@ -62603,32 +54913,9 @@ skolem:lemma2386 a r:Inference; 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:lemma4392. - -skolem:lemma2387 a r:Inference; - r:gives { - (2 1 1 7) :sort (1 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 7) list:firstRest (2 (1 1 7))}] - skolem:lemma4684 - skolem:lemma4680 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 1) (2 7)) list:append (1 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2388 a r:Inference; +skolem:lemma2241 a r:Inference; r:gives { (1 1 2 7) :digitsToNumber 1127 . }; @@ -62646,9 +54933,9 @@ skolem:lemma2388 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2389 a r:Inference; +skolem:lemma2242 a r:Inference; r:gives { (7 2 1 1) :digitsToNumber 7211 . }; @@ -62666,9 +54953,9 @@ skolem:lemma2389 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2390 a r:Inference; +skolem:lemma2243 a r:Inference; r:gives { 2118 :numberToDigits (2 1 1 8). }; @@ -62687,32 +54974,9 @@ skolem:lemma2390 a r:Inference; 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:lemma4392. - -skolem:lemma2391 a r:Inference; - r:gives { - (2 1 1 8) :sort (1 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 8) list:firstRest (2 (1 1 8))}] - skolem:lemma4685 - skolem:lemma4680 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 1) (2 8)) list:append (1 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2392 a r:Inference; +skolem:lemma2244 a r:Inference; r:gives { (1 1 2 8) :digitsToNumber 1128 . }; @@ -62730,9 +54994,9 @@ skolem:lemma2392 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2393 a r:Inference; +skolem:lemma2245 a r:Inference; r:gives { (8 2 1 1) :digitsToNumber 8211 . }; @@ -62750,9 +55014,9 @@ skolem:lemma2393 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2394 a r:Inference; +skolem:lemma2246 a r:Inference; r:gives { 2119 :numberToDigits (2 1 1 9). }; @@ -62771,32 +55035,9 @@ skolem:lemma2394 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2395 a r:Inference; - r:gives { - (2 1 1 9) :sort (1 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1 9) list:firstRest (2 (1 1 9))}] - skolem:lemma4686 - skolem:lemma4680 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 1) (2 9)) list:append (1 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 1 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_2"]; r:boundTo (1 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2396 a r:Inference; +skolem:lemma2247 a r:Inference; r:gives { (1 1 2 9) :digitsToNumber 1129 . }; @@ -62814,9 +55055,9 @@ skolem:lemma2396 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2397 a r:Inference; +skolem:lemma2248 a r:Inference; r:gives { (9 2 1 1) :digitsToNumber 9211 . }; @@ -62834,9 +55075,9 @@ skolem:lemma2397 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2398 a r:Inference; +skolem:lemma2249 a r:Inference; r:gives { 2120 :numberToDigits (2 1 2 0). }; @@ -62855,32 +55096,9 @@ skolem:lemma2398 a r:Inference; 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:lemma4392. - -skolem:lemma2399 a r:Inference; - r:gives { - (2 1 2 0) :sort (0 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 0) list:firstRest (2 (1 2 0))}] - skolem:lemma4687 - skolem:lemma4688 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 2) (2)) list:append (0 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2400 a r:Inference; +skolem:lemma2250 a r:Inference; r:gives { 2121 :numberToDigits (2 1 2 1). }; @@ -62899,32 +55117,9 @@ skolem:lemma2400 a r:Inference; 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:lemma4392. - -skolem:lemma2401 a r:Inference; - r:gives { - (2 1 2 1) :sort (1 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 1) list:firstRest (2 (1 2 1))}] - skolem:lemma4689 - skolem:lemma4690 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 1 2) (2)) list:append (1 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2402 a r:Inference; +skolem:lemma2251 a r:Inference; r:gives { 2122 :numberToDigits (2 1 2 2). }; @@ -62943,32 +55138,9 @@ skolem:lemma2402 a r:Inference; 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:lemma4392. - -skolem:lemma2403 a r:Inference; - r:gives { - (2 1 2 2) :sort (1 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 2) list:firstRest (2 (1 2 2))}] - skolem:lemma4691 - skolem:lemma4692 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 2 2) (2)) list:append (1 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 2 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2404 a r:Inference; +skolem:lemma2252 a r:Inference; r:gives { (1 2 2 2) :digitsToNumber 1222 . }; @@ -62986,9 +55158,9 @@ skolem:lemma2404 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2405 a r:Inference; +skolem:lemma2253 a r:Inference; r:gives { (2 2 2 1) :digitsToNumber 2221 . }; @@ -63006,9 +55178,9 @@ skolem:lemma2405 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2406 a r:Inference; +skolem:lemma2254 a r:Inference; r:gives { 2123 :numberToDigits (2 1 2 3). }; @@ -63027,32 +55199,9 @@ skolem:lemma2406 a r:Inference; 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:lemma4392. - -skolem:lemma2407 a r:Inference; - r:gives { - (2 1 2 3) :sort (1 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 3) list:firstRest (2 (1 2 3))}] - skolem:lemma4693 - skolem:lemma4694 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 2) (2 3)) list:append (1 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2408 a r:Inference; +skolem:lemma2255 a r:Inference; r:gives { (1 2 2 3) :digitsToNumber 1223 . }; @@ -63070,9 +55219,9 @@ skolem:lemma2408 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2409 a r:Inference; +skolem:lemma2256 a r:Inference; r:gives { (3 2 2 1) :digitsToNumber 3221 . }; @@ -63090,9 +55239,9 @@ skolem:lemma2409 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2410 a r:Inference; +skolem:lemma2257 a r:Inference; r:gives { 2124 :numberToDigits (2 1 2 4). }; @@ -63111,32 +55260,9 @@ skolem:lemma2410 a r:Inference; 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:lemma4392. - -skolem:lemma2411 a r:Inference; - r:gives { - (2 1 2 4) :sort (1 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 4) list:firstRest (2 (1 2 4))}] - skolem:lemma4695 - skolem:lemma4694 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 2) (2 4)) list:append (1 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2412 a r:Inference; +skolem:lemma2258 a r:Inference; r:gives { (1 2 2 4) :digitsToNumber 1224 . }; @@ -63154,9 +55280,9 @@ skolem:lemma2412 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2413 a r:Inference; +skolem:lemma2259 a r:Inference; r:gives { (4 2 2 1) :digitsToNumber 4221 . }; @@ -63174,9 +55300,9 @@ skolem:lemma2413 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2414 a r:Inference; +skolem:lemma2260 a r:Inference; r:gives { 2125 :numberToDigits (2 1 2 5). }; @@ -63195,32 +55321,9 @@ skolem:lemma2414 a r:Inference; 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:lemma4392. - -skolem:lemma2415 a r:Inference; - r:gives { - (2 1 2 5) :sort (1 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 5) list:firstRest (2 (1 2 5))}] - skolem:lemma4696 - skolem:lemma4694 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 2) (2 5)) list:append (1 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2416 a r:Inference; +skolem:lemma2261 a r:Inference; r:gives { (1 2 2 5) :digitsToNumber 1225 . }; @@ -63238,9 +55341,9 @@ skolem:lemma2416 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2417 a r:Inference; +skolem:lemma2262 a r:Inference; r:gives { (5 2 2 1) :digitsToNumber 5221 . }; @@ -63258,9 +55361,9 @@ skolem:lemma2417 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2418 a r:Inference; +skolem:lemma2263 a r:Inference; r:gives { 2126 :numberToDigits (2 1 2 6). }; @@ -63279,32 +55382,9 @@ skolem:lemma2418 a r:Inference; 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:lemma4392. - -skolem:lemma2419 a r:Inference; - r:gives { - (2 1 2 6) :sort (1 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 6) list:firstRest (2 (1 2 6))}] - skolem:lemma4697 - skolem:lemma4694 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 2) (2 6)) list:append (1 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2420 a r:Inference; +skolem:lemma2264 a r:Inference; r:gives { (1 2 2 6) :digitsToNumber 1226 . }; @@ -63322,9 +55402,9 @@ skolem:lemma2420 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2421 a r:Inference; +skolem:lemma2265 a r:Inference; r:gives { (6 2 2 1) :digitsToNumber 6221 . }; @@ -63342,9 +55422,9 @@ skolem:lemma2421 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2422 a r:Inference; +skolem:lemma2266 a r:Inference; r:gives { 2127 :numberToDigits (2 1 2 7). }; @@ -63363,32 +55443,9 @@ skolem:lemma2422 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2423 a r:Inference; - r:gives { - (2 1 2 7) :sort (1 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 7) list:firstRest (2 (1 2 7))}] - skolem:lemma4698 - skolem:lemma4694 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 2) (2 7)) list:append (1 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2424 a r:Inference; +skolem:lemma2267 a r:Inference; r:gives { (1 2 2 7) :digitsToNumber 1227 . }; @@ -63406,9 +55463,9 @@ skolem:lemma2424 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2425 a r:Inference; +skolem:lemma2268 a r:Inference; r:gives { (7 2 2 1) :digitsToNumber 7221 . }; @@ -63426,9 +55483,9 @@ skolem:lemma2425 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2426 a r:Inference; +skolem:lemma2269 a r:Inference; r:gives { 2128 :numberToDigits (2 1 2 8). }; @@ -63447,32 +55504,9 @@ skolem:lemma2426 a r:Inference; 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:lemma4392. - -skolem:lemma2427 a r:Inference; - r:gives { - (2 1 2 8) :sort (1 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 8) list:firstRest (2 (1 2 8))}] - skolem:lemma4699 - skolem:lemma4694 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 2) (2 8)) list:append (1 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2428 a r:Inference; +skolem:lemma2270 a r:Inference; r:gives { (1 2 2 8) :digitsToNumber 1228 . }; @@ -63490,9 +55524,9 @@ skolem:lemma2428 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2429 a r:Inference; +skolem:lemma2271 a r:Inference; r:gives { (8 2 2 1) :digitsToNumber 8221 . }; @@ -63510,9 +55544,9 @@ skolem:lemma2429 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2430 a r:Inference; +skolem:lemma2272 a r:Inference; r:gives { 2129 :numberToDigits (2 1 2 9). }; @@ -63531,32 +55565,9 @@ skolem:lemma2430 a r:Inference; 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:lemma4392. - -skolem:lemma2431 a r:Inference; - r:gives { - (2 1 2 9) :sort (1 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2 9) list:firstRest (2 (1 2 9))}] - skolem:lemma4700 - skolem:lemma4694 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 2) (2 9)) list:append (1 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 2 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_2"]; r:boundTo (1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2432 a r:Inference; +skolem:lemma2273 a r:Inference; r:gives { (1 2 2 9) :digitsToNumber 1229 . }; @@ -63574,9 +55585,9 @@ skolem:lemma2432 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2433 a r:Inference; +skolem:lemma2274 a r:Inference; r:gives { (9 2 2 1) :digitsToNumber 9221 . }; @@ -63594,9 +55605,9 @@ skolem:lemma2433 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2434 a r:Inference; +skolem:lemma2275 a r:Inference; r:gives { 2130 :numberToDigits (2 1 3 0). }; @@ -63615,32 +55626,9 @@ skolem:lemma2434 a r:Inference; 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:lemma4392. - -skolem:lemma2435 a r:Inference; - r:gives { - (2 1 3 0) :sort (0 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 0) list:firstRest (2 (1 3 0))}] - skolem:lemma4701 - skolem:lemma4660 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 1) (2 3)) list:append (0 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2436 a r:Inference; +skolem:lemma2276 a r:Inference; r:gives { 2131 :numberToDigits (2 1 3 1). }; @@ -63659,32 +55647,9 @@ skolem:lemma2436 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2437 a r:Inference; - r:gives { - (2 1 3 1) :sort (1 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 1) list:firstRest (2 (1 3 1))}] - skolem:lemma4702 - skolem:lemma4680 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 1) (2 3)) list:append (1 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 3)]; - r:rule skolem:lemma4396. - -skolem:lemma2438 a r:Inference; +skolem:lemma2277 a r:Inference; r:gives { 2132 :numberToDigits (2 1 3 2). }; @@ -63703,32 +55668,9 @@ skolem:lemma2438 a r:Inference; 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:lemma4392. - -skolem:lemma2439 a r:Inference; - r:gives { - (2 1 3 2) :sort (1 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 2) list:firstRest (2 (1 3 2))}] - skolem:lemma4703 - skolem:lemma4694 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 2) (2 3)) list:append (1 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2440 a r:Inference; +skolem:lemma2278 a r:Inference; r:gives { 2133 :numberToDigits (2 1 3 3). }; @@ -63747,32 +55689,9 @@ skolem:lemma2440 a r:Inference; 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:lemma4392. - -skolem:lemma2441 a r:Inference; - r:gives { - (2 1 3 3) :sort (1 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 3) list:firstRest (2 (1 3 3))}] - skolem:lemma4704 - skolem:lemma4705 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((1) (2 3 3)) list:append (1 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 3)]; - 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 3)]; - 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2442 a r:Inference; +skolem:lemma2279 a r:Inference; r:gives { (1 2 3 3) :digitsToNumber 1233 . }; @@ -63790,9 +55709,9 @@ skolem:lemma2442 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2443 a r:Inference; +skolem:lemma2280 a r:Inference; r:gives { (3 3 2 1) :digitsToNumber 3321 . }; @@ -63810,9 +55729,9 @@ skolem:lemma2443 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2444 a r:Inference; +skolem:lemma2281 a r:Inference; r:gives { 2134 :numberToDigits (2 1 3 4). }; @@ -63831,32 +55750,9 @@ skolem:lemma2444 a r:Inference; 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:lemma4392. - -skolem:lemma2445 a r:Inference; - r:gives { - (2 1 3 4) :sort (1 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 4) list:firstRest (2 (1 3 4))}] - skolem:lemma4706 - skolem:lemma4705 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((1) (2 3 4)) list:append (1 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2446 a r:Inference; +skolem:lemma2282 a r:Inference; r:gives { (1 2 3 4) :digitsToNumber 1234 . }; @@ -63874,9 +55770,9 @@ skolem:lemma2446 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2447 a r:Inference; +skolem:lemma2283 a r:Inference; r:gives { (4 3 2 1) :digitsToNumber 4321 . }; @@ -63894,9 +55790,9 @@ skolem:lemma2447 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2448 a r:Inference; +skolem:lemma2284 a r:Inference; r:gives { 2135 :numberToDigits (2 1 3 5). }; @@ -63915,32 +55811,9 @@ skolem:lemma2448 a r:Inference; 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:lemma4392. - -skolem:lemma2449 a r:Inference; - r:gives { - (2 1 3 5) :sort (1 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 5) list:firstRest (2 (1 3 5))}] - skolem:lemma4707 - skolem:lemma4705 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((1) (2 3 5)) list:append (1 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2450 a r:Inference; +skolem:lemma2285 a r:Inference; r:gives { (1 2 3 5) :digitsToNumber 1235 . }; @@ -63958,9 +55831,9 @@ skolem:lemma2450 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2451 a r:Inference; +skolem:lemma2286 a r:Inference; r:gives { (5 3 2 1) :digitsToNumber 5321 . }; @@ -63978,9 +55851,9 @@ skolem:lemma2451 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2452 a r:Inference; +skolem:lemma2287 a r:Inference; r:gives { 2136 :numberToDigits (2 1 3 6). }; @@ -63999,32 +55872,9 @@ skolem:lemma2452 a r:Inference; 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:lemma4392. - -skolem:lemma2453 a r:Inference; - r:gives { - (2 1 3 6) :sort (1 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 6) list:firstRest (2 (1 3 6))}] - skolem:lemma4708 - skolem:lemma4705 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((1) (2 3 6)) list:append (1 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2454 a r:Inference; +skolem:lemma2288 a r:Inference; r:gives { (1 2 3 6) :digitsToNumber 1236 . }; @@ -64042,9 +55892,9 @@ skolem:lemma2454 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2455 a r:Inference; +skolem:lemma2289 a r:Inference; r:gives { (6 3 2 1) :digitsToNumber 6321 . }; @@ -64062,9 +55912,9 @@ skolem:lemma2455 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2456 a r:Inference; +skolem:lemma2290 a r:Inference; r:gives { 2137 :numberToDigits (2 1 3 7). }; @@ -64083,32 +55933,9 @@ skolem:lemma2456 a r:Inference; 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:lemma4392. - -skolem:lemma2457 a r:Inference; - r:gives { - (2 1 3 7) :sort (1 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 7) list:firstRest (2 (1 3 7))}] - skolem:lemma4709 - skolem:lemma4705 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((1) (2 3 7)) list:append (1 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2458 a r:Inference; +skolem:lemma2291 a r:Inference; r:gives { (1 2 3 7) :digitsToNumber 1237 . }; @@ -64126,9 +55953,9 @@ skolem:lemma2458 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2459 a r:Inference; +skolem:lemma2292 a r:Inference; r:gives { (7 3 2 1) :digitsToNumber 7321 . }; @@ -64146,9 +55973,9 @@ skolem:lemma2459 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2460 a r:Inference; +skolem:lemma2293 a r:Inference; r:gives { 2138 :numberToDigits (2 1 3 8). }; @@ -64167,34 +55994,11 @@ skolem:lemma2460 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2461 a r:Inference; +skolem:lemma2294 a r:Inference; r:gives { - (2 1 3 8) :sort (1 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 8) list:firstRest (2 (1 3 8))}] - skolem:lemma4710 - skolem:lemma4705 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((1) (2 3 8)) list:append (1 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2462 a r:Inference; - r:gives { - (1 2 3 8) :digitsToNumber 1238 . + (1 2 3 8) :digitsToNumber 1238 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] @@ -64210,9 +56014,9 @@ skolem:lemma2462 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2463 a r:Inference; +skolem:lemma2295 a r:Inference; r:gives { (8 3 2 1) :digitsToNumber 8321 . }; @@ -64230,9 +56034,9 @@ skolem:lemma2463 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2464 a r:Inference; +skolem:lemma2296 a r:Inference; r:gives { 2139 :numberToDigits (2 1 3 9). }; @@ -64251,32 +56055,9 @@ skolem:lemma2464 a r:Inference; 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:lemma4392. - -skolem:lemma2465 a r:Inference; - r:gives { - (2 1 3 9) :sort (1 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3 9) list:firstRest (2 (1 3 9))}] - skolem:lemma4711 - skolem:lemma4705 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((1) (2 3 9)) list:append (1 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 3 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_2"]; r:boundTo (1 3 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2466 a r:Inference; +skolem:lemma2297 a r:Inference; r:gives { (1 2 3 9) :digitsToNumber 1239 . }; @@ -64294,9 +56075,9 @@ skolem:lemma2466 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2467 a r:Inference; +skolem:lemma2298 a r:Inference; r:gives { (9 3 2 1) :digitsToNumber 9321 . }; @@ -64314,9 +56095,9 @@ skolem:lemma2467 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2468 a r:Inference; +skolem:lemma2299 a r:Inference; r:gives { 2140 :numberToDigits (2 1 4 0). }; @@ -64335,32 +56116,9 @@ skolem:lemma2468 a r:Inference; 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:lemma4392. - -skolem:lemma2469 a r:Inference; - r:gives { - (2 1 4 0) :sort (0 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 0) list:firstRest (2 (1 4 0))}] - skolem:lemma4712 - skolem:lemma4660 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 1) (2 4)) list:append (0 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2470 a r:Inference; +skolem:lemma2300 a r:Inference; r:gives { 2141 :numberToDigits (2 1 4 1). }; @@ -64379,32 +56137,9 @@ skolem:lemma2470 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2471 a r:Inference; - r:gives { - (2 1 4 1) :sort (1 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 1) list:firstRest (2 (1 4 1))}] - skolem:lemma4713 - skolem:lemma4680 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 1) (2 4)) list:append (1 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 4)]; - r:rule skolem:lemma4396. - -skolem:lemma2472 a r:Inference; +skolem:lemma2301 a r:Inference; r:gives { 2142 :numberToDigits (2 1 4 2). }; @@ -64423,32 +56158,9 @@ skolem:lemma2472 a r:Inference; 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:lemma4392. - -skolem:lemma2473 a r:Inference; - r:gives { - (2 1 4 2) :sort (1 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 2) list:firstRest (2 (1 4 2))}] - skolem:lemma4714 - skolem:lemma4694 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 2) (2 4)) list:append (1 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2474 a r:Inference; +skolem:lemma2302 a r:Inference; r:gives { 2143 :numberToDigits (2 1 4 3). }; @@ -64467,32 +56179,9 @@ skolem:lemma2474 a r:Inference; 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:lemma4392. - -skolem:lemma2475 a r:Inference; - r:gives { - (2 1 4 3) :sort (1 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 3) list:firstRest (2 (1 4 3))}] - skolem:lemma4715 - skolem:lemma4705 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((1) (2 3 4)) list:append (1 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 3)]; - 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 3)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2476 a r:Inference; +skolem:lemma2303 a r:Inference; r:gives { 2144 :numberToDigits (2 1 4 4). }; @@ -64511,32 +56200,9 @@ skolem:lemma2476 a r:Inference; 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:lemma4392. - -skolem:lemma2477 a r:Inference; - r:gives { - (2 1 4 4) :sort (1 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 4) list:firstRest (2 (1 4 4))}] - skolem:lemma4716 - skolem:lemma4705 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((1) (2 4 4)) list:append (1 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2478 a r:Inference; +skolem:lemma2304 a r:Inference; r:gives { (1 2 4 4) :digitsToNumber 1244 . }; @@ -64554,9 +56220,9 @@ skolem:lemma2478 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2479 a r:Inference; +skolem:lemma2305 a r:Inference; r:gives { (4 4 2 1) :digitsToNumber 4421 . }; @@ -64574,9 +56240,9 @@ skolem:lemma2479 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2480 a r:Inference; +skolem:lemma2306 a r:Inference; r:gives { 2145 :numberToDigits (2 1 4 5). }; @@ -64595,32 +56261,9 @@ skolem:lemma2480 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2481 a r:Inference; - r:gives { - (2 1 4 5) :sort (1 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 5) list:firstRest (2 (1 4 5))}] - skolem:lemma4717 - skolem:lemma4705 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((1) (2 4 5)) list:append (1 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma2482 a r:Inference; +skolem:lemma2307 a r:Inference; r:gives { (1 2 4 5) :digitsToNumber 1245 . }; @@ -64638,9 +56281,9 @@ skolem:lemma2482 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2483 a r:Inference; +skolem:lemma2308 a r:Inference; r:gives { (5 4 2 1) :digitsToNumber 5421 . }; @@ -64658,9 +56301,9 @@ skolem:lemma2483 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2484 a r:Inference; +skolem:lemma2309 a r:Inference; r:gives { 2146 :numberToDigits (2 1 4 6). }; @@ -64679,32 +56322,9 @@ skolem:lemma2484 a r:Inference; 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:lemma4392. - -skolem:lemma2485 a r:Inference; - r:gives { - (2 1 4 6) :sort (1 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 6) list:firstRest (2 (1 4 6))}] - skolem:lemma4718 - skolem:lemma4705 - skolem:lemma4719 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((1) (2 4 6)) list:append (1 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2486 a r:Inference; +skolem:lemma2310 a r:Inference; r:gives { (1 2 4 6) :digitsToNumber 1246 . }; @@ -64722,9 +56342,9 @@ skolem:lemma2486 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2487 a r:Inference; +skolem:lemma2311 a r:Inference; r:gives { (6 4 2 1) :digitsToNumber 6421 . }; @@ -64742,9 +56362,70 @@ skolem:lemma2487 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2488 a r:Inference; +skolem:lemma2312 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:lemma3438. + +skolem:lemma2313 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:lemma3439. + +skolem:lemma2314 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:lemma3439. + +skolem:lemma2315 a r:Inference; r:gives { 2148 :numberToDigits (2 1 4 8). }; @@ -64763,32 +56444,9 @@ skolem:lemma2488 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2489 a r:Inference; - r:gives { - (2 1 4 8) :sort (1 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 8) list:firstRest (2 (1 4 8))}] - skolem:lemma4720 - skolem:lemma4705 - skolem:lemma4532 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((1) (2 4 8)) list:append (1 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2490 a r:Inference; +skolem:lemma2316 a r:Inference; r:gives { (1 2 4 8) :digitsToNumber 1248 . }; @@ -64806,9 +56464,9 @@ skolem:lemma2490 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2491 a r:Inference; +skolem:lemma2317 a r:Inference; r:gives { (8 4 2 1) :digitsToNumber 8421 . }; @@ -64826,9 +56484,9 @@ skolem:lemma2491 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2492 a r:Inference; +skolem:lemma2318 a r:Inference; r:gives { 2149 :numberToDigits (2 1 4 9). }; @@ -64847,32 +56505,9 @@ skolem:lemma2492 a r:Inference; 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:lemma4392. - -skolem:lemma2493 a r:Inference; - r:gives { - (2 1 4 9) :sort (1 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4 9) list:firstRest (2 (1 4 9))}] - skolem:lemma4721 - skolem:lemma4705 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((1) (2 4 9)) list:append (1 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 4 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_2"]; r:boundTo (1 4 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2494 a r:Inference; +skolem:lemma2319 a r:Inference; r:gives { (1 2 4 9) :digitsToNumber 1249 . }; @@ -64890,9 +56525,9 @@ skolem:lemma2494 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2495 a r:Inference; +skolem:lemma2320 a r:Inference; r:gives { (9 4 2 1) :digitsToNumber 9421 . }; @@ -64910,9 +56545,9 @@ skolem:lemma2495 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2496 a r:Inference; +skolem:lemma2321 a r:Inference; r:gives { 2150 :numberToDigits (2 1 5 0). }; @@ -64931,32 +56566,9 @@ skolem:lemma2496 a r:Inference; 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:lemma4392. - -skolem:lemma2497 a r:Inference; - r:gives { - (2 1 5 0) :sort (0 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 0) list:firstRest (2 (1 5 0))}] - skolem:lemma4722 - skolem:lemma4660 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 1) (2 5)) list:append (0 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2498 a r:Inference; +skolem:lemma2322 a r:Inference; r:gives { 2151 :numberToDigits (2 1 5 1). }; @@ -64975,32 +56587,9 @@ skolem:lemma2498 a r:Inference; 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:lemma4392. - -skolem:lemma2499 a r:Inference; - r:gives { - (2 1 5 1) :sort (1 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 1) list:firstRest (2 (1 5 1))}] - skolem:lemma4723 - skolem:lemma4680 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 1) (2 5)) list:append (1 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2500 a r:Inference; +skolem:lemma2323 a r:Inference; r:gives { 2152 :numberToDigits (2 1 5 2). }; @@ -65019,32 +56608,9 @@ skolem:lemma2500 a r:Inference; 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:lemma4392. - -skolem:lemma2501 a r:Inference; - r:gives { - (2 1 5 2) :sort (1 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 2) list:firstRest (2 (1 5 2))}] - skolem:lemma4724 - skolem:lemma4694 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 2) (2 5)) list:append (1 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2502 a r:Inference; +skolem:lemma2324 a r:Inference; r:gives { 2153 :numberToDigits (2 1 5 3). }; @@ -65063,32 +56629,9 @@ skolem:lemma2502 a r:Inference; 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:lemma4392. - -skolem:lemma2503 a r:Inference; - r:gives { - (2 1 5 3) :sort (1 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 3) list:firstRest (2 (1 5 3))}] - skolem:lemma4725 - skolem:lemma4705 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((1) (2 3 5)) list:append (1 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 3)]; - 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 3)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2504 a r:Inference; +skolem:lemma2325 a r:Inference; r:gives { 2154 :numberToDigits (2 1 5 4). }; @@ -65107,32 +56650,9 @@ skolem:lemma2504 a r:Inference; 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:lemma4392. - -skolem:lemma2505 a r:Inference; - r:gives { - (2 1 5 4) :sort (1 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 4) list:firstRest (2 (1 5 4))}] - skolem:lemma4726 - skolem:lemma4705 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((1) (2 4 5)) list:append (1 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 4)]; - 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 4)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2506 a r:Inference; +skolem:lemma2326 a r:Inference; r:gives { 2155 :numberToDigits (2 1 5 5). }; @@ -65151,32 +56671,9 @@ skolem:lemma2506 a r:Inference; 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:lemma4392. - -skolem:lemma2507 a r:Inference; - r:gives { - (2 1 5 5) :sort (1 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 5) list:firstRest (2 (1 5 5))}] - skolem:lemma4727 - skolem:lemma4705 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((1) (2 5 5)) list:append (1 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2508 a r:Inference; +skolem:lemma2327 a r:Inference; r:gives { (1 2 5 5) :digitsToNumber 1255 . }; @@ -65194,9 +56691,9 @@ skolem:lemma2508 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2509 a r:Inference; +skolem:lemma2328 a r:Inference; r:gives { (5 5 2 1) :digitsToNumber 5521 . }; @@ -65214,42 +56711,9 @@ skolem:lemma2509 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2510 a r:Inference; - r:gives { - 4266 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4728 - skolem:lemma4729 - [ a r:Fact; r:gives {(2 4 6 6) list:reverse (6 6 4 2)}] - skolem:lemma3298 - skolem:lemma3299 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2466]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2511 a r:Inference; +skolem:lemma2329 a r:Inference; r:gives { 2156 :numberToDigits (2 1 5 6). }; @@ -65268,32 +56732,9 @@ skolem:lemma2511 a r:Inference; 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:lemma4392. - -skolem:lemma2512 a r:Inference; - r:gives { - (2 1 5 6) :sort (1 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 6) list:firstRest (2 (1 5 6))}] - skolem:lemma4730 - skolem:lemma4705 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((1) (2 5 6)) list:append (1 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2513 a r:Inference; +skolem:lemma2330 a r:Inference; r:gives { (1 2 5 6) :digitsToNumber 1256 . }; @@ -65311,9 +56752,9 @@ skolem:lemma2513 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2514 a r:Inference; +skolem:lemma2331 a r:Inference; r:gives { (6 5 2 1) :digitsToNumber 6521 . }; @@ -65331,9 +56772,9 @@ skolem:lemma2514 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2515 a r:Inference; +skolem:lemma2332 a r:Inference; r:gives { 2157 :numberToDigits (2 1 5 7). }; @@ -65352,32 +56793,9 @@ skolem:lemma2515 a r:Inference; 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:lemma4392. - -skolem:lemma2516 a r:Inference; - r:gives { - (2 1 5 7) :sort (1 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 7) list:firstRest (2 (1 5 7))}] - skolem:lemma4731 - skolem:lemma4705 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((1) (2 5 7)) list:append (1 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2517 a r:Inference; +skolem:lemma2333 a r:Inference; r:gives { (1 2 5 7) :digitsToNumber 1257 . }; @@ -65395,9 +56813,9 @@ skolem:lemma2517 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2518 a r:Inference; +skolem:lemma2334 a r:Inference; r:gives { (7 5 2 1) :digitsToNumber 7521 . }; @@ -65415,9 +56833,9 @@ skolem:lemma2518 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2519 a r:Inference; +skolem:lemma2335 a r:Inference; r:gives { 2158 :numberToDigits (2 1 5 8). }; @@ -65436,32 +56854,9 @@ skolem:lemma2519 a r:Inference; 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:lemma4392. - -skolem:lemma2520 a r:Inference; - r:gives { - (2 1 5 8) :sort (1 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 8) list:firstRest (2 (1 5 8))}] - skolem:lemma4732 - skolem:lemma4705 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((1) (2 5 8)) list:append (1 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2521 a r:Inference; +skolem:lemma2336 a r:Inference; r:gives { (1 2 5 8) :digitsToNumber 1258 . }; @@ -65479,9 +56874,9 @@ skolem:lemma2521 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2522 a r:Inference; +skolem:lemma2337 a r:Inference; r:gives { (8 5 2 1) :digitsToNumber 8521 . }; @@ -65499,9 +56894,9 @@ skolem:lemma2522 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2523 a r:Inference; +skolem:lemma2338 a r:Inference; r:gives { 2159 :numberToDigits (2 1 5 9). }; @@ -65520,32 +56915,9 @@ skolem:lemma2523 a r:Inference; 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:lemma4392. - -skolem:lemma2524 a r:Inference; - r:gives { - (2 1 5 9) :sort (1 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5 9) list:firstRest (2 (1 5 9))}] - skolem:lemma4733 - skolem:lemma4705 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((1) (2 5 9)) list:append (1 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 5 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_2"]; r:boundTo (1 5 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2525 a r:Inference; +skolem:lemma2339 a r:Inference; r:gives { (1 2 5 9) :digitsToNumber 1259 . }; @@ -65563,9 +56935,9 @@ skolem:lemma2525 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2526 a r:Inference; +skolem:lemma2340 a r:Inference; r:gives { (9 5 2 1) :digitsToNumber 9521 . }; @@ -65583,9 +56955,9 @@ skolem:lemma2526 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2527 a r:Inference; +skolem:lemma2341 a r:Inference; r:gives { 2160 :numberToDigits (2 1 6 0). }; @@ -65604,32 +56976,9 @@ skolem:lemma2527 a r:Inference; 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:lemma4392. - -skolem:lemma2528 a r:Inference; - r:gives { - (2 1 6 0) :sort (0 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 0) list:firstRest (2 (1 6 0))}] - skolem:lemma4734 - skolem:lemma4660 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 1) (2 6)) list:append (0 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2529 a r:Inference; +skolem:lemma2342 a r:Inference; r:gives { 2161 :numberToDigits (2 1 6 1). }; @@ -65648,32 +56997,9 @@ skolem:lemma2529 a r:Inference; 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:lemma4392. - -skolem:lemma2530 a r:Inference; - r:gives { - (2 1 6 1) :sort (1 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 1) list:firstRest (2 (1 6 1))}] - skolem:lemma4735 - skolem:lemma4680 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 1) (2 6)) list:append (1 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2531 a r:Inference; +skolem:lemma2343 a r:Inference; r:gives { 2162 :numberToDigits (2 1 6 2). }; @@ -65692,32 +57018,9 @@ skolem:lemma2531 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2532 a r:Inference; - r:gives { - (2 1 6 2) :sort (1 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 2) list:firstRest (2 (1 6 2))}] - skolem:lemma4736 - skolem:lemma4694 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 2) (2 6)) list:append (1 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma2533 a r:Inference; +skolem:lemma2344 a r:Inference; r:gives { 2163 :numberToDigits (2 1 6 3). }; @@ -65736,32 +57039,9 @@ skolem:lemma2533 a r:Inference; 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:lemma4392. - -skolem:lemma2534 a r:Inference; - r:gives { - (2 1 6 3) :sort (1 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 3) list:firstRest (2 (1 6 3))}] - skolem:lemma4737 - skolem:lemma4705 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((1) (2 3 6)) list:append (1 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 3)]; - 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 3)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2535 a r:Inference; +skolem:lemma2345 a r:Inference; r:gives { 2164 :numberToDigits (2 1 6 4). }; @@ -65780,32 +57060,9 @@ skolem:lemma2535 a r:Inference; 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:lemma4392. - -skolem:lemma2536 a r:Inference; - r:gives { - (2 1 6 4) :sort (1 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 4) list:firstRest (2 (1 6 4))}] - skolem:lemma4738 - skolem:lemma4705 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((1) (2 4 6)) list:append (1 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 4)]; - 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 4)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2537 a r:Inference; +skolem:lemma2346 a r:Inference; r:gives { 2165 :numberToDigits (2 1 6 5). }; @@ -65824,32 +57081,9 @@ skolem:lemma2537 a r:Inference; 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:lemma4392. - -skolem:lemma2538 a r:Inference; - r:gives { - (2 1 6 5) :sort (1 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 5) list:firstRest (2 (1 6 5))}] - skolem:lemma4740 - skolem:lemma4705 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((1) (2 5 6)) list:append (1 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 5)]; - 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 5)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2539 a r:Inference; +skolem:lemma2347 a r:Inference; r:gives { 2166 :numberToDigits (2 1 6 6). }; @@ -65868,32 +57102,9 @@ skolem:lemma2539 a r:Inference; 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:lemma4392. - -skolem:lemma2540 a r:Inference; - r:gives { - (2 1 6 6) :sort (1 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 6) list:firstRest (2 (1 6 6))}] - skolem:lemma4741 - skolem:lemma4705 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((1) (2 6 6)) list:append (1 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2541 a r:Inference; +skolem:lemma2348 a r:Inference; r:gives { (1 2 6 6) :digitsToNumber 1266 . }; @@ -65911,9 +57122,9 @@ skolem:lemma2541 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2542 a r:Inference; +skolem:lemma2349 a r:Inference; r:gives { (6 6 2 1) :digitsToNumber 6621 . }; @@ -65931,42 +57142,9 @@ skolem:lemma2542 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2543 a r:Inference; - r:gives { - 5355 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 3}] - [ a r:Fact; r:gives {(3 1) math:sum 4}] - [ a r:Fact; r:gives {{ - :recursion :count 3. - } log:becomes { - :recursion :count 4. - }}] - skolem:lemma4742 - skolem:lemma4743 - [ a r:Fact; r:gives {(3 5 5 5) list:reverse (5 5 5 3)}] - skolem:lemma4744 - skolem:lemma4745 - [ a r:Fact; r:gives {(5553 3555) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3555]; - 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_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2544 a r:Inference; +skolem:lemma2350 a r:Inference; r:gives { 2167 :numberToDigits (2 1 6 7). }; @@ -65985,32 +57163,9 @@ skolem:lemma2544 a r:Inference; 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:lemma4392. - -skolem:lemma2545 a r:Inference; - r:gives { - (2 1 6 7) :sort (1 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 7) list:firstRest (2 (1 6 7))}] - skolem:lemma4746 - skolem:lemma4705 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((1) (2 6 7)) list:append (1 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2546 a r:Inference; +skolem:lemma2351 a r:Inference; r:gives { (1 2 6 7) :digitsToNumber 1267 . }; @@ -66028,9 +57183,9 @@ skolem:lemma2546 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2547 a r:Inference; +skolem:lemma2352 a r:Inference; r:gives { (7 6 2 1) :digitsToNumber 7621 . }; @@ -66048,9 +57203,9 @@ skolem:lemma2547 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2548 a r:Inference; +skolem:lemma2353 a r:Inference; r:gives { 2168 :numberToDigits (2 1 6 8). }; @@ -66069,32 +57224,9 @@ skolem:lemma2548 a r:Inference; 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:lemma4392. - -skolem:lemma2549 a r:Inference; - r:gives { - (2 1 6 8) :sort (1 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 8) list:firstRest (2 (1 6 8))}] - skolem:lemma4747 - skolem:lemma4705 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((1) (2 6 8)) list:append (1 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2550 a r:Inference; +skolem:lemma2354 a r:Inference; r:gives { (1 2 6 8) :digitsToNumber 1268 . }; @@ -66112,9 +57244,9 @@ skolem:lemma2550 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2551 a r:Inference; +skolem:lemma2355 a r:Inference; r:gives { (8 6 2 1) :digitsToNumber 8621 . }; @@ -66132,9 +57264,9 @@ skolem:lemma2551 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2552 a r:Inference; +skolem:lemma2356 a r:Inference; r:gives { 2169 :numberToDigits (2 1 6 9). }; @@ -66153,32 +57285,9 @@ skolem:lemma2552 a r:Inference; 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:lemma4392. - -skolem:lemma2553 a r:Inference; - r:gives { - (2 1 6 9) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6 9) list:firstRest (2 (1 6 9))}] - skolem:lemma4748 - skolem:lemma4705 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((1) (2 6 9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 6 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_2"]; r:boundTo (1 6 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2554 a r:Inference; +skolem:lemma2357 a r:Inference; r:gives { (1 2 6 9) :digitsToNumber 1269 . }; @@ -66196,9 +57305,9 @@ skolem:lemma2554 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2555 a r:Inference; +skolem:lemma2358 a r:Inference; r:gives { (9 6 2 1) :digitsToNumber 9621 . }; @@ -66216,9 +57325,9 @@ skolem:lemma2555 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2556 a r:Inference; +skolem:lemma2359 a r:Inference; r:gives { 2170 :numberToDigits (2 1 7 0). }; @@ -66237,32 +57346,9 @@ skolem:lemma2556 a r:Inference; 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:lemma4392. - -skolem:lemma2557 a r:Inference; - r:gives { - (2 1 7 0) :sort (0 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 0) list:firstRest (2 (1 7 0))}] - skolem:lemma4749 - skolem:lemma4660 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 1) (2 7)) list:append (0 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2558 a r:Inference; +skolem:lemma2360 a r:Inference; r:gives { 2171 :numberToDigits (2 1 7 1). }; @@ -66281,32 +57367,9 @@ skolem:lemma2558 a r:Inference; 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:lemma4392. - -skolem:lemma2559 a r:Inference; - r:gives { - (2 1 7 1) :sort (1 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 1) list:firstRest (2 (1 7 1))}] - skolem:lemma4750 - skolem:lemma4680 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 1) (2 7)) list:append (1 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2560 a r:Inference; +skolem:lemma2361 a r:Inference; r:gives { 2172 :numberToDigits (2 1 7 2). }; @@ -66325,32 +57388,9 @@ skolem:lemma2560 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2561 a r:Inference; - r:gives { - (2 1 7 2) :sort (1 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 2) list:firstRest (2 (1 7 2))}] - skolem:lemma4751 - skolem:lemma4694 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 2) (2 7)) list:append (1 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2562 a r:Inference; +skolem:lemma2362 a r:Inference; r:gives { 2173 :numberToDigits (2 1 7 3). }; @@ -66369,32 +57409,30 @@ skolem:lemma2562 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2563 a r:Inference; +skolem:lemma2363 a r:Inference; r:gives { - (2 1 7 3) :sort (1 2 3 7). + 2174 :numberToDigits (2 1 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 1 7 3) list:firstRest (2 (1 7 3))}] - skolem:lemma4752 - skolem:lemma4705 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((1) (2 3 7)) list:append (1 2 3 7)}] + [ 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_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 3)]; - 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 3)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma2564 a r:Inference; +skolem:lemma2364 a r:Inference; r:gives { 2175 :numberToDigits (2 1 7 5). }; @@ -66413,32 +57451,9 @@ skolem:lemma2564 a r:Inference; 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:lemma4392. - -skolem:lemma2565 a r:Inference; - r:gives { - (2 1 7 5) :sort (1 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 5) list:firstRest (2 (1 7 5))}] - skolem:lemma4753 - skolem:lemma4705 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((1) (2 5 7)) list:append (1 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 5)]; - 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 5)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2566 a r:Inference; +skolem:lemma2365 a r:Inference; r:gives { 2176 :numberToDigits (2 1 7 6). }; @@ -66457,32 +57472,9 @@ skolem:lemma2566 a r:Inference; 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:lemma4392. - -skolem:lemma2567 a r:Inference; - r:gives { - (2 1 7 6) :sort (1 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 6) list:firstRest (2 (1 7 6))}] - skolem:lemma4754 - skolem:lemma4705 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((1) (2 6 7)) list:append (1 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 6)]; - 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 6)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2568 a r:Inference; +skolem:lemma2366 a r:Inference; r:gives { 2177 :numberToDigits (2 1 7 7). }; @@ -66501,32 +57493,9 @@ skolem:lemma2568 a r:Inference; 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:lemma4392. - -skolem:lemma2569 a r:Inference; - r:gives { - (2 1 7 7) :sort (1 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 7) list:firstRest (2 (1 7 7))}] - skolem:lemma4755 - skolem:lemma4705 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((1) (2 7 7)) list:append (1 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2570 a r:Inference; +skolem:lemma2367 a r:Inference; r:gives { (1 2 7 7) :digitsToNumber 1277 . }; @@ -66544,9 +57513,9 @@ skolem:lemma2570 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2571 a r:Inference; +skolem:lemma2368 a r:Inference; r:gives { (7 7 2 1) :digitsToNumber 7721 . }; @@ -66564,42 +57533,9 @@ skolem:lemma2571 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2572 a r:Inference; - r:gives { - 6444 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4756 - skolem:lemma4757 - [ a r:Fact; r:gives {(4 4 4 6) list:reverse (6 4 4 4)}] - skolem:lemma4758 - skolem:lemma4759 - [ a r:Fact; r:gives {(6444 4446) math:difference 1998}] - [ a r:Fact; r:gives {1998 math:notEqualTo 6174}] - skolem:lemma2007 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2573 a r:Inference; +skolem:lemma2369 a r:Inference; r:gives { 2178 :numberToDigits (2 1 7 8). }; @@ -66618,32 +57554,9 @@ skolem:lemma2573 a r:Inference; 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:lemma4392. - -skolem:lemma2574 a r:Inference; - r:gives { - (2 1 7 8) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 8) list:firstRest (2 (1 7 8))}] - skolem:lemma4760 - skolem:lemma4705 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((1) (2 7 8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2575 a r:Inference; +skolem:lemma2370 a r:Inference; r:gives { (1 2 7 8) :digitsToNumber 1278 . }; @@ -66661,9 +57574,9 @@ skolem:lemma2575 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2576 a r:Inference; +skolem:lemma2371 a r:Inference; r:gives { (8 7 2 1) :digitsToNumber 8721 . }; @@ -66681,9 +57594,9 @@ skolem:lemma2576 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2577 a r:Inference; +skolem:lemma2372 a r:Inference; r:gives { 2179 :numberToDigits (2 1 7 9). }; @@ -66702,32 +57615,9 @@ skolem:lemma2577 a r:Inference; 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:lemma4392. - -skolem:lemma2578 a r:Inference; - r:gives { - (2 1 7 9) :sort (1 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7 9) list:firstRest (2 (1 7 9))}] - skolem:lemma4761 - skolem:lemma4705 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((1) (2 7 9)) list:append (1 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 7 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_2"]; r:boundTo (1 7 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2579 a r:Inference; +skolem:lemma2373 a r:Inference; r:gives { (1 2 7 9) :digitsToNumber 1279 . }; @@ -66745,9 +57635,9 @@ skolem:lemma2579 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2580 a r:Inference; +skolem:lemma2374 a r:Inference; r:gives { (9 7 2 1) :digitsToNumber 9721 . }; @@ -66765,9 +57655,9 @@ skolem:lemma2580 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2581 a r:Inference; +skolem:lemma2375 a r:Inference; r:gives { 2180 :numberToDigits (2 1 8 0). }; @@ -66786,34 +57676,11 @@ skolem:lemma2581 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2582 a r:Inference; +skolem:lemma2376 a r:Inference; r:gives { - (2 1 8 0) :sort (0 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 0) list:firstRest (2 (1 8 0))}] - skolem:lemma4762 - skolem:lemma4660 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 1) (2 8)) list:append (0 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2583 a r:Inference; - r:gives { - 2181 :numberToDigits (2 1 8 1). + 2181 :numberToDigits (2 1 8 1). }; r:evidence ( [ a r:Fact; r:gives {(2181 1000) math:integerQuotient 2}] @@ -66830,32 +57697,9 @@ skolem:lemma2583 a r:Inference; 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:lemma4392. - -skolem:lemma2584 a r:Inference; - r:gives { - (2 1 8 1) :sort (1 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 1) list:firstRest (2 (1 8 1))}] - skolem:lemma4763 - skolem:lemma4680 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 1) (2 8)) list:append (1 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2585 a r:Inference; +skolem:lemma2377 a r:Inference; r:gives { 2182 :numberToDigits (2 1 8 2). }; @@ -66874,32 +57718,9 @@ skolem:lemma2585 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2586 a r:Inference; - r:gives { - (2 1 8 2) :sort (1 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 2) list:firstRest (2 (1 8 2))}] - skolem:lemma4764 - skolem:lemma4694 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 2) (2 8)) list:append (1 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2587 a r:Inference; +skolem:lemma2378 a r:Inference; r:gives { 2183 :numberToDigits (2 1 8 3). }; @@ -66918,32 +57739,9 @@ skolem:lemma2587 a r:Inference; 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:lemma4392. - -skolem:lemma2588 a r:Inference; - r:gives { - (2 1 8 3) :sort (1 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 3) list:firstRest (2 (1 8 3))}] - skolem:lemma4765 - skolem:lemma4705 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((1) (2 3 8)) list:append (1 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 3)]; - 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 3)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2589 a r:Inference; +skolem:lemma2379 a r:Inference; r:gives { 2184 :numberToDigits (2 1 8 4). }; @@ -66962,32 +57760,9 @@ skolem:lemma2589 a r:Inference; 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:lemma4392. - -skolem:lemma2590 a r:Inference; - r:gives { - (2 1 8 4) :sort (1 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 4) list:firstRest (2 (1 8 4))}] - skolem:lemma4766 - skolem:lemma4705 - skolem:lemma4621 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((1) (2 4 8)) list:append (1 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 4)]; - 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 4)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2591 a r:Inference; +skolem:lemma2380 a r:Inference; r:gives { 2185 :numberToDigits (2 1 8 5). }; @@ -67006,32 +57781,9 @@ skolem:lemma2591 a r:Inference; 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:lemma4392. - -skolem:lemma2592 a r:Inference; - r:gives { - (2 1 8 5) :sort (1 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 5) list:firstRest (2 (1 8 5))}] - skolem:lemma4767 - skolem:lemma4705 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((1) (2 5 8)) list:append (1 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 5)]; - 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 5)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2593 a r:Inference; +skolem:lemma2381 a r:Inference; r:gives { 2186 :numberToDigits (2 1 8 6). }; @@ -67050,32 +57802,9 @@ skolem:lemma2593 a r:Inference; 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:lemma4392. - -skolem:lemma2594 a r:Inference; - r:gives { - (2 1 8 6) :sort (1 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 6) list:firstRest (2 (1 8 6))}] - skolem:lemma4768 - skolem:lemma4705 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((1) (2 6 8)) list:append (1 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 6)]; - 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 6)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2595 a r:Inference; +skolem:lemma2382 a r:Inference; r:gives { 2187 :numberToDigits (2 1 8 7). }; @@ -67094,32 +57823,9 @@ skolem:lemma2595 a r:Inference; 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:lemma4392. - -skolem:lemma2596 a r:Inference; - r:gives { - (2 1 8 7) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 7) list:firstRest (2 (1 8 7))}] - skolem:lemma4769 - skolem:lemma4705 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((1) (2 7 8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 7)]; - 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 7)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2597 a r:Inference; +skolem:lemma2383 a r:Inference; r:gives { 2188 :numberToDigits (2 1 8 8). }; @@ -67138,32 +57844,9 @@ skolem:lemma2597 a r:Inference; 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:lemma4392. - -skolem:lemma2598 a r:Inference; - r:gives { - (2 1 8 8) :sort (1 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 8) list:firstRest (2 (1 8 8))}] - skolem:lemma4770 - skolem:lemma4705 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((1) (2 8 8)) list:append (1 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2599 a r:Inference; +skolem:lemma2384 a r:Inference; r:gives { (1 2 8 8) :digitsToNumber 1288 . }; @@ -67181,9 +57864,9 @@ skolem:lemma2599 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2600 a r:Inference; +skolem:lemma2385 a r:Inference; r:gives { (8 8 2 1) :digitsToNumber 8821 . }; @@ -67201,42 +57884,9 @@ skolem:lemma2600 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2601 a r:Inference; - r:gives { - 7533 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4771 - skolem:lemma4772 - [ a r:Fact; r:gives {(3 3 5 7) list:reverse (7 5 3 3)}] - skolem:lemma4578 - skolem:lemma4579 - [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] - [ a r:Fact; r:gives {4176 math:notEqualTo 6174}] - skolem:lemma2026 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7533]; - 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 (3 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3357]; - 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_8"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2602 a r:Inference; +skolem:lemma2386 a r:Inference; r:gives { 2189 :numberToDigits (2 1 8 9). }; @@ -67255,32 +57905,9 @@ skolem:lemma2602 a r:Inference; 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:lemma4392. - -skolem:lemma2603 a r:Inference; - r:gives { - (2 1 8 9) :sort (1 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8 9) list:firstRest (2 (1 8 9))}] - skolem:lemma4773 - skolem:lemma4705 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((1) (2 8 9)) list:append (1 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 8 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_2"]; r:boundTo (1 8 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2604 a r:Inference; +skolem:lemma2387 a r:Inference; r:gives { (1 2 8 9) :digitsToNumber 1289 . }; @@ -67298,9 +57925,9 @@ skolem:lemma2604 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2605 a r:Inference; +skolem:lemma2388 a r:Inference; r:gives { (9 8 2 1) :digitsToNumber 9821 . }; @@ -67318,9 +57945,9 @@ skolem:lemma2605 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2606 a r:Inference; +skolem:lemma2389 a r:Inference; r:gives { 2190 :numberToDigits (2 1 9 0). }; @@ -67339,32 +57966,9 @@ skolem:lemma2606 a r:Inference; 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:lemma4392. - -skolem:lemma2607 a r:Inference; - r:gives { - (2 1 9 0) :sort (0 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 0) list:firstRest (2 (1 9 0))}] - skolem:lemma4774 - skolem:lemma4660 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 1) (2 9)) list:append (0 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2608 a r:Inference; +skolem:lemma2390 a r:Inference; r:gives { 2191 :numberToDigits (2 1 9 1). }; @@ -67383,32 +57987,9 @@ skolem:lemma2608 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2609 a r:Inference; - r:gives { - (2 1 9 1) :sort (1 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 1) list:firstRest (2 (1 9 1))}] - skolem:lemma4775 - skolem:lemma4680 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 1) (2 9)) list:append (1 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2610 a r:Inference; +skolem:lemma2391 a r:Inference; r:gives { 2192 :numberToDigits (2 1 9 2). }; @@ -67427,32 +58008,9 @@ skolem:lemma2610 a r:Inference; 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:lemma4392. - -skolem:lemma2611 a r:Inference; - r:gives { - (2 1 9 2) :sort (1 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 2) list:firstRest (2 (1 9 2))}] - skolem:lemma4776 - skolem:lemma4694 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 2) (2 9)) list:append (1 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2612 a r:Inference; +skolem:lemma2392 a r:Inference; r:gives { 2193 :numberToDigits (2 1 9 3). }; @@ -67471,32 +58029,9 @@ skolem:lemma2612 a r:Inference; 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:lemma4392. - -skolem:lemma2613 a r:Inference; - r:gives { - (2 1 9 3) :sort (1 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 3) list:firstRest (2 (1 9 3))}] - skolem:lemma4777 - skolem:lemma4705 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((1) (2 3 9)) list:append (1 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 3)]; - 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 3)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2614 a r:Inference; +skolem:lemma2393 a r:Inference; r:gives { 2194 :numberToDigits (2 1 9 4). }; @@ -67515,32 +58050,9 @@ skolem:lemma2614 a r:Inference; 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:lemma4392. - -skolem:lemma2615 a r:Inference; - r:gives { - (2 1 9 4) :sort (1 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 4) list:firstRest (2 (1 9 4))}] - skolem:lemma4778 - skolem:lemma4705 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((1) (2 4 9)) list:append (1 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 4)]; - 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 4)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2616 a r:Inference; +skolem:lemma2394 a r:Inference; r:gives { 2195 :numberToDigits (2 1 9 5). }; @@ -67559,32 +58071,9 @@ skolem:lemma2616 a r:Inference; 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:lemma4392. - -skolem:lemma2617 a r:Inference; - r:gives { - (2 1 9 5) :sort (1 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 5) list:firstRest (2 (1 9 5))}] - skolem:lemma4779 - skolem:lemma4705 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((1) (2 5 9)) list:append (1 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 5)]; - 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 5)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2618 a r:Inference; +skolem:lemma2395 a r:Inference; r:gives { 2196 :numberToDigits (2 1 9 6). }; @@ -67603,32 +58092,9 @@ skolem:lemma2618 a r:Inference; 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:lemma4392. - -skolem:lemma2619 a r:Inference; - r:gives { - (2 1 9 6) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 6) list:firstRest (2 (1 9 6))}] - skolem:lemma4780 - skolem:lemma4705 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((1) (2 6 9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 6)]; - 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 6)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2620 a r:Inference; +skolem:lemma2396 a r:Inference; r:gives { 2197 :numberToDigits (2 1 9 7). }; @@ -67647,32 +58113,9 @@ skolem:lemma2620 a r:Inference; 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:lemma4392. - -skolem:lemma2621 a r:Inference; - r:gives { - (2 1 9 7) :sort (1 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 7) list:firstRest (2 (1 9 7))}] - skolem:lemma4781 - skolem:lemma4705 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((1) (2 7 9)) list:append (1 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 7)]; - 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 7)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2622 a r:Inference; +skolem:lemma2397 a r:Inference; r:gives { 2198 :numberToDigits (2 1 9 8). }; @@ -67691,32 +58134,9 @@ skolem:lemma2622 a r:Inference; 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:lemma4392. - -skolem:lemma2623 a r:Inference; - r:gives { - (2 1 9 8) :sort (1 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 8) list:firstRest (2 (1 9 8))}] - skolem:lemma4782 - skolem:lemma4705 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((1) (2 8 9)) list:append (1 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 8)]; - 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 8)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2624 a r:Inference; +skolem:lemma2398 a r:Inference; r:gives { 2199 :numberToDigits (2 1 9 9). }; @@ -67735,32 +58155,9 @@ skolem:lemma2624 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2625 a r:Inference; - r:gives { - (2 1 9 9) :sort (1 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9 9) list:firstRest (2 (1 9 9))}] - skolem:lemma4783 - skolem:lemma4705 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((1) (2 9 9)) list:append (1 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 9 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_2"]; r:boundTo (1 9 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2626 a r:Inference; +skolem:lemma2399 a r:Inference; r:gives { (1 2 9 9) :digitsToNumber 1299 . }; @@ -67778,9 +58175,9 @@ skolem:lemma2626 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2627 a r:Inference; +skolem:lemma2400 a r:Inference; r:gives { (9 9 2 1) :digitsToNumber 9921 . }; @@ -67798,42 +58195,9 @@ skolem:lemma2627 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2628 a r:Inference; - r:gives { - 8622 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4784 - skolem:lemma4785 - [ a r:Fact; r:gives {(2 2 6 8) list:reverse (8 6 2 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {6354 math:notEqualTo 6174}] - skolem:lemma2244 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8622]; - 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 (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2268]; - 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_8"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2629 a r:Inference; +skolem:lemma2401 a r:Inference; r:gives { 2200 :numberToDigits (2 2 0 0). }; @@ -67852,32 +58216,9 @@ skolem:lemma2629 a r:Inference; 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:lemma4392. - -skolem:lemma2630 a r:Inference; - r:gives { - (2 2 0 0) :sort (0 0 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 0) list:firstRest (2 (2 0 0))}] - skolem:lemma4786 - skolem:lemma4787 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0 2) (2)) list:append (0 0 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2631 a r:Inference; +skolem:lemma2402 a r:Inference; r:gives { 2201 :numberToDigits (2 2 0 1). }; @@ -67896,32 +58237,9 @@ skolem:lemma2631 a r:Inference; 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:lemma4392. - -skolem:lemma2632 a r:Inference; - r:gives { - (2 2 0 1) :sort (0 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 1) list:firstRest (2 (2 0 1))}] - skolem:lemma4788 - skolem:lemma4789 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 2) (2)) list:append (0 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2633 a r:Inference; +skolem:lemma2403 a r:Inference; r:gives { 2202 :numberToDigits (2 2 0 2). }; @@ -67940,32 +58258,9 @@ skolem:lemma2633 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma2634 a r:Inference; - r:gives { - (2 2 0 2) :sort (0 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 2) list:firstRest (2 (2 0 2))}] - skolem:lemma4790 - skolem:lemma4791 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 2 2) (2)) list:append (0 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 2 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2635 a r:Inference; +skolem:lemma2404 a r:Inference; r:gives { 2203 :numberToDigits (2 2 0 3). }; @@ -67984,32 +58279,9 @@ skolem:lemma2635 a r:Inference; 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:lemma4392. - -skolem:lemma2636 a r:Inference; - r:gives { - (2 2 0 3) :sort (0 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 3) list:firstRest (2 (2 0 3))}] - skolem:lemma4792 - skolem:lemma4793 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 2) (2 3)) list:append (0 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2637 a r:Inference; +skolem:lemma2405 a r:Inference; r:gives { 2204 :numberToDigits (2 2 0 4). }; @@ -68028,32 +58300,9 @@ skolem:lemma2637 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2638 a r:Inference; - r:gives { - (2 2 0 4) :sort (0 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 4) list:firstRest (2 (2 0 4))}] - skolem:lemma4794 - skolem:lemma4793 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 2) (2 4)) list:append (0 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 4)]; - r:rule skolem:lemma4396. - -skolem:lemma2639 a r:Inference; +skolem:lemma2406 a r:Inference; r:gives { 2205 :numberToDigits (2 2 0 5). }; @@ -68072,32 +58321,9 @@ skolem:lemma2639 a r:Inference; 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:lemma4392. - -skolem:lemma2640 a r:Inference; - r:gives { - (2 2 0 5) :sort (0 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 5) list:firstRest (2 (2 0 5))}] - skolem:lemma4795 - skolem:lemma4793 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 2) (2 5)) list:append (0 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2641 a r:Inference; +skolem:lemma2407 a r:Inference; r:gives { 2206 :numberToDigits (2 2 0 6). }; @@ -68116,32 +58342,9 @@ skolem:lemma2641 a r:Inference; 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:lemma4392. - -skolem:lemma2642 a r:Inference; - r:gives { - (2 2 0 6) :sort (0 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 6) list:firstRest (2 (2 0 6))}] - skolem:lemma4796 - skolem:lemma4793 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 2) (2 6)) list:append (0 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2643 a r:Inference; +skolem:lemma2408 a r:Inference; r:gives { 2207 :numberToDigits (2 2 0 7). }; @@ -68160,32 +58363,9 @@ skolem:lemma2643 a r:Inference; 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:lemma4392. - -skolem:lemma2644 a r:Inference; - r:gives { - (2 2 0 7) :sort (0 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 7) list:firstRest (2 (2 0 7))}] - skolem:lemma4797 - skolem:lemma4793 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 2) (2 7)) list:append (0 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2645 a r:Inference; +skolem:lemma2409 a r:Inference; r:gives { 2208 :numberToDigits (2 2 0 8). }; @@ -68204,32 +58384,9 @@ skolem:lemma2645 a r:Inference; 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:lemma4392. - -skolem:lemma2646 a r:Inference; - r:gives { - (2 2 0 8) :sort (0 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 8) list:firstRest (2 (2 0 8))}] - skolem:lemma4798 - skolem:lemma4793 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 2) (2 8)) list:append (0 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2647 a r:Inference; +skolem:lemma2410 a r:Inference; r:gives { 2209 :numberToDigits (2 2 0 9). }; @@ -68248,32 +58405,9 @@ skolem:lemma2647 a r:Inference; 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:lemma4392. - -skolem:lemma2648 a r:Inference; - r:gives { - (2 2 0 9) :sort (0 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0 9) list:firstRest (2 (2 0 9))}] - skolem:lemma4799 - skolem:lemma4793 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 2) (2 9)) list:append (0 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 0 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_2"]; r:boundTo (2 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2649 a r:Inference; +skolem:lemma2411 a r:Inference; r:gives { 2210 :numberToDigits (2 2 1 0). }; @@ -68292,32 +58426,9 @@ skolem:lemma2649 a r:Inference; 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:lemma4392. - -skolem:lemma2650 a r:Inference; - r:gives { - (2 2 1 0) :sort (0 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 0) list:firstRest (2 (2 1 0))}] - skolem:lemma4800 - skolem:lemma4801 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1 2) (2)) list:append (0 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2651 a r:Inference; +skolem:lemma2412 a r:Inference; r:gives { 2211 :numberToDigits (2 2 1 1). }; @@ -68336,32 +58447,9 @@ skolem:lemma2651 a r:Inference; 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:lemma4392. - -skolem:lemma2652 a r:Inference; - r:gives { - (2 2 1 1) :sort (1 1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 1) list:firstRest (2 (2 1 1))}] - skolem:lemma4802 - skolem:lemma4803 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 1 2) (2)) list:append (1 1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 1 2 2)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2653 a r:Inference; +skolem:lemma2413 a r:Inference; r:gives { 2212 :numberToDigits (2 2 1 2). }; @@ -68380,32 +58468,9 @@ skolem:lemma2653 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2654 a r:Inference; - r:gives { - (2 2 1 2) :sort (1 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 2) list:firstRest (2 (2 1 2))}] - skolem:lemma4804 - skolem:lemma4805 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 2 2) (2)) list:append (1 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 2 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma2655 a r:Inference; +skolem:lemma2414 a r:Inference; r:gives { 2213 :numberToDigits (2 2 1 3). }; @@ -68424,32 +58489,9 @@ skolem:lemma2655 a r:Inference; 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:lemma4392. - -skolem:lemma2656 a r:Inference; - r:gives { - (2 2 1 3) :sort (1 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 3) list:firstRest (2 (2 1 3))}] - skolem:lemma4806 - skolem:lemma4807 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 2) (2 3)) list:append (1 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2657 a r:Inference; +skolem:lemma2415 a r:Inference; r:gives { 2214 :numberToDigits (2 2 1 4). }; @@ -68468,32 +58510,9 @@ skolem:lemma2657 a r:Inference; 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:lemma4392. - -skolem:lemma2658 a r:Inference; - r:gives { - (2 2 1 4) :sort (1 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 4) list:firstRest (2 (2 1 4))}] - skolem:lemma4808 - skolem:lemma4807 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 2) (2 4)) list:append (1 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2659 a r:Inference; +skolem:lemma2416 a r:Inference; r:gives { 2215 :numberToDigits (2 2 1 5). }; @@ -68512,32 +58531,9 @@ skolem:lemma2659 a r:Inference; 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:lemma4392. - -skolem:lemma2660 a r:Inference; - r:gives { - (2 2 1 5) :sort (1 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 5) list:firstRest (2 (2 1 5))}] - skolem:lemma4809 - skolem:lemma4807 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 2) (2 5)) list:append (1 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2661 a r:Inference; +skolem:lemma2417 a r:Inference; r:gives { 2216 :numberToDigits (2 2 1 6). }; @@ -68556,32 +58552,9 @@ skolem:lemma2661 a r:Inference; 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:lemma4392. - -skolem:lemma2662 a r:Inference; - r:gives { - (2 2 1 6) :sort (1 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 6) list:firstRest (2 (2 1 6))}] - skolem:lemma4810 - skolem:lemma4807 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 2) (2 6)) list:append (1 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2663 a r:Inference; +skolem:lemma2418 a r:Inference; r:gives { 2217 :numberToDigits (2 2 1 7). }; @@ -68600,32 +58573,9 @@ skolem:lemma2663 a r:Inference; 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:lemma4392. - -skolem:lemma2664 a r:Inference; - r:gives { - (2 2 1 7) :sort (1 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 7) list:firstRest (2 (2 1 7))}] - skolem:lemma4811 - skolem:lemma4807 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 2) (2 7)) list:append (1 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2665 a r:Inference; +skolem:lemma2419 a r:Inference; r:gives { 2218 :numberToDigits (2 2 1 8). }; @@ -68644,32 +58594,9 @@ skolem:lemma2665 a r:Inference; 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:lemma4392. - -skolem:lemma2666 a r:Inference; - r:gives { - (2 2 1 8) :sort (1 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 8) list:firstRest (2 (2 1 8))}] - skolem:lemma4812 - skolem:lemma4807 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 2) (2 8)) list:append (1 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2667 a r:Inference; +skolem:lemma2420 a r:Inference; r:gives { 2219 :numberToDigits (2 2 1 9). }; @@ -68688,32 +58615,9 @@ skolem:lemma2667 a r:Inference; 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:lemma4392. - -skolem:lemma2668 a r:Inference; - r:gives { - (2 2 1 9) :sort (1 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1 9) list:firstRest (2 (2 1 9))}] - skolem:lemma4813 - skolem:lemma4807 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 2) (2 9)) list:append (1 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 1 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_2"]; r:boundTo (2 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2669 a r:Inference; +skolem:lemma2421 a r:Inference; r:gives { 2220 :numberToDigits (2 2 2 0). }; @@ -68732,32 +58636,9 @@ skolem:lemma2669 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2670 a r:Inference; - r:gives { - (2 2 2 0) :sort (0 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 0) list:firstRest (2 (2 2 0))}] - skolem:lemma4814 - skolem:lemma4815 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 2 2) (2)) list:append (0 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 2 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma2671 a r:Inference; +skolem:lemma2422 a r:Inference; r:gives { 2221 :numberToDigits (2 2 2 1). }; @@ -68776,105 +58657,9 @@ skolem:lemma2671 a r:Inference; 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:lemma4392. - -skolem:lemma2672 a r:Inference; - r:gives { - (2 2 2 1) :sort (1 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 1) list:firstRest (2 (2 2 1))}] - skolem:lemma4816 - skolem:lemma4817 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 2 2) (2)) list:append (1 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 2 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma2673 a r:Inference; - r:gives { - 2222 :numberToDigits (2 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2222 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2222 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2222]; - 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:lemma4392. - -skolem:lemma2674 a r:Inference; - r:gives { - (2 2 2 2) :sort (2 2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 2) list:firstRest (2 (2 2 2))}] - skolem:lemma4818 - skolem:lemma4819 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((2 2 2) (2)) list:append (2 2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (2 2 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma2675 a r:Inference; - r:gives { - (2 2 2 2) :digitsToNumber 2222 . - }; - 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 2) math:sum 2222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 2222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma4397. - -skolem:lemma2676 a r:Inference; - r:gives { - 0 :kaprekar 0 . - }; - r:evidence ( - [ a r:Fact; r:gives {true log:callWithCut true}] - ); - r:rule skolem:lemma4820. + r:rule skolem:lemma3438. -skolem:lemma2677 a r:Inference; +skolem:lemma2423 a r:Inference; r:gives { 2223 :numberToDigits (2 2 2 3). }; @@ -68893,32 +58678,9 @@ skolem:lemma2677 a r:Inference; 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:lemma4392. - -skolem:lemma2678 a r:Inference; - r:gives { - (2 2 2 3) :sort (2 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 3) list:firstRest (2 (2 2 3))}] - skolem:lemma4821 - skolem:lemma4822 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((2 2) (2 3)) list:append (2 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2679 a r:Inference; +skolem:lemma2424 a r:Inference; r:gives { (2 2 2 3) :digitsToNumber 2223 . }; @@ -68936,9 +58698,9 @@ skolem:lemma2679 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2680 a r:Inference; +skolem:lemma2425 a r:Inference; r:gives { (3 2 2 2) :digitsToNumber 3222 . }; @@ -68956,9 +58718,9 @@ skolem:lemma2680 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2681 a r:Inference; +skolem:lemma2426 a r:Inference; r:gives { 2224 :numberToDigits (2 2 2 4). }; @@ -68977,32 +58739,9 @@ skolem:lemma2681 a r:Inference; 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:lemma4392. - -skolem:lemma2682 a r:Inference; - r:gives { - (2 2 2 4) :sort (2 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 4) list:firstRest (2 (2 2 4))}] - skolem:lemma4823 - skolem:lemma4822 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((2 2) (2 4)) list:append (2 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2683 a r:Inference; +skolem:lemma2427 a r:Inference; r:gives { (2 2 2 4) :digitsToNumber 2224 . }; @@ -69020,9 +58759,9 @@ skolem:lemma2683 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2684 a r:Inference; +skolem:lemma2428 a r:Inference; r:gives { (4 2 2 2) :digitsToNumber 4222 . }; @@ -69040,9 +58779,9 @@ skolem:lemma2684 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2685 a r:Inference; +skolem:lemma2429 a r:Inference; r:gives { 2225 :numberToDigits (2 2 2 5). }; @@ -69061,32 +58800,9 @@ skolem:lemma2685 a r:Inference; 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:lemma4392. - -skolem:lemma2686 a r:Inference; - r:gives { - (2 2 2 5) :sort (2 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 5) list:firstRest (2 (2 2 5))}] - skolem:lemma4824 - skolem:lemma4822 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((2 2) (2 5)) list:append (2 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2687 a r:Inference; +skolem:lemma2430 a r:Inference; r:gives { (2 2 2 5) :digitsToNumber 2225 . }; @@ -69104,9 +58820,9 @@ skolem:lemma2687 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2688 a r:Inference; +skolem:lemma2431 a r:Inference; r:gives { (5 2 2 2) :digitsToNumber 5222 . }; @@ -69124,9 +58840,9 @@ skolem:lemma2688 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2689 a r:Inference; +skolem:lemma2432 a r:Inference; r:gives { 2226 :numberToDigits (2 2 2 6). }; @@ -69145,32 +58861,9 @@ skolem:lemma2689 a r:Inference; 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:lemma4392. - -skolem:lemma2690 a r:Inference; - r:gives { - (2 2 2 6) :sort (2 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 6) list:firstRest (2 (2 2 6))}] - skolem:lemma4825 - skolem:lemma4822 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((2 2) (2 6)) list:append (2 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2691 a r:Inference; +skolem:lemma2433 a r:Inference; r:gives { (2 2 2 6) :digitsToNumber 2226 . }; @@ -69188,9 +58881,9 @@ skolem:lemma2691 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2692 a r:Inference; +skolem:lemma2434 a r:Inference; r:gives { (6 2 2 2) :digitsToNumber 6222 . }; @@ -69208,9 +58901,9 @@ skolem:lemma2692 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2693 a r:Inference; +skolem:lemma2435 a r:Inference; r:gives { 2227 :numberToDigits (2 2 2 7). }; @@ -69229,40 +58922,17 @@ skolem:lemma2693 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2694 a r:Inference; +skolem:lemma2436 a r:Inference; r:gives { - (2 2 2 7) :sort (2 2 2 7). + (2 2 2 7) :digitsToNumber 2227 . }; r:evidence ( - [ a r:Fact; r:gives {(2 2 2 7) list:firstRest (2 (2 2 7))}] - skolem:lemma4826 - skolem:lemma4822 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((2 2) (2 7)) list:append (2 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2695 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}] + [ 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]; @@ -69272,9 +58942,9 @@ skolem:lemma2695 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2696 a r:Inference; +skolem:lemma2437 a r:Inference; r:gives { (7 2 2 2) :digitsToNumber 7222 . }; @@ -69292,9 +58962,9 @@ skolem:lemma2696 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2697 a r:Inference; +skolem:lemma2438 a r:Inference; r:gives { 2228 :numberToDigits (2 2 2 8). }; @@ -69313,32 +58983,9 @@ skolem:lemma2697 a r:Inference; 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:lemma4392. - -skolem:lemma2698 a r:Inference; - r:gives { - (2 2 2 8) :sort (2 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 8) list:firstRest (2 (2 2 8))}] - skolem:lemma4827 - skolem:lemma4822 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((2 2) (2 8)) list:append (2 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2699 a r:Inference; +skolem:lemma2439 a r:Inference; r:gives { (2 2 2 8) :digitsToNumber 2228 . }; @@ -69356,9 +59003,9 @@ skolem:lemma2699 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2700 a r:Inference; +skolem:lemma2440 a r:Inference; r:gives { (8 2 2 2) :digitsToNumber 8222 . }; @@ -69376,9 +59023,9 @@ skolem:lemma2700 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2701 a r:Inference; +skolem:lemma2441 a r:Inference; r:gives { 2229 :numberToDigits (2 2 2 9). }; @@ -69397,32 +59044,9 @@ skolem:lemma2701 a r:Inference; 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:lemma4392. - -skolem:lemma2702 a r:Inference; - r:gives { - (2 2 2 9) :sort (2 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2 9) list:firstRest (2 (2 2 9))}] - skolem:lemma4828 - skolem:lemma4822 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((2 2) (2 9)) list:append (2 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 2 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_2"]; r:boundTo (2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2703 a r:Inference; +skolem:lemma2442 a r:Inference; r:gives { (2 2 2 9) :digitsToNumber 2229 . }; @@ -69440,9 +59064,9 @@ skolem:lemma2703 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2704 a r:Inference; +skolem:lemma2443 a r:Inference; r:gives { (9 2 2 2) :digitsToNumber 9222 . }; @@ -69460,9 +59084,9 @@ skolem:lemma2704 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2705 a r:Inference; +skolem:lemma2444 a r:Inference; r:gives { 2230 :numberToDigits (2 2 3 0). }; @@ -69481,32 +59105,9 @@ skolem:lemma2705 a r:Inference; 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:lemma4392. - -skolem:lemma2706 a r:Inference; - r:gives { - (2 2 3 0) :sort (0 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 0) list:firstRest (2 (2 3 0))}] - skolem:lemma4829 - skolem:lemma4793 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 2) (2 3)) list:append (0 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2707 a r:Inference; +skolem:lemma2445 a r:Inference; r:gives { 2231 :numberToDigits (2 2 3 1). }; @@ -69525,32 +59126,9 @@ skolem:lemma2707 a r:Inference; 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:lemma4392. - -skolem:lemma2708 a r:Inference; - r:gives { - (2 2 3 1) :sort (1 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 1) list:firstRest (2 (2 3 1))}] - skolem:lemma4830 - skolem:lemma4807 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 2) (2 3)) list:append (1 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2709 a r:Inference; +skolem:lemma2446 a r:Inference; r:gives { 2232 :numberToDigits (2 2 3 2). }; @@ -69569,32 +59147,9 @@ skolem:lemma2709 a r:Inference; 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:lemma4392. - -skolem:lemma2710 a r:Inference; - r:gives { - (2 2 3 2) :sort (2 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 2) list:firstRest (2 (2 3 2))}] - skolem:lemma4831 - skolem:lemma4822 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((2 2) (2 3)) list:append (2 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2711 a r:Inference; +skolem:lemma2447 a r:Inference; r:gives { 2233 :numberToDigits (2 2 3 3). }; @@ -69613,32 +59168,9 @@ skolem:lemma2711 a r:Inference; 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:lemma4392. - -skolem:lemma2712 a r:Inference; - r:gives { - (2 2 3 3) :sort (2 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 3) list:firstRest (2 (2 3 3))}] - skolem:lemma4832 - skolem:lemma4833 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((2) (2 3 3)) list:append (2 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 3)]; - 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 3)]; - 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2713 a r:Inference; +skolem:lemma2448 a r:Inference; r:gives { (2 2 3 3) :digitsToNumber 2233 . }; @@ -69656,9 +59188,9 @@ skolem:lemma2713 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2714 a r:Inference; +skolem:lemma2449 a r:Inference; r:gives { (3 3 2 2) :digitsToNumber 3322 . }; @@ -69676,9 +59208,9 @@ skolem:lemma2714 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2715 a r:Inference; +skolem:lemma2450 a r:Inference; r:gives { 2234 :numberToDigits (2 2 3 4). }; @@ -69697,32 +59229,9 @@ skolem:lemma2715 a r:Inference; 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:lemma4392. - -skolem:lemma2716 a r:Inference; - r:gives { - (2 2 3 4) :sort (2 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 4) list:firstRest (2 (2 3 4))}] - skolem:lemma4834 - skolem:lemma4833 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((2) (2 3 4)) list:append (2 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2717 a r:Inference; +skolem:lemma2451 a r:Inference; r:gives { (2 2 3 4) :digitsToNumber 2234 . }; @@ -69740,9 +59249,9 @@ skolem:lemma2717 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2718 a r:Inference; +skolem:lemma2452 a r:Inference; r:gives { (4 3 2 2) :digitsToNumber 4322 . }; @@ -69760,9 +59269,9 @@ skolem:lemma2718 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2719 a r:Inference; +skolem:lemma2453 a r:Inference; r:gives { 2235 :numberToDigits (2 2 3 5). }; @@ -69781,32 +59290,9 @@ skolem:lemma2719 a r:Inference; 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:lemma4392. - -skolem:lemma2720 a r:Inference; - r:gives { - (2 2 3 5) :sort (2 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 5) list:firstRest (2 (2 3 5))}] - skolem:lemma4835 - skolem:lemma4833 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((2) (2 3 5)) list:append (2 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2721 a r:Inference; +skolem:lemma2454 a r:Inference; r:gives { (2 2 3 5) :digitsToNumber 2235 . }; @@ -69824,9 +59310,9 @@ skolem:lemma2721 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2722 a r:Inference; +skolem:lemma2455 a r:Inference; r:gives { (5 3 2 2) :digitsToNumber 5322 . }; @@ -69844,9 +59330,9 @@ skolem:lemma2722 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2723 a r:Inference; +skolem:lemma2456 a r:Inference; r:gives { 2236 :numberToDigits (2 2 3 6). }; @@ -69865,32 +59351,9 @@ skolem:lemma2723 a r:Inference; 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:lemma4392. - -skolem:lemma2724 a r:Inference; - r:gives { - (2 2 3 6) :sort (2 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 6) list:firstRest (2 (2 3 6))}] - skolem:lemma4836 - skolem:lemma4833 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((2) (2 3 6)) list:append (2 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2725 a r:Inference; +skolem:lemma2457 a r:Inference; r:gives { (2 2 3 6) :digitsToNumber 2236 . }; @@ -69908,9 +59371,9 @@ skolem:lemma2725 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2726 a r:Inference; +skolem:lemma2458 a r:Inference; r:gives { (6 3 2 2) :digitsToNumber 6322 . }; @@ -69928,9 +59391,9 @@ skolem:lemma2726 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2727 a r:Inference; +skolem:lemma2459 a r:Inference; r:gives { 2237 :numberToDigits (2 2 3 7). }; @@ -69949,32 +59412,9 @@ skolem:lemma2727 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2728 a r:Inference; - r:gives { - (2 2 3 7) :sort (2 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 7) list:firstRest (2 (2 3 7))}] - skolem:lemma4837 - skolem:lemma4833 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((2) (2 3 7)) list:append (2 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2729 a r:Inference; +skolem:lemma2460 a r:Inference; r:gives { (2 2 3 7) :digitsToNumber 2237 . }; @@ -69992,9 +59432,9 @@ skolem:lemma2729 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2730 a r:Inference; +skolem:lemma2461 a r:Inference; r:gives { (7 3 2 2) :digitsToNumber 7322 . }; @@ -70012,9 +59452,9 @@ skolem:lemma2730 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2731 a r:Inference; +skolem:lemma2462 a r:Inference; r:gives { 2238 :numberToDigits (2 2 3 8). }; @@ -70033,32 +59473,9 @@ skolem:lemma2731 a r:Inference; 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:lemma4392. - -skolem:lemma2732 a r:Inference; - r:gives { - (2 2 3 8) :sort (2 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 8) list:firstRest (2 (2 3 8))}] - skolem:lemma4838 - skolem:lemma4833 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((2) (2 3 8)) list:append (2 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2733 a r:Inference; +skolem:lemma2463 a r:Inference; r:gives { (2 2 3 8) :digitsToNumber 2238 . }; @@ -70076,9 +59493,9 @@ skolem:lemma2733 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2734 a r:Inference; +skolem:lemma2464 a r:Inference; r:gives { (8 3 2 2) :digitsToNumber 8322 . }; @@ -70096,9 +59513,9 @@ skolem:lemma2734 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2735 a r:Inference; +skolem:lemma2465 a r:Inference; r:gives { 2239 :numberToDigits (2 2 3 9). }; @@ -70117,32 +59534,9 @@ skolem:lemma2735 a r:Inference; 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:lemma4392. - -skolem:lemma2736 a r:Inference; - r:gives { - (2 2 3 9) :sort (2 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3 9) list:firstRest (2 (2 3 9))}] - skolem:lemma4839 - skolem:lemma4833 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((2) (2 3 9)) list:append (2 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 3 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_2"]; r:boundTo (2 3 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2737 a r:Inference; +skolem:lemma2466 a r:Inference; r:gives { (2 2 3 9) :digitsToNumber 2239 . }; @@ -70160,9 +59554,9 @@ skolem:lemma2737 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2738 a r:Inference; +skolem:lemma2467 a r:Inference; r:gives { (9 3 2 2) :digitsToNumber 9322 . }; @@ -70180,9 +59574,9 @@ skolem:lemma2738 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2739 a r:Inference; +skolem:lemma2468 a r:Inference; r:gives { 2240 :numberToDigits (2 2 4 0). }; @@ -70201,32 +59595,9 @@ skolem:lemma2739 a r:Inference; 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:lemma4392. - -skolem:lemma2740 a r:Inference; - r:gives { - (2 2 4 0) :sort (0 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 0) list:firstRest (2 (2 4 0))}] - skolem:lemma4840 - skolem:lemma4793 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 2) (2 4)) list:append (0 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2741 a r:Inference; +skolem:lemma2469 a r:Inference; r:gives { 2241 :numberToDigits (2 2 4 1). }; @@ -70245,32 +59616,9 @@ skolem:lemma2741 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2742 a r:Inference; - r:gives { - (2 2 4 1) :sort (1 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 1) list:firstRest (2 (2 4 1))}] - skolem:lemma4841 - skolem:lemma4807 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 2) (2 4)) list:append (1 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 4)]; - r:rule skolem:lemma4396. - -skolem:lemma2743 a r:Inference; +skolem:lemma2470 a r:Inference; r:gives { 2242 :numberToDigits (2 2 4 2). }; @@ -70289,32 +59637,9 @@ skolem:lemma2743 a r:Inference; 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:lemma4392. - -skolem:lemma2744 a r:Inference; - r:gives { - (2 2 4 2) :sort (2 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 2) list:firstRest (2 (2 4 2))}] - skolem:lemma4842 - skolem:lemma4822 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((2 2) (2 4)) list:append (2 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2745 a r:Inference; +skolem:lemma2471 a r:Inference; r:gives { 2243 :numberToDigits (2 2 4 3). }; @@ -70333,32 +59658,9 @@ skolem:lemma2745 a r:Inference; 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:lemma4392. - -skolem:lemma2746 a r:Inference; - r:gives { - (2 2 4 3) :sort (2 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 3) list:firstRest (2 (2 4 3))}] - skolem:lemma4843 - skolem:lemma4833 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((2) (2 3 4)) list:append (2 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 3)]; - 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 3)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2747 a r:Inference; +skolem:lemma2472 a r:Inference; r:gives { 2244 :numberToDigits (2 2 4 4). }; @@ -70377,32 +59679,9 @@ skolem:lemma2747 a r:Inference; 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:lemma4392. - -skolem:lemma2748 a r:Inference; - r:gives { - (2 2 4 4) :sort (2 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 4) list:firstRest (2 (2 4 4))}] - skolem:lemma4844 - skolem:lemma4833 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((2) (2 4 4)) list:append (2 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2749 a r:Inference; +skolem:lemma2473 a r:Inference; r:gives { (2 2 4 4) :digitsToNumber 2244 . }; @@ -70420,9 +59699,9 @@ skolem:lemma2749 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2750 a r:Inference; +skolem:lemma2474 a r:Inference; r:gives { (4 4 2 2) :digitsToNumber 4422 . }; @@ -70440,9 +59719,9 @@ skolem:lemma2750 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2751 a r:Inference; +skolem:lemma2475 a r:Inference; r:gives { 2245 :numberToDigits (2 2 4 5). }; @@ -70461,32 +59740,9 @@ skolem:lemma2751 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2752 a r:Inference; - r:gives { - (2 2 4 5) :sort (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 5) list:firstRest (2 (2 4 5))}] - skolem:lemma4845 - skolem:lemma4833 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((2) (2 4 5)) list:append (2 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma2753 a r:Inference; +skolem:lemma2476 a r:Inference; r:gives { (2 2 4 5) :digitsToNumber 2245 . }; @@ -70504,9 +59760,9 @@ skolem:lemma2753 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2754 a r:Inference; +skolem:lemma2477 a r:Inference; r:gives { (5 4 2 2) :digitsToNumber 5422 . }; @@ -70524,9 +59780,9 @@ skolem:lemma2754 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2755 a r:Inference; +skolem:lemma2478 a r:Inference; r:gives { 2246 :numberToDigits (2 2 4 6). }; @@ -70545,32 +59801,9 @@ skolem:lemma2755 a r:Inference; 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:lemma4392. - -skolem:lemma2756 a r:Inference; - r:gives { - (2 2 4 6) :sort (2 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 6) list:firstRest (2 (2 4 6))}] - skolem:lemma4846 - skolem:lemma4833 - skolem:lemma4719 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((2) (2 4 6)) list:append (2 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2757 a r:Inference; +skolem:lemma2479 a r:Inference; r:gives { (2 2 4 6) :digitsToNumber 2246 . }; @@ -70588,9 +59821,9 @@ skolem:lemma2757 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2758 a r:Inference; +skolem:lemma2480 a r:Inference; r:gives { (6 4 2 2) :digitsToNumber 6422 . }; @@ -70608,9 +59841,9 @@ skolem:lemma2758 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2759 a r:Inference; +skolem:lemma2481 a r:Inference; r:gives { 2247 :numberToDigits (2 2 4 7). }; @@ -70629,32 +59862,9 @@ skolem:lemma2759 a r:Inference; 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:lemma4392. - -skolem:lemma2760 a r:Inference; - r:gives { - (2 2 4 7) :sort (2 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 7) list:firstRest (2 (2 4 7))}] - skolem:lemma4847 - skolem:lemma4833 - skolem:lemma4530 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((2) (2 4 7)) list:append (2 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2761 a r:Inference; +skolem:lemma2482 a r:Inference; r:gives { (2 2 4 7) :digitsToNumber 2247 . }; @@ -70672,9 +59882,9 @@ skolem:lemma2761 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2762 a r:Inference; +skolem:lemma2483 a r:Inference; r:gives { (7 4 2 2) :digitsToNumber 7422 . }; @@ -70692,9 +59902,70 @@ skolem:lemma2762 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2763 a r:Inference; +skolem:lemma2484 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: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. + +skolem:lemma2487 a r:Inference; r:gives { 2249 :numberToDigits (2 2 4 9). }; @@ -70713,32 +59984,9 @@ skolem:lemma2763 a r:Inference; 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:lemma4392. - -skolem:lemma2764 a r:Inference; - r:gives { - (2 2 4 9) :sort (2 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4 9) list:firstRest (2 (2 4 9))}] - skolem:lemma4848 - skolem:lemma4833 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((2) (2 4 9)) list:append (2 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 4 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_2"]; r:boundTo (2 4 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2765 a r:Inference; +skolem:lemma2488 a r:Inference; r:gives { (2 2 4 9) :digitsToNumber 2249 . }; @@ -70756,9 +60004,9 @@ skolem:lemma2765 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2766 a r:Inference; +skolem:lemma2489 a r:Inference; r:gives { (9 4 2 2) :digitsToNumber 9422 . }; @@ -70776,9 +60024,9 @@ skolem:lemma2766 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2767 a r:Inference; +skolem:lemma2490 a r:Inference; r:gives { 2250 :numberToDigits (2 2 5 0). }; @@ -70797,32 +60045,9 @@ skolem:lemma2767 a r:Inference; 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:lemma4392. - -skolem:lemma2768 a r:Inference; - r:gives { - (2 2 5 0) :sort (0 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 0) list:firstRest (2 (2 5 0))}] - skolem:lemma4849 - skolem:lemma4793 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 2) (2 5)) list:append (0 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2769 a r:Inference; +skolem:lemma2491 a r:Inference; r:gives { 2251 :numberToDigits (2 2 5 1). }; @@ -70841,32 +60066,9 @@ skolem:lemma2769 a r:Inference; 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:lemma4392. - -skolem:lemma2770 a r:Inference; - r:gives { - (2 2 5 1) :sort (1 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 1) list:firstRest (2 (2 5 1))}] - skolem:lemma4850 - skolem:lemma4807 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 2) (2 5)) list:append (1 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2771 a r:Inference; +skolem:lemma2492 a r:Inference; r:gives { 2252 :numberToDigits (2 2 5 2). }; @@ -70885,32 +60087,9 @@ skolem:lemma2771 a r:Inference; 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:lemma4392. - -skolem:lemma2772 a r:Inference; - r:gives { - (2 2 5 2) :sort (2 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 2) list:firstRest (2 (2 5 2))}] - skolem:lemma4851 - skolem:lemma4822 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((2 2) (2 5)) list:append (2 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2773 a r:Inference; +skolem:lemma2493 a r:Inference; r:gives { 2253 :numberToDigits (2 2 5 3). }; @@ -70929,32 +60108,9 @@ skolem:lemma2773 a r:Inference; 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:lemma4392. - -skolem:lemma2774 a r:Inference; - r:gives { - (2 2 5 3) :sort (2 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 3) list:firstRest (2 (2 5 3))}] - skolem:lemma4852 - skolem:lemma4833 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((2) (2 3 5)) list:append (2 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 3)]; - 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 3)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2775 a r:Inference; +skolem:lemma2494 a r:Inference; r:gives { 2254 :numberToDigits (2 2 5 4). }; @@ -70973,32 +60129,9 @@ skolem:lemma2775 a r:Inference; 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:lemma4392. - -skolem:lemma2776 a r:Inference; - r:gives { - (2 2 5 4) :sort (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 4) list:firstRest (2 (2 5 4))}] - skolem:lemma4853 - skolem:lemma4833 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((2) (2 4 5)) list:append (2 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 4)]; - 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 4)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2777 a r:Inference; +skolem:lemma2495 a r:Inference; r:gives { 2255 :numberToDigits (2 2 5 5). }; @@ -71017,32 +60150,9 @@ skolem:lemma2777 a r:Inference; 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:lemma4392. - -skolem:lemma2778 a r:Inference; - r:gives { - (2 2 5 5) :sort (2 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 5) list:firstRest (2 (2 5 5))}] - skolem:lemma4854 - skolem:lemma4833 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((2) (2 5 5)) list:append (2 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2779 a r:Inference; +skolem:lemma2496 a r:Inference; r:gives { (2 2 5 5) :digitsToNumber 2255 . }; @@ -71060,9 +60170,9 @@ skolem:lemma2779 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2780 a r:Inference; +skolem:lemma2497 a r:Inference; r:gives { (5 5 2 2) :digitsToNumber 5522 . }; @@ -71080,42 +60190,9 @@ skolem:lemma2780 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2781 a r:Inference; - r:gives { - 3267 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4855 - skolem:lemma4856 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2782 a r:Inference; +skolem:lemma2498 a r:Inference; r:gives { 2256 :numberToDigits (2 2 5 6). }; @@ -71134,32 +60211,9 @@ skolem:lemma2782 a r:Inference; 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:lemma4392. - -skolem:lemma2783 a r:Inference; - r:gives { - (2 2 5 6) :sort (2 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 6) list:firstRest (2 (2 5 6))}] - skolem:lemma4857 - skolem:lemma4833 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((2) (2 5 6)) list:append (2 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2784 a r:Inference; +skolem:lemma2499 a r:Inference; r:gives { (2 2 5 6) :digitsToNumber 2256 . }; @@ -71177,9 +60231,9 @@ skolem:lemma2784 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2785 a r:Inference; +skolem:lemma2500 a r:Inference; r:gives { (6 5 2 2) :digitsToNumber 6522 . }; @@ -71197,9 +60251,9 @@ skolem:lemma2785 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2786 a r:Inference; +skolem:lemma2501 a r:Inference; r:gives { 2257 :numberToDigits (2 2 5 7). }; @@ -71218,32 +60272,9 @@ skolem:lemma2786 a r:Inference; 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:lemma4392. - -skolem:lemma2787 a r:Inference; - r:gives { - (2 2 5 7) :sort (2 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 7) list:firstRest (2 (2 5 7))}] - skolem:lemma4858 - skolem:lemma4833 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((2) (2 5 7)) list:append (2 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2788 a r:Inference; +skolem:lemma2502 a r:Inference; r:gives { (2 2 5 7) :digitsToNumber 2257 . }; @@ -71261,9 +60292,9 @@ skolem:lemma2788 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2789 a r:Inference; +skolem:lemma2503 a r:Inference; r:gives { (7 5 2 2) :digitsToNumber 7522 . }; @@ -71281,9 +60312,9 @@ skolem:lemma2789 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2790 a r:Inference; +skolem:lemma2504 a r:Inference; r:gives { 2258 :numberToDigits (2 2 5 8). }; @@ -71302,32 +60333,9 @@ skolem:lemma2790 a r:Inference; 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:lemma4392. - -skolem:lemma2791 a r:Inference; - r:gives { - (2 2 5 8) :sort (2 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 8) list:firstRest (2 (2 5 8))}] - skolem:lemma4859 - skolem:lemma4833 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((2) (2 5 8)) list:append (2 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2792 a r:Inference; +skolem:lemma2505 a r:Inference; r:gives { (2 2 5 8) :digitsToNumber 2258 . }; @@ -71345,9 +60353,9 @@ skolem:lemma2792 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2793 a r:Inference; +skolem:lemma2506 a r:Inference; r:gives { (8 5 2 2) :digitsToNumber 8522 . }; @@ -71365,9 +60373,9 @@ skolem:lemma2793 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2794 a r:Inference; +skolem:lemma2507 a r:Inference; r:gives { 2259 :numberToDigits (2 2 5 9). }; @@ -71386,32 +60394,9 @@ skolem:lemma2794 a r:Inference; 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:lemma4392. - -skolem:lemma2795 a r:Inference; - r:gives { - (2 2 5 9) :sort (2 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5 9) list:firstRest (2 (2 5 9))}] - skolem:lemma4860 - skolem:lemma4833 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((2) (2 5 9)) list:append (2 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 5 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_2"]; r:boundTo (2 5 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2796 a r:Inference; +skolem:lemma2508 a r:Inference; r:gives { (2 2 5 9) :digitsToNumber 2259 . }; @@ -71429,9 +60414,9 @@ skolem:lemma2796 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2797 a r:Inference; +skolem:lemma2509 a r:Inference; r:gives { (9 5 2 2) :digitsToNumber 9522 . }; @@ -71449,9 +60434,9 @@ skolem:lemma2797 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2798 a r:Inference; +skolem:lemma2510 a r:Inference; r:gives { 2260 :numberToDigits (2 2 6 0). }; @@ -71470,32 +60455,9 @@ skolem:lemma2798 a r:Inference; 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:lemma4392. - -skolem:lemma2799 a r:Inference; - r:gives { - (2 2 6 0) :sort (0 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 0) list:firstRest (2 (2 6 0))}] - skolem:lemma4861 - skolem:lemma4793 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 2) (2 6)) list:append (0 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2800 a r:Inference; +skolem:lemma2511 a r:Inference; r:gives { 2261 :numberToDigits (2 2 6 1). }; @@ -71514,32 +60476,9 @@ skolem:lemma2800 a r:Inference; 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:lemma4392. - -skolem:lemma2801 a r:Inference; - r:gives { - (2 2 6 1) :sort (1 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 1) list:firstRest (2 (2 6 1))}] - skolem:lemma4862 - skolem:lemma4807 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 2) (2 6)) list:append (1 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2802 a r:Inference; +skolem:lemma2512 a r:Inference; r:gives { 2262 :numberToDigits (2 2 6 2). }; @@ -71558,32 +60497,9 @@ skolem:lemma2802 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2803 a r:Inference; - r:gives { - (2 2 6 2) :sort (2 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 2) list:firstRest (2 (2 6 2))}] - skolem:lemma4863 - skolem:lemma4822 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((2 2) (2 6)) list:append (2 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma2804 a r:Inference; +skolem:lemma2513 a r:Inference; r:gives { 2263 :numberToDigits (2 2 6 3). }; @@ -71602,32 +60518,9 @@ skolem:lemma2804 a r:Inference; 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:lemma4392. - -skolem:lemma2805 a r:Inference; - r:gives { - (2 2 6 3) :sort (2 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 3) list:firstRest (2 (2 6 3))}] - skolem:lemma4864 - skolem:lemma4833 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((2) (2 3 6)) list:append (2 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 3)]; - 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 3)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2806 a r:Inference; +skolem:lemma2514 a r:Inference; r:gives { 2264 :numberToDigits (2 2 6 4). }; @@ -71646,32 +60539,9 @@ skolem:lemma2806 a r:Inference; 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:lemma4392. - -skolem:lemma2807 a r:Inference; - r:gives { - (2 2 6 4) :sort (2 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 4) list:firstRest (2 (2 6 4))}] - skolem:lemma4865 - skolem:lemma4833 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((2) (2 4 6)) list:append (2 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 4)]; - 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 4)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2808 a r:Inference; +skolem:lemma2515 a r:Inference; r:gives { 2265 :numberToDigits (2 2 6 5). }; @@ -71690,32 +60560,9 @@ skolem:lemma2808 a r:Inference; 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:lemma4392. - -skolem:lemma2809 a r:Inference; - r:gives { - (2 2 6 5) :sort (2 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 5) list:firstRest (2 (2 6 5))}] - skolem:lemma4866 - skolem:lemma4833 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((2) (2 5 6)) list:append (2 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 5)]; - 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 5)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2810 a r:Inference; +skolem:lemma2516 a r:Inference; r:gives { 2266 :numberToDigits (2 2 6 6). }; @@ -71734,32 +60581,9 @@ skolem:lemma2810 a r:Inference; 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:lemma4392. - -skolem:lemma2811 a r:Inference; - r:gives { - (2 2 6 6) :sort (2 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 6) list:firstRest (2 (2 6 6))}] - skolem:lemma4867 - skolem:lemma4833 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((2) (2 6 6)) list:append (2 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2812 a r:Inference; +skolem:lemma2517 a r:Inference; r:gives { (2 2 6 6) :digitsToNumber 2266 . }; @@ -71777,9 +60601,9 @@ skolem:lemma2812 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2813 a r:Inference; +skolem:lemma2518 a r:Inference; r:gives { (6 6 2 2) :digitsToNumber 6622 . }; @@ -71797,42 +60621,9 @@ skolem:lemma2813 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2814 a r:Inference; - r:gives { - 4356 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4868 - skolem:lemma4869 - [ a r:Fact; r:gives {(3 4 5 6) list:reverse (6 5 4 3)}] - skolem:lemma4572 - skolem:lemma4573 - [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3456]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2815 a r:Inference; +skolem:lemma2519 a r:Inference; r:gives { 2267 :numberToDigits (2 2 6 7). }; @@ -71851,40 +60642,17 @@ skolem:lemma2815 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2816 a r:Inference; +skolem:lemma2520 a r:Inference; r:gives { - (2 2 6 7) :sort (2 2 6 7). + (2 2 6 7) :digitsToNumber 2267 . }; r:evidence ( - [ a r:Fact; r:gives {(2 2 6 7) list:firstRest (2 (2 6 7))}] - skolem:lemma4870 - skolem:lemma4833 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((2) (2 6 7)) list:append (2 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2817 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}] + [ 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]; @@ -71894,9 +60662,9 @@ skolem:lemma2817 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2818 a r:Inference; +skolem:lemma2521 a r:Inference; r:gives { (7 6 2 2) :digitsToNumber 7622 . }; @@ -71914,9 +60682,9 @@ skolem:lemma2818 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2819 a r:Inference; +skolem:lemma2522 a r:Inference; r:gives { 2268 :numberToDigits (2 2 6 8). }; @@ -71935,32 +60703,9 @@ skolem:lemma2819 a r:Inference; 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:lemma4392. - -skolem:lemma2820 a r:Inference; - r:gives { - (2 2 6 8) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 8) list:firstRest (2 (2 6 8))}] - skolem:lemma4871 - skolem:lemma4833 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((2) (2 6 8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2821 a r:Inference; +skolem:lemma2523 a r:Inference; r:gives { (2 2 6 8) :digitsToNumber 2268 . }; @@ -71978,9 +60723,9 @@ skolem:lemma2821 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2822 a r:Inference; +skolem:lemma2524 a r:Inference; r:gives { (8 6 2 2) :digitsToNumber 8622 . }; @@ -71998,9 +60743,9 @@ skolem:lemma2822 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2823 a r:Inference; +skolem:lemma2525 a r:Inference; r:gives { 2269 :numberToDigits (2 2 6 9). }; @@ -72019,32 +60764,9 @@ skolem:lemma2823 a r:Inference; 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:lemma4392. - -skolem:lemma2824 a r:Inference; - r:gives { - (2 2 6 9) :sort (2 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6 9) list:firstRest (2 (2 6 9))}] - skolem:lemma4872 - skolem:lemma4833 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((2) (2 6 9)) list:append (2 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 6 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_2"]; r:boundTo (2 6 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2825 a r:Inference; +skolem:lemma2526 a r:Inference; r:gives { (2 2 6 9) :digitsToNumber 2269 . }; @@ -72062,9 +60784,9 @@ skolem:lemma2825 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2826 a r:Inference; +skolem:lemma2527 a r:Inference; r:gives { (9 6 2 2) :digitsToNumber 9622 . }; @@ -72082,9 +60804,9 @@ skolem:lemma2826 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2827 a r:Inference; +skolem:lemma2528 a r:Inference; r:gives { 2270 :numberToDigits (2 2 7 0). }; @@ -72103,32 +60825,9 @@ skolem:lemma2827 a r:Inference; 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:lemma4392. - -skolem:lemma2828 a r:Inference; - r:gives { - (2 2 7 0) :sort (0 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 0) list:firstRest (2 (2 7 0))}] - skolem:lemma4873 - skolem:lemma4793 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 2) (2 7)) list:append (0 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2829 a r:Inference; +skolem:lemma2529 a r:Inference; r:gives { 2271 :numberToDigits (2 2 7 1). }; @@ -72147,32 +60846,9 @@ skolem:lemma2829 a r:Inference; 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:lemma4392. - -skolem:lemma2830 a r:Inference; - r:gives { - (2 2 7 1) :sort (1 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 1) list:firstRest (2 (2 7 1))}] - skolem:lemma4874 - skolem:lemma4807 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 2) (2 7)) list:append (1 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2831 a r:Inference; +skolem:lemma2530 a r:Inference; r:gives { 2272 :numberToDigits (2 2 7 2). }; @@ -72191,32 +60867,9 @@ skolem:lemma2831 a r:Inference; 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:lemma4392. - -skolem:lemma2832 a r:Inference; - r:gives { - (2 2 7 2) :sort (2 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 2) list:firstRest (2 (2 7 2))}] - skolem:lemma4875 - skolem:lemma4822 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((2 2) (2 7)) list:append (2 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2833 a r:Inference; +skolem:lemma2531 a r:Inference; r:gives { 2273 :numberToDigits (2 2 7 3). }; @@ -72235,32 +60888,9 @@ skolem:lemma2833 a r:Inference; 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:lemma4392. - -skolem:lemma2834 a r:Inference; - r:gives { - (2 2 7 3) :sort (2 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 3) list:firstRest (2 (2 7 3))}] - skolem:lemma4876 - skolem:lemma4833 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((2) (2 3 7)) list:append (2 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 3)]; - 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 3)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2835 a r:Inference; +skolem:lemma2532 a r:Inference; r:gives { 2274 :numberToDigits (2 2 7 4). }; @@ -72279,32 +60909,9 @@ skolem:lemma2835 a r:Inference; 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:lemma4392. - -skolem:lemma2836 a r:Inference; - r:gives { - (2 2 7 4) :sort (2 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 4) list:firstRest (2 (2 7 4))}] - skolem:lemma4877 - skolem:lemma4833 - skolem:lemma4594 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((2) (2 4 7)) list:append (2 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 4)]; - 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 4)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2837 a r:Inference; +skolem:lemma2533 a r:Inference; r:gives { 2275 :numberToDigits (2 2 7 5). }; @@ -72323,32 +60930,9 @@ skolem:lemma2837 a r:Inference; 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:lemma4392. - -skolem:lemma2838 a r:Inference; - r:gives { - (2 2 7 5) :sort (2 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 5) list:firstRest (2 (2 7 5))}] - skolem:lemma4878 - skolem:lemma4833 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((2) (2 5 7)) list:append (2 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 5)]; - 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 5)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2839 a r:Inference; +skolem:lemma2534 a r:Inference; r:gives { 2276 :numberToDigits (2 2 7 6). }; @@ -72367,32 +60951,9 @@ skolem:lemma2839 a r:Inference; 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:lemma4392. - -skolem:lemma2840 a r:Inference; - r:gives { - (2 2 7 6) :sort (2 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 6) list:firstRest (2 (2 7 6))}] - skolem:lemma4879 - skolem:lemma4833 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((2) (2 6 7)) list:append (2 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 6)]; - 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 6)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2841 a r:Inference; +skolem:lemma2535 a r:Inference; r:gives { 2277 :numberToDigits (2 2 7 7). }; @@ -72411,32 +60972,9 @@ skolem:lemma2841 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2842 a r:Inference; - r:gives { - (2 2 7 7) :sort (2 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 7) list:firstRest (2 (2 7 7))}] - skolem:lemma4880 - skolem:lemma4833 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((2) (2 7 7)) list:append (2 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2843 a r:Inference; +skolem:lemma2536 a r:Inference; r:gives { (2 2 7 7) :digitsToNumber 2277 . }; @@ -72454,9 +60992,9 @@ skolem:lemma2843 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2844 a r:Inference; +skolem:lemma2537 a r:Inference; r:gives { (7 7 2 2) :digitsToNumber 7722 . }; @@ -72474,42 +61012,9 @@ skolem:lemma2844 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2845 a r:Inference; - r:gives { - 5445 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4881 - skolem:lemma4882 - [ a r:Fact; r:gives {(4 4 5 5) list:reverse (5 5 4 4)}] - skolem:lemma4883 - skolem:lemma4884 - [ a r:Fact; r:gives {(5544 4455) math:difference 1089}] - [ a r:Fact; r:gives {1089 math:notEqualTo 6174}] - skolem:lemma2369 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5544]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2846 a r:Inference; +skolem:lemma2538 a r:Inference; r:gives { 2278 :numberToDigits (2 2 7 8). }; @@ -72528,32 +61033,9 @@ skolem:lemma2846 a r:Inference; 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:lemma4392. - -skolem:lemma2847 a r:Inference; - r:gives { - (2 2 7 8) :sort (2 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 8) list:firstRest (2 (2 7 8))}] - skolem:lemma4885 - skolem:lemma4833 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((2) (2 7 8)) list:append (2 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2848 a r:Inference; +skolem:lemma2539 a r:Inference; r:gives { (2 2 7 8) :digitsToNumber 2278 . }; @@ -72571,9 +61053,9 @@ skolem:lemma2848 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2849 a r:Inference; +skolem:lemma2540 a r:Inference; r:gives { (8 7 2 2) :digitsToNumber 8722 . }; @@ -72591,9 +61073,9 @@ skolem:lemma2849 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2850 a r:Inference; +skolem:lemma2541 a r:Inference; r:gives { 2279 :numberToDigits (2 2 7 9). }; @@ -72612,32 +61094,9 @@ skolem:lemma2850 a r:Inference; 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:lemma4392. - -skolem:lemma2851 a r:Inference; - r:gives { - (2 2 7 9) :sort (2 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7 9) list:firstRest (2 (2 7 9))}] - skolem:lemma4886 - skolem:lemma4833 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((2) (2 7 9)) list:append (2 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 7 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_2"]; r:boundTo (2 7 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2852 a r:Inference; +skolem:lemma2542 a r:Inference; r:gives { (2 2 7 9) :digitsToNumber 2279 . }; @@ -72655,9 +61114,9 @@ skolem:lemma2852 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2853 a r:Inference; +skolem:lemma2543 a r:Inference; r:gives { (9 7 2 2) :digitsToNumber 9722 . }; @@ -72675,9 +61134,9 @@ skolem:lemma2853 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2854 a r:Inference; +skolem:lemma2544 a r:Inference; r:gives { 2280 :numberToDigits (2 2 8 0). }; @@ -72696,32 +61155,9 @@ skolem:lemma2854 a r:Inference; 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:lemma4392. - -skolem:lemma2855 a r:Inference; - r:gives { - (2 2 8 0) :sort (0 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 0) list:firstRest (2 (2 8 0))}] - skolem:lemma4887 - skolem:lemma4793 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 2) (2 8)) list:append (0 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2856 a r:Inference; +skolem:lemma2545 a r:Inference; r:gives { 2281 :numberToDigits (2 2 8 1). }; @@ -72740,32 +61176,9 @@ skolem:lemma2856 a r:Inference; 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:lemma4392. - -skolem:lemma2857 a r:Inference; - r:gives { - (2 2 8 1) :sort (1 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 1) list:firstRest (2 (2 8 1))}] - skolem:lemma4888 - skolem:lemma4807 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 2) (2 8)) list:append (1 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2858 a r:Inference; +skolem:lemma2546 a r:Inference; r:gives { 2282 :numberToDigits (2 2 8 2). }; @@ -72784,32 +61197,9 @@ skolem:lemma2858 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2859 a r:Inference; - r:gives { - (2 2 8 2) :sort (2 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 2) list:firstRest (2 (2 8 2))}] - skolem:lemma4889 - skolem:lemma4822 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((2 2) (2 8)) list:append (2 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2860 a r:Inference; +skolem:lemma2547 a r:Inference; r:gives { 2283 :numberToDigits (2 2 8 3). }; @@ -72828,32 +61218,30 @@ skolem:lemma2860 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2861 a r:Inference; +skolem:lemma2548 a r:Inference; r:gives { - (2 2 8 3) :sort (2 2 3 8). + 2284 :numberToDigits (2 2 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 2 8 3) list:firstRest (2 (2 8 3))}] - skolem:lemma4890 - skolem:lemma4833 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((2) (2 3 8)) list:append (2 2 3 8)}] + [ 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_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 3)]; - 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 3)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma2862 a r:Inference; +skolem:lemma2549 a r:Inference; r:gives { 2285 :numberToDigits (2 2 8 5). }; @@ -72872,32 +61260,9 @@ skolem:lemma2862 a r:Inference; 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:lemma4392. - -skolem:lemma2863 a r:Inference; - r:gives { - (2 2 8 5) :sort (2 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 5) list:firstRest (2 (2 8 5))}] - skolem:lemma4891 - skolem:lemma4833 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((2) (2 5 8)) list:append (2 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 5)]; - 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 5)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2864 a r:Inference; +skolem:lemma2550 a r:Inference; r:gives { 2286 :numberToDigits (2 2 8 6). }; @@ -72916,32 +61281,9 @@ skolem:lemma2864 a r:Inference; 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:lemma4392. - -skolem:lemma2865 a r:Inference; - r:gives { - (2 2 8 6) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 6) list:firstRest (2 (2 8 6))}] - skolem:lemma4892 - skolem:lemma4833 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((2) (2 6 8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 6)]; - 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 6)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2866 a r:Inference; +skolem:lemma2551 a r:Inference; r:gives { 2287 :numberToDigits (2 2 8 7). }; @@ -72960,32 +61302,9 @@ skolem:lemma2866 a r:Inference; 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:lemma4392. - -skolem:lemma2867 a r:Inference; - r:gives { - (2 2 8 7) :sort (2 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 7) list:firstRest (2 (2 8 7))}] - skolem:lemma4893 - skolem:lemma4833 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((2) (2 7 8)) list:append (2 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 7)]; - 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 7)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2868 a r:Inference; +skolem:lemma2552 a r:Inference; r:gives { 2288 :numberToDigits (2 2 8 8). }; @@ -73004,32 +61323,9 @@ skolem:lemma2868 a r:Inference; 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:lemma4392. - -skolem:lemma2869 a r:Inference; - r:gives { - (2 2 8 8) :sort (2 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 8) list:firstRest (2 (2 8 8))}] - skolem:lemma4894 - skolem:lemma4833 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((2) (2 8 8)) list:append (2 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2870 a r:Inference; +skolem:lemma2553 a r:Inference; r:gives { (2 2 8 8) :digitsToNumber 2288 . }; @@ -73047,9 +61343,9 @@ skolem:lemma2870 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2871 a r:Inference; +skolem:lemma2554 a r:Inference; r:gives { (8 8 2 2) :digitsToNumber 8822 . }; @@ -73067,42 +61363,9 @@ skolem:lemma2871 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2872 a r:Inference; - r:gives { - 6534 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4895 - skolem:lemma4896 - [ a r:Fact; r:gives {(3 4 5 6) list:reverse (6 5 4 3)}] - skolem:lemma4572 - skolem:lemma4573 - [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] - [ a r:Fact; r:gives {3087 math:notEqualTo 6174}] - skolem:lemma2062 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3456]; - 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_8"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2873 a r:Inference; +skolem:lemma2555 a r:Inference; r:gives { 2289 :numberToDigits (2 2 8 9). }; @@ -73121,32 +61384,9 @@ skolem:lemma2873 a r:Inference; 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:lemma4392. - -skolem:lemma2874 a r:Inference; - r:gives { - (2 2 8 9) :sort (2 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8 9) list:firstRest (2 (2 8 9))}] - skolem:lemma4897 - skolem:lemma4833 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((2) (2 8 9)) list:append (2 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 8 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_2"]; r:boundTo (2 8 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2875 a r:Inference; +skolem:lemma2556 a r:Inference; r:gives { (2 2 8 9) :digitsToNumber 2289 . }; @@ -73164,9 +61404,9 @@ skolem:lemma2875 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2876 a r:Inference; +skolem:lemma2557 a r:Inference; r:gives { (9 8 2 2) :digitsToNumber 9822 . }; @@ -73184,9 +61424,9 @@ skolem:lemma2876 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2877 a r:Inference; +skolem:lemma2558 a r:Inference; r:gives { 2290 :numberToDigits (2 2 9 0). }; @@ -73205,32 +61445,9 @@ skolem:lemma2877 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2878 a r:Inference; - r:gives { - (2 2 9 0) :sort (0 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 0) list:firstRest (2 (2 9 0))}] - skolem:lemma4898 - skolem:lemma4793 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 2) (2 9)) list:append (0 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2879 a r:Inference; +skolem:lemma2559 a r:Inference; r:gives { 2291 :numberToDigits (2 2 9 1). }; @@ -73249,32 +61466,9 @@ skolem:lemma2879 a r:Inference; 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:lemma4392. - -skolem:lemma2880 a r:Inference; - r:gives { - (2 2 9 1) :sort (1 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 1) list:firstRest (2 (2 9 1))}] - skolem:lemma4899 - skolem:lemma4807 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 2) (2 9)) list:append (1 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2881 a r:Inference; +skolem:lemma2560 a r:Inference; r:gives { 2292 :numberToDigits (2 2 9 2). }; @@ -73293,32 +61487,9 @@ skolem:lemma2881 a r:Inference; 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:lemma4392. - -skolem:lemma2882 a r:Inference; - r:gives { - (2 2 9 2) :sort (2 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 2) list:firstRest (2 (2 9 2))}] - skolem:lemma4900 - skolem:lemma4822 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((2 2) (2 9)) list:append (2 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2883 a r:Inference; +skolem:lemma2561 a r:Inference; r:gives { 2293 :numberToDigits (2 2 9 3). }; @@ -73337,32 +61508,9 @@ skolem:lemma2883 a r:Inference; 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:lemma4392. - -skolem:lemma2884 a r:Inference; - r:gives { - (2 2 9 3) :sort (2 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 3) list:firstRest (2 (2 9 3))}] - skolem:lemma4901 - skolem:lemma4833 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((2) (2 3 9)) list:append (2 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 3)]; - 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 3)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2885 a r:Inference; +skolem:lemma2562 a r:Inference; r:gives { 2294 :numberToDigits (2 2 9 4). }; @@ -73381,32 +61529,9 @@ skolem:lemma2885 a r:Inference; 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:lemma4392. - -skolem:lemma2886 a r:Inference; - r:gives { - (2 2 9 4) :sort (2 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 4) list:firstRest (2 (2 9 4))}] - skolem:lemma4902 - skolem:lemma4833 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((2) (2 4 9)) list:append (2 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 4)]; - 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 4)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2887 a r:Inference; +skolem:lemma2563 a r:Inference; r:gives { 2295 :numberToDigits (2 2 9 5). }; @@ -73425,32 +61550,9 @@ skolem:lemma2887 a r:Inference; 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:lemma4392. - -skolem:lemma2888 a r:Inference; - r:gives { - (2 2 9 5) :sort (2 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 5) list:firstRest (2 (2 9 5))}] - skolem:lemma4903 - skolem:lemma4833 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((2) (2 5 9)) list:append (2 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 5)]; - 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 5)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2889 a r:Inference; +skolem:lemma2564 a r:Inference; r:gives { 2296 :numberToDigits (2 2 9 6). }; @@ -73469,32 +61571,9 @@ skolem:lemma2889 a r:Inference; 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:lemma4392. - -skolem:lemma2890 a r:Inference; - r:gives { - (2 2 9 6) :sort (2 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 6) list:firstRest (2 (2 9 6))}] - skolem:lemma4904 - skolem:lemma4833 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((2) (2 6 9)) list:append (2 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 6)]; - 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 6)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2891 a r:Inference; +skolem:lemma2565 a r:Inference; r:gives { 2297 :numberToDigits (2 2 9 7). }; @@ -73513,32 +61592,9 @@ skolem:lemma2891 a r:Inference; 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:lemma4392. - -skolem:lemma2892 a r:Inference; - r:gives { - (2 2 9 7) :sort (2 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 7) list:firstRest (2 (2 9 7))}] - skolem:lemma4905 - skolem:lemma4833 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((2) (2 7 9)) list:append (2 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 7)]; - 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 7)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2893 a r:Inference; +skolem:lemma2566 a r:Inference; r:gives { 2298 :numberToDigits (2 2 9 8). }; @@ -73557,32 +61613,9 @@ skolem:lemma2893 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2894 a r:Inference; - r:gives { - (2 2 9 8) :sort (2 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 8) list:firstRest (2 (2 9 8))}] - skolem:lemma4906 - skolem:lemma4833 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((2) (2 8 9)) list:append (2 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 8)]; - 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 8)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma2895 a r:Inference; +skolem:lemma2567 a r:Inference; r:gives { 2299 :numberToDigits (2 2 9 9). }; @@ -73601,32 +61634,9 @@ skolem:lemma2895 a r:Inference; 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:lemma4392. - -skolem:lemma2896 a r:Inference; - r:gives { - (2 2 9 9) :sort (2 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9 9) list:firstRest (2 (2 9 9))}] - skolem:lemma4907 - skolem:lemma4833 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((2) (2 9 9)) list:append (2 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 9 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_2"]; r:boundTo (2 9 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2897 a r:Inference; +skolem:lemma2568 a r:Inference; r:gives { (2 2 9 9) :digitsToNumber 2299 . }; @@ -73644,9 +61654,9 @@ skolem:lemma2897 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2898 a r:Inference; +skolem:lemma2569 a r:Inference; r:gives { (9 9 2 2) :digitsToNumber 9922 . }; @@ -73664,42 +61674,9 @@ skolem:lemma2898 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/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:lemma4397. - -skolem:lemma2899 a r:Inference; - r:gives { - 7623 :kaprekar 6174 . - }; - r:evidence ( - [ a r:Fact; r:gives {:recursion :count 1}] - [ a r:Fact; r:gives {(1 1) math:sum 2}] - [ a r:Fact; r:gives {{ - :recursion :count 1. - } log:becomes { - :recursion :count 2. - }}] - skolem:lemma4908 - skolem:lemma4909 - [ a r:Fact; r:gives {(2 3 6 7) list:reverse (7 6 3 2)}] - skolem:lemma3070 - skolem:lemma3071 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {5265 math:notEqualTo 6174}] - skolem:lemma2211 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2367]; - 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_8"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6174]; - r:rule skolem:lemma2008. + r:rule skolem:lemma3439. -skolem:lemma2900 a r:Inference; +skolem:lemma2570 a r:Inference; r:gives { 2300 :numberToDigits (2 3 0 0). }; @@ -73718,32 +61695,9 @@ skolem:lemma2900 a r:Inference; 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:lemma4392. - -skolem:lemma2901 a r:Inference; - r:gives { - (2 3 0 0) :sort (0 0 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 0) list:firstRest (2 (3 0 0))}] - skolem:lemma4910 - skolem:lemma4407 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 0) (2 3)) list:append (0 0 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (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 (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2902 a r:Inference; +skolem:lemma2571 a r:Inference; r:gives { 2301 :numberToDigits (2 3 0 1). }; @@ -73762,32 +61716,9 @@ skolem:lemma2902 a r:Inference; 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:lemma4392. - -skolem:lemma2903 a r:Inference; - r:gives { - (2 3 0 1) :sort (0 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 1) list:firstRest (2 (3 0 1))}] - skolem:lemma4911 - skolem:lemma4442 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 1) (2 3)) list:append (0 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2904 a r:Inference; +skolem:lemma2572 a r:Inference; r:gives { 2302 :numberToDigits (2 3 0 2). }; @@ -73806,32 +61737,9 @@ skolem:lemma2904 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma2905 a r:Inference; - r:gives { - (2 3 0 2) :sort (0 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 2) list:firstRest (2 (3 0 2))}] - skolem:lemma4912 - skolem:lemma4479 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 2) (2 3)) list:append (0 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2906 a r:Inference; +skolem:lemma2573 a r:Inference; r:gives { 2303 :numberToDigits (2 3 0 3). }; @@ -73850,32 +61758,9 @@ skolem:lemma2906 a r:Inference; 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:lemma4392. - -skolem:lemma2907 a r:Inference; - r:gives { - (2 3 0 3) :sort (0 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 3) list:firstRest (2 (3 0 3))}] - skolem:lemma4913 - skolem:lemma4506 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((0) (2 3 3)) list:append (0 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2908 a r:Inference; +skolem:lemma2574 a r:Inference; r:gives { 2304 :numberToDigits (2 3 0 4). }; @@ -73894,32 +61779,9 @@ skolem:lemma2908 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2909 a r:Inference; - r:gives { - (2 3 0 4) :sort (0 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 4) list:firstRest (2 (3 0 4))}] - skolem:lemma4914 - skolem:lemma4506 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((0) (2 3 4)) list:append (0 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 (3 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 (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma2910 a r:Inference; +skolem:lemma2575 a r:Inference; r:gives { 2305 :numberToDigits (2 3 0 5). }; @@ -73938,32 +61800,9 @@ skolem:lemma2910 a r:Inference; 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:lemma4392. - -skolem:lemma2911 a r:Inference; - r:gives { - (2 3 0 5) :sort (0 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 5) list:firstRest (2 (3 0 5))}] - skolem:lemma4915 - skolem:lemma4506 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((0) (2 3 5)) list:append (0 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 (3 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 (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2912 a r:Inference; +skolem:lemma2576 a r:Inference; r:gives { 2306 :numberToDigits (2 3 0 6). }; @@ -73982,32 +61821,9 @@ skolem:lemma2912 a r:Inference; 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:lemma4392. - -skolem:lemma2913 a r:Inference; - r:gives { - (2 3 0 6) :sort (0 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 6) list:firstRest (2 (3 0 6))}] - skolem:lemma4916 - skolem:lemma4506 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((0) (2 3 6)) list:append (0 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 (3 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 (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2914 a r:Inference; +skolem:lemma2577 a r:Inference; r:gives { 2307 :numberToDigits (2 3 0 7). }; @@ -74026,32 +61842,9 @@ skolem:lemma2914 a r:Inference; 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:lemma4392. - -skolem:lemma2915 a r:Inference; - r:gives { - (2 3 0 7) :sort (0 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 7) list:firstRest (2 (3 0 7))}] - skolem:lemma4917 - skolem:lemma4506 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((0) (2 3 7)) list:append (0 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 (3 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 (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2916 a r:Inference; +skolem:lemma2578 a r:Inference; r:gives { 2308 :numberToDigits (2 3 0 8). }; @@ -74070,32 +61863,9 @@ skolem:lemma2916 a r:Inference; 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:lemma4392. - -skolem:lemma2917 a r:Inference; - r:gives { - (2 3 0 8) :sort (0 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 8) list:firstRest (2 (3 0 8))}] - skolem:lemma4918 - skolem:lemma4506 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((0) (2 3 8)) list:append (0 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 (3 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 (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2918 a r:Inference; +skolem:lemma2579 a r:Inference; r:gives { 2309 :numberToDigits (2 3 0 9). }; @@ -74114,32 +61884,9 @@ skolem:lemma2918 a r:Inference; 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:lemma4392. - -skolem:lemma2919 a r:Inference; - r:gives { - (2 3 0 9) :sort (0 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0 9) list:firstRest (2 (3 0 9))}] - skolem:lemma4919 - skolem:lemma4506 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((0) (2 3 9)) list:append (0 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 0 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_2"]; r:boundTo (3 0 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 (3 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 (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2920 a r:Inference; +skolem:lemma2580 a r:Inference; r:gives { 2310 :numberToDigits (2 3 1 0). }; @@ -74158,32 +61905,9 @@ skolem:lemma2920 a r:Inference; 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:lemma4392. - -skolem:lemma2921 a r:Inference; - r:gives { - (2 3 1 0) :sort (0 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 0) list:firstRest (2 (3 1 0))}] - skolem:lemma4920 - skolem:lemma4660 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 1) (2 3)) list:append (0 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2922 a r:Inference; +skolem:lemma2581 a r:Inference; r:gives { 2311 :numberToDigits (2 3 1 1). }; @@ -74202,32 +61926,9 @@ skolem:lemma2922 a r:Inference; 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:lemma4392. - -skolem:lemma2923 a r:Inference; - r:gives { - (2 3 1 1) :sort (1 1 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 1) list:firstRest (2 (3 1 1))}] - skolem:lemma4921 - skolem:lemma4680 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 1) (2 3)) list:append (1 1 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2924 a r:Inference; +skolem:lemma2582 a r:Inference; r:gives { 2312 :numberToDigits (2 3 1 2). }; @@ -74246,32 +61947,9 @@ skolem:lemma2924 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2925 a r:Inference; - r:gives { - (2 3 1 2) :sort (1 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 2) list:firstRest (2 (3 1 2))}] - skolem:lemma4922 - skolem:lemma4694 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 2) (2 3)) list:append (1 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 3)]; - r:rule skolem:lemma4396. - -skolem:lemma2926 a r:Inference; +skolem:lemma2583 a r:Inference; r:gives { 2313 :numberToDigits (2 3 1 3). }; @@ -74290,32 +61968,9 @@ skolem:lemma2926 a r:Inference; 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:lemma4392. - -skolem:lemma2927 a r:Inference; - r:gives { - (2 3 1 3) :sort (1 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 3) list:firstRest (2 (3 1 3))}] - skolem:lemma4923 - skolem:lemma4705 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((1) (2 3 3)) list:append (1 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 3)]; - 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 3)]; - 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2928 a r:Inference; +skolem:lemma2584 a r:Inference; r:gives { 2314 :numberToDigits (2 3 1 4). }; @@ -74334,32 +61989,9 @@ skolem:lemma2928 a r:Inference; 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:lemma4392. - -skolem:lemma2929 a r:Inference; - r:gives { - (2 3 1 4) :sort (1 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 4) list:firstRest (2 (3 1 4))}] - skolem:lemma4924 - skolem:lemma4705 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((1) (2 3 4)) list:append (1 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2930 a r:Inference; +skolem:lemma2585 a r:Inference; r:gives { 2315 :numberToDigits (2 3 1 5). }; @@ -74378,32 +62010,9 @@ skolem:lemma2930 a r:Inference; 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:lemma4392. - -skolem:lemma2931 a r:Inference; - r:gives { - (2 3 1 5) :sort (1 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 5) list:firstRest (2 (3 1 5))}] - skolem:lemma4925 - skolem:lemma4705 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((1) (2 3 5)) list:append (1 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2932 a r:Inference; +skolem:lemma2586 a r:Inference; r:gives { 2316 :numberToDigits (2 3 1 6). }; @@ -74422,32 +62031,9 @@ skolem:lemma2932 a r:Inference; 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:lemma4392. - -skolem:lemma2933 a r:Inference; - r:gives { - (2 3 1 6) :sort (1 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 6) list:firstRest (2 (3 1 6))}] - skolem:lemma4926 - skolem:lemma4705 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((1) (2 3 6)) list:append (1 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2934 a r:Inference; +skolem:lemma2587 a r:Inference; r:gives { 2317 :numberToDigits (2 3 1 7). }; @@ -74466,34 +62052,11 @@ skolem:lemma2934 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2935 a r:Inference; +skolem:lemma2588 a r:Inference; r:gives { - (2 3 1 7) :sort (1 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 7) list:firstRest (2 (3 1 7))}] - skolem:lemma4927 - skolem:lemma4705 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((1) (2 3 7)) list:append (1 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma2936 a r:Inference; - r:gives { - 2318 :numberToDigits (2 3 1 8). + 2318 :numberToDigits (2 3 1 8). }; r:evidence ( [ a r:Fact; r:gives {(2318 1000) math:integerQuotient 2}] @@ -74510,32 +62073,9 @@ skolem:lemma2936 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2937 a r:Inference; - r:gives { - (2 3 1 8) :sort (1 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 8) list:firstRest (2 (3 1 8))}] - skolem:lemma4928 - skolem:lemma4705 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((1) (2 3 8)) list:append (1 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2938 a r:Inference; +skolem:lemma2589 a r:Inference; r:gives { 2319 :numberToDigits (2 3 1 9). }; @@ -74554,32 +62094,9 @@ skolem:lemma2938 a r:Inference; 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:lemma4392. - -skolem:lemma2939 a r:Inference; - r:gives { - (2 3 1 9) :sort (1 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1 9) list:firstRest (2 (3 1 9))}] - skolem:lemma4929 - skolem:lemma4705 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((1) (2 3 9)) list:append (1 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 1 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_2"]; r:boundTo (3 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2940 a r:Inference; +skolem:lemma2590 a r:Inference; r:gives { 2320 :numberToDigits (2 3 2 0). }; @@ -74598,32 +62115,9 @@ skolem:lemma2940 a r:Inference; 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:lemma4392. - -skolem:lemma2941 a r:Inference; - r:gives { - (2 3 2 0) :sort (0 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 0) list:firstRest (2 (3 2 0))}] - skolem:lemma4930 - skolem:lemma4793 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((0 2) (2 3)) list:append (0 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2942 a r:Inference; +skolem:lemma2591 a r:Inference; r:gives { 2321 :numberToDigits (2 3 2 1). }; @@ -74642,32 +62136,9 @@ skolem:lemma2942 a r:Inference; 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:lemma4392. - -skolem:lemma2943 a r:Inference; - r:gives { - (2 3 2 1) :sort (1 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 1) list:firstRest (2 (3 2 1))}] - skolem:lemma4931 - skolem:lemma4807 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((1 2) (2 3)) list:append (1 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2944 a r:Inference; +skolem:lemma2592 a r:Inference; r:gives { 2322 :numberToDigits (2 3 2 2). }; @@ -74686,32 +62157,9 @@ skolem:lemma2944 a r:Inference; 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:lemma4392. - -skolem:lemma2945 a r:Inference; - r:gives { - (2 3 2 2) :sort (2 2 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 2) list:firstRest (2 (3 2 2))}] - skolem:lemma4932 - skolem:lemma4822 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {((2 2) (2 3)) list:append (2 2 2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2946 a r:Inference; +skolem:lemma2593 a r:Inference; r:gives { 2323 :numberToDigits (2 3 2 3). }; @@ -74730,32 +62178,9 @@ skolem:lemma2946 a r:Inference; 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:lemma4392. - -skolem:lemma2947 a r:Inference; - r:gives { - (2 3 2 3) :sort (2 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 3) list:firstRest (2 (3 2 3))}] - skolem:lemma4933 - skolem:lemma4833 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((2) (2 3 3)) list:append (2 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 3)]; - 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 3)]; - 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2948 a r:Inference; +skolem:lemma2594 a r:Inference; r:gives { 2324 :numberToDigits (2 3 2 4). }; @@ -74774,32 +62199,9 @@ skolem:lemma2948 a r:Inference; 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:lemma4392. - -skolem:lemma2949 a r:Inference; - r:gives { - (2 3 2 4) :sort (2 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 4) list:firstRest (2 (3 2 4))}] - skolem:lemma4934 - skolem:lemma4833 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((2) (2 3 4)) list:append (2 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2950 a r:Inference; +skolem:lemma2595 a r:Inference; r:gives { 2325 :numberToDigits (2 3 2 5). }; @@ -74818,32 +62220,9 @@ skolem:lemma2950 a r:Inference; 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:lemma4392. - -skolem:lemma2951 a r:Inference; - r:gives { - (2 3 2 5) :sort (2 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 5) list:firstRest (2 (3 2 5))}] - skolem:lemma4935 - skolem:lemma4833 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((2) (2 3 5)) list:append (2 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2952 a r:Inference; +skolem:lemma2596 a r:Inference; r:gives { 2326 :numberToDigits (2 3 2 6). }; @@ -74862,32 +62241,9 @@ skolem:lemma2952 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2953 a r:Inference; - r:gives { - (2 3 2 6) :sort (2 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 6) list:firstRest (2 (3 2 6))}] - skolem:lemma4936 - skolem:lemma4833 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((2) (2 3 6)) list:append (2 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma2954 a r:Inference; +skolem:lemma2597 a r:Inference; r:gives { 2327 :numberToDigits (2 3 2 7). }; @@ -74906,32 +62262,9 @@ skolem:lemma2954 a r:Inference; 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:lemma4392. - -skolem:lemma2955 a r:Inference; - r:gives { - (2 3 2 7) :sort (2 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 7) list:firstRest (2 (3 2 7))}] - skolem:lemma4937 - skolem:lemma4833 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((2) (2 3 7)) list:append (2 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2956 a r:Inference; +skolem:lemma2598 a r:Inference; r:gives { 2328 :numberToDigits (2 3 2 8). }; @@ -74950,32 +62283,9 @@ skolem:lemma2956 a r:Inference; 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:lemma4392. - -skolem:lemma2957 a r:Inference; - r:gives { - (2 3 2 8) :sort (2 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 8) list:firstRest (2 (3 2 8))}] - skolem:lemma4938 - skolem:lemma4833 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((2) (2 3 8)) list:append (2 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2958 a r:Inference; +skolem:lemma2599 a r:Inference; r:gives { 2329 :numberToDigits (2 3 2 9). }; @@ -74994,32 +62304,9 @@ skolem:lemma2958 a r:Inference; 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:lemma4392. - -skolem:lemma2959 a r:Inference; - r:gives { - (2 3 2 9) :sort (2 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2 9) list:firstRest (2 (3 2 9))}] - skolem:lemma4939 - skolem:lemma4833 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((2) (2 3 9)) list:append (2 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 2 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_2"]; r:boundTo (3 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2960 a r:Inference; +skolem:lemma2600 a r:Inference; r:gives { 2330 :numberToDigits (2 3 3 0). }; @@ -75038,32 +62325,9 @@ skolem:lemma2960 a r:Inference; 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:lemma4392. - -skolem:lemma2961 a r:Inference; - r:gives { - (2 3 3 0) :sort (0 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 0) list:firstRest (2 (3 3 0))}] - skolem:lemma4940 - skolem:lemma4506 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((0) (2 3 3)) list:append (0 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 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 (3 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2962 a r:Inference; +skolem:lemma2601 a r:Inference; r:gives { 2331 :numberToDigits (2 3 3 1). }; @@ -75082,32 +62346,9 @@ skolem:lemma2962 a r:Inference; 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:lemma4392. - -skolem:lemma2963 a r:Inference; - r:gives { - (2 3 3 1) :sort (1 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 1) list:firstRest (2 (3 3 1))}] - skolem:lemma4941 - skolem:lemma4705 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((1) (2 3 3)) list:append (1 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 1)]; - 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 3)]; - 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2964 a r:Inference; +skolem:lemma2602 a r:Inference; r:gives { 2332 :numberToDigits (2 3 3 2). }; @@ -75126,32 +62367,9 @@ skolem:lemma2964 a r:Inference; 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:lemma4392. - -skolem:lemma2965 a r:Inference; - r:gives { - (2 3 3 2) :sort (2 2 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 2) list:firstRest (2 (3 3 2))}] - skolem:lemma4942 - skolem:lemma4833 - skolem:lemma4507 - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {((2) (2 3 3)) list:append (2 2 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 2)]; - 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 3)]; - 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2966 a r:Inference; +skolem:lemma2603 a r:Inference; r:gives { 2333 :numberToDigits (2 3 3 3). }; @@ -75170,32 +62388,9 @@ skolem:lemma2966 a r:Inference; 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:lemma4392. - -skolem:lemma2967 a r:Inference; - r:gives { - (2 3 3 3) :sort (2 3 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 3) list:firstRest (2 (3 3 3))}] - skolem:lemma4943 - skolem:lemma4395 - skolem:lemma4944 - [ a r:Fact; r:gives {(2 3 3 3) list:firstRest (2 (3 3 3))}] - [ a r:Fact; r:gives {(() (2 3 3 3)) list:append (2 3 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 3)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2968 a r:Inference; +skolem:lemma2604 a r:Inference; r:gives { (2 3 3 3) :digitsToNumber 2333 . }; @@ -75213,9 +62408,9 @@ skolem:lemma2968 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2969 a r:Inference; +skolem:lemma2605 a r:Inference; r:gives { (3 3 3 2) :digitsToNumber 3332 . }; @@ -75233,9 +62428,9 @@ skolem:lemma2969 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2970 a r:Inference; +skolem:lemma2606 a r:Inference; r:gives { 2334 :numberToDigits (2 3 3 4). }; @@ -75254,32 +62449,9 @@ skolem:lemma2970 a r:Inference; 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:lemma4392. - -skolem:lemma2971 a r:Inference; - r:gives { - (2 3 3 4) :sort (2 3 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 4) list:firstRest (2 (3 3 4))}] - skolem:lemma4945 - skolem:lemma4395 - skolem:lemma4946 - [ a r:Fact; r:gives {(2 3 3 4) list:firstRest (2 (3 3 4))}] - [ a r:Fact; r:gives {(() (2 3 3 4)) list:append (2 3 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2972 a r:Inference; +skolem:lemma2607 a r:Inference; r:gives { (2 3 3 4) :digitsToNumber 2334 . }; @@ -75297,9 +62469,9 @@ skolem:lemma2972 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2973 a r:Inference; +skolem:lemma2608 a r:Inference; r:gives { (4 3 3 2) :digitsToNumber 4332 . }; @@ -75317,9 +62489,9 @@ skolem:lemma2973 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2974 a r:Inference; +skolem:lemma2609 a r:Inference; r:gives { 2335 :numberToDigits (2 3 3 5). }; @@ -75338,32 +62510,9 @@ skolem:lemma2974 a r:Inference; 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:lemma4392. - -skolem:lemma2975 a r:Inference; - r:gives { - (2 3 3 5) :sort (2 3 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 5) list:firstRest (2 (3 3 5))}] - skolem:lemma4947 - skolem:lemma4395 - skolem:lemma4948 - [ a r:Fact; r:gives {(2 3 3 5) list:firstRest (2 (3 3 5))}] - [ a r:Fact; r:gives {(() (2 3 3 5)) list:append (2 3 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2976 a r:Inference; +skolem:lemma2610 a r:Inference; r:gives { (2 3 3 5) :digitsToNumber 2335 . }; @@ -75381,9 +62530,9 @@ skolem:lemma2976 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2977 a r:Inference; +skolem:lemma2611 a r:Inference; r:gives { (5 3 3 2) :digitsToNumber 5332 . }; @@ -75401,9 +62550,9 @@ skolem:lemma2977 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2978 a r:Inference; +skolem:lemma2612 a r:Inference; r:gives { 2336 :numberToDigits (2 3 3 6). }; @@ -75422,32 +62571,9 @@ skolem:lemma2978 a r:Inference; 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:lemma4392. - -skolem:lemma2979 a r:Inference; - r:gives { - (2 3 3 6) :sort (2 3 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 6) list:firstRest (2 (3 3 6))}] - skolem:lemma4949 - skolem:lemma4395 - skolem:lemma4950 - [ a r:Fact; r:gives {(2 3 3 6) list:firstRest (2 (3 3 6))}] - [ a r:Fact; r:gives {(() (2 3 3 6)) list:append (2 3 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2980 a r:Inference; +skolem:lemma2613 a r:Inference; r:gives { (2 3 3 6) :digitsToNumber 2336 . }; @@ -75465,9 +62591,9 @@ skolem:lemma2980 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2981 a r:Inference; +skolem:lemma2614 a r:Inference; r:gives { (6 3 3 2) :digitsToNumber 6332 . }; @@ -75485,9 +62611,9 @@ skolem:lemma2981 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2982 a r:Inference; +skolem:lemma2615 a r:Inference; r:gives { 2337 :numberToDigits (2 3 3 7). }; @@ -75506,32 +62632,9 @@ skolem:lemma2982 a r:Inference; 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:lemma4392. - -skolem:lemma2983 a r:Inference; - r:gives { - (2 3 3 7) :sort (2 3 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 7) list:firstRest (2 (3 3 7))}] - skolem:lemma4951 - skolem:lemma4395 - skolem:lemma4952 - [ a r:Fact; r:gives {(2 3 3 7) list:firstRest (2 (3 3 7))}] - [ a r:Fact; r:gives {(() (2 3 3 7)) list:append (2 3 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2984 a r:Inference; +skolem:lemma2616 a r:Inference; r:gives { (2 3 3 7) :digitsToNumber 2337 . }; @@ -75549,9 +62652,9 @@ skolem:lemma2984 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2985 a r:Inference; +skolem:lemma2617 a r:Inference; r:gives { (7 3 3 2) :digitsToNumber 7332 . }; @@ -75569,9 +62672,9 @@ skolem:lemma2985 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2986 a r:Inference; +skolem:lemma2618 a r:Inference; r:gives { 2338 :numberToDigits (2 3 3 8). }; @@ -75590,32 +62693,9 @@ skolem:lemma2986 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma2987 a r:Inference; - r:gives { - (2 3 3 8) :sort (2 3 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 8) list:firstRest (2 (3 3 8))}] - skolem:lemma4953 - skolem:lemma4395 - skolem:lemma4954 - [ a r:Fact; r:gives {(2 3 3 8) list:firstRest (2 (3 3 8))}] - [ a r:Fact; r:gives {(() (2 3 3 8)) list:append (2 3 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma2988 a r:Inference; +skolem:lemma2619 a r:Inference; r:gives { (2 3 3 8) :digitsToNumber 2338 . }; @@ -75633,9 +62713,9 @@ skolem:lemma2988 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2989 a r:Inference; +skolem:lemma2620 a r:Inference; r:gives { (8 3 3 2) :digitsToNumber 8332 . }; @@ -75653,9 +62733,9 @@ skolem:lemma2989 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2990 a r:Inference; +skolem:lemma2621 a r:Inference; r:gives { 2339 :numberToDigits (2 3 3 9). }; @@ -75674,32 +62754,9 @@ skolem:lemma2990 a r:Inference; 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:lemma4392. - -skolem:lemma2991 a r:Inference; - r:gives { - (2 3 3 9) :sort (2 3 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3 9) list:firstRest (2 (3 3 9))}] - skolem:lemma4955 - skolem:lemma4395 - skolem:lemma4956 - [ a r:Fact; r:gives {(2 3 3 9) list:firstRest (2 (3 3 9))}] - [ a r:Fact; r:gives {(() (2 3 3 9)) list:append (2 3 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 3 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_2"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2992 a r:Inference; +skolem:lemma2622 a r:Inference; r:gives { (2 3 3 9) :digitsToNumber 2339 . }; @@ -75717,9 +62774,9 @@ skolem:lemma2992 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2993 a r:Inference; +skolem:lemma2623 a r:Inference; r:gives { (9 3 3 2) :digitsToNumber 9332 . }; @@ -75737,9 +62794,9 @@ skolem:lemma2993 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma2994 a r:Inference; +skolem:lemma2624 a r:Inference; r:gives { 2340 :numberToDigits (2 3 4 0). }; @@ -75758,32 +62815,9 @@ skolem:lemma2994 a r:Inference; 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:lemma4392. - -skolem:lemma2995 a r:Inference; - r:gives { - (2 3 4 0) :sort (0 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 0) list:firstRest (2 (3 4 0))}] - skolem:lemma4957 - skolem:lemma4506 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((0) (2 3 4)) list:append (0 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 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 (3 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 (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2996 a r:Inference; +skolem:lemma2625 a r:Inference; r:gives { 2341 :numberToDigits (2 3 4 1). }; @@ -75802,32 +62836,9 @@ skolem:lemma2996 a r:Inference; 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:lemma4392. - -skolem:lemma2997 a r:Inference; - r:gives { - (2 3 4 1) :sort (1 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 1) list:firstRest (2 (3 4 1))}] - skolem:lemma4958 - skolem:lemma4705 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((1) (2 3 4)) list:append (1 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 1)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma2998 a r:Inference; +skolem:lemma2626 a r:Inference; r:gives { 2342 :numberToDigits (2 3 4 2). }; @@ -75846,32 +62857,9 @@ skolem:lemma2998 a r:Inference; 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:lemma4392. - -skolem:lemma2999 a r:Inference; - r:gives { - (2 3 4 2) :sort (2 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 2) list:firstRest (2 (3 4 2))}] - skolem:lemma4959 - skolem:lemma4833 - skolem:lemma4509 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((2) (2 3 4)) list:append (2 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 2)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3000 a r:Inference; +skolem:lemma2627 a r:Inference; r:gives { 2343 :numberToDigits (2 3 4 3). }; @@ -75890,32 +62878,9 @@ skolem:lemma3000 a r:Inference; 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:lemma4392. - -skolem:lemma3001 a r:Inference; - r:gives { - (2 3 4 3) :sort (2 3 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 3) list:firstRest (2 (3 4 3))}] - skolem:lemma4960 - skolem:lemma4395 - skolem:lemma4961 - [ a r:Fact; r:gives {(2 3 3 4) list:firstRest (2 (3 3 4))}] - [ a r:Fact; r:gives {(() (2 3 3 4)) list:append (2 3 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3002 a r:Inference; +skolem:lemma2628 a r:Inference; r:gives { 2344 :numberToDigits (2 3 4 4). }; @@ -75934,32 +62899,9 @@ skolem:lemma3002 a r:Inference; 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:lemma4392. - -skolem:lemma3003 a r:Inference; - r:gives { - (2 3 4 4) :sort (2 3 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 4) list:firstRest (2 (3 4 4))}] - skolem:lemma4962 - skolem:lemma4395 - skolem:lemma4963 - [ a r:Fact; r:gives {(2 3 4 4) list:firstRest (2 (3 4 4))}] - [ a r:Fact; r:gives {(() (2 3 4 4)) list:append (2 3 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3004 a r:Inference; +skolem:lemma2629 a r:Inference; r:gives { (2 3 4 4) :digitsToNumber 2344 . }; @@ -75977,9 +62919,9 @@ skolem:lemma3004 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3005 a r:Inference; +skolem:lemma2630 a r:Inference; r:gives { (4 4 3 2) :digitsToNumber 4432 . }; @@ -75997,9 +62939,9 @@ skolem:lemma3005 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3006 a r:Inference; +skolem:lemma2631 a r:Inference; r:gives { 2345 :numberToDigits (2 3 4 5). }; @@ -76018,32 +62960,9 @@ skolem:lemma3006 a r:Inference; 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:lemma4392. - -skolem:lemma3007 a r:Inference; - r:gives { - (2 3 4 5) :sort (2 3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - skolem:lemma4964 - skolem:lemma4395 - skolem:lemma4965 - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - [ a r:Fact; r:gives {(() (2 3 4 5)) list:append (2 3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3008 a r:Inference; +skolem:lemma2632 a r:Inference; r:gives { (2 3 4 5) :digitsToNumber 2345 . }; @@ -76061,9 +62980,9 @@ skolem:lemma3008 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3009 a r:Inference; +skolem:lemma2633 a r:Inference; r:gives { (5 4 3 2) :digitsToNumber 5432 . }; @@ -76081,9 +63000,9 @@ skolem:lemma3009 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3010 a r:Inference; +skolem:lemma2634 a r:Inference; r:gives { 2346 :numberToDigits (2 3 4 6). }; @@ -76102,32 +63021,9 @@ skolem:lemma3010 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3011 a r:Inference; - r:gives { - (2 3 4 6) :sort (2 3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - skolem:lemma4966 - skolem:lemma4395 - skolem:lemma4967 - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - [ a r:Fact; r:gives {(() (2 3 4 6)) list:append (2 3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3012 a r:Inference; +skolem:lemma2635 a r:Inference; r:gives { (2 3 4 6) :digitsToNumber 2346 . }; @@ -76145,9 +63041,9 @@ skolem:lemma3012 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3013 a r:Inference; +skolem:lemma2636 a r:Inference; r:gives { (6 4 3 2) :digitsToNumber 6432 . }; @@ -76165,9 +63061,9 @@ skolem:lemma3013 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3014 a r:Inference; +skolem:lemma2637 a r:Inference; r:gives { 2347 :numberToDigits (2 3 4 7). }; @@ -76186,32 +63082,9 @@ skolem:lemma3014 a r:Inference; 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:lemma4392. - -skolem:lemma3015 a r:Inference; - r:gives { - (2 3 4 7) :sort (2 3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - skolem:lemma4968 - skolem:lemma4395 - skolem:lemma4969 - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - [ a r:Fact; r:gives {(() (2 3 4 7)) list:append (2 3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3016 a r:Inference; +skolem:lemma2638 a r:Inference; r:gives { (2 3 4 7) :digitsToNumber 2347 . }; @@ -76229,9 +63102,9 @@ skolem:lemma3016 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3017 a r:Inference; +skolem:lemma2639 a r:Inference; r:gives { (7 4 3 2) :digitsToNumber 7432 . }; @@ -76249,9 +63122,9 @@ skolem:lemma3017 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3018 a r:Inference; +skolem:lemma2640 a r:Inference; r:gives { 2348 :numberToDigits (2 3 4 8). }; @@ -76270,32 +63143,9 @@ skolem:lemma3018 a r:Inference; 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:lemma4392. - -skolem:lemma3019 a r:Inference; - r:gives { - (2 3 4 8) :sort (2 3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - skolem:lemma4970 - skolem:lemma4395 - skolem:lemma4971 - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - [ a r:Fact; r:gives {(() (2 3 4 8)) list:append (2 3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3020 a r:Inference; +skolem:lemma2641 a r:Inference; r:gives { (2 3 4 8) :digitsToNumber 2348 . }; @@ -76313,9 +63163,9 @@ skolem:lemma3020 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3021 a r:Inference; +skolem:lemma2642 a r:Inference; r:gives { (8 4 3 2) :digitsToNumber 8432 . }; @@ -76333,9 +63183,9 @@ skolem:lemma3021 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3022 a r:Inference; +skolem:lemma2643 a r:Inference; r:gives { 2349 :numberToDigits (2 3 4 9). }; @@ -76354,32 +63204,9 @@ skolem:lemma3022 a r:Inference; 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:lemma4392. - -skolem:lemma3023 a r:Inference; - r:gives { - (2 3 4 9) :sort (2 3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - skolem:lemma4972 - skolem:lemma4395 - skolem:lemma4973 - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - [ a r:Fact; r:gives {(() (2 3 4 9)) list:append (2 3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 4 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_2"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3024 a r:Inference; +skolem:lemma2644 a r:Inference; r:gives { (2 3 4 9) :digitsToNumber 2349 . }; @@ -76397,9 +63224,9 @@ skolem:lemma3024 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3025 a r:Inference; +skolem:lemma2645 a r:Inference; r:gives { (9 4 3 2) :digitsToNumber 9432 . }; @@ -76417,9 +63244,9 @@ skolem:lemma3025 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3026 a r:Inference; +skolem:lemma2646 a r:Inference; r:gives { 2350 :numberToDigits (2 3 5 0). }; @@ -76438,32 +63265,9 @@ skolem:lemma3026 a r:Inference; 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:lemma4392. - -skolem:lemma3027 a r:Inference; - r:gives { - (2 3 5 0) :sort (0 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 0) list:firstRest (2 (3 5 0))}] - skolem:lemma4974 - skolem:lemma4506 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((0) (2 3 5)) list:append (0 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 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 (3 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 (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3028 a r:Inference; +skolem:lemma2647 a r:Inference; r:gives { 2351 :numberToDigits (2 3 5 1). }; @@ -76482,32 +63286,9 @@ skolem:lemma3028 a r:Inference; 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:lemma4392. - -skolem:lemma3029 a r:Inference; - r:gives { - (2 3 5 1) :sort (1 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 1) list:firstRest (2 (3 5 1))}] - skolem:lemma4975 - skolem:lemma4705 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((1) (2 3 5)) list:append (1 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 1)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3030 a r:Inference; +skolem:lemma2648 a r:Inference; r:gives { 2352 :numberToDigits (2 3 5 2). }; @@ -76526,32 +63307,9 @@ skolem:lemma3030 a r:Inference; 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:lemma4392. - -skolem:lemma3031 a r:Inference; - r:gives { - (2 3 5 2) :sort (2 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 2) list:firstRest (2 (3 5 2))}] - skolem:lemma4976 - skolem:lemma4833 - skolem:lemma4511 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((2) (2 3 5)) list:append (2 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 2)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3032 a r:Inference; +skolem:lemma2649 a r:Inference; r:gives { 2353 :numberToDigits (2 3 5 3). }; @@ -76570,32 +63328,9 @@ skolem:lemma3032 a r:Inference; 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:lemma4392. - -skolem:lemma3033 a r:Inference; - r:gives { - (2 3 5 3) :sort (2 3 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 3) list:firstRest (2 (3 5 3))}] - skolem:lemma4977 - skolem:lemma4395 - skolem:lemma4978 - [ a r:Fact; r:gives {(2 3 3 5) list:firstRest (2 (3 3 5))}] - [ a r:Fact; r:gives {(() (2 3 3 5)) list:append (2 3 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3034 a r:Inference; +skolem:lemma2650 a r:Inference; r:gives { 2354 :numberToDigits (2 3 5 4). }; @@ -76614,32 +63349,9 @@ skolem:lemma3034 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3035 a r:Inference; - r:gives { - (2 3 5 4) :sort (2 3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 4) list:firstRest (2 (3 5 4))}] - skolem:lemma4979 - skolem:lemma4395 - skolem:lemma4980 - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - [ a r:Fact; r:gives {(() (2 3 4 5)) list:append (2 3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3036 a r:Inference; +skolem:lemma2651 a r:Inference; r:gives { 2355 :numberToDigits (2 3 5 5). }; @@ -76658,32 +63370,9 @@ skolem:lemma3036 a r:Inference; 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:lemma4392. - -skolem:lemma3037 a r:Inference; - r:gives { - (2 3 5 5) :sort (2 3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 5) list:firstRest (2 (3 5 5))}] - skolem:lemma4981 - skolem:lemma4395 - skolem:lemma4982 - [ a r:Fact; r:gives {(2 3 5 5) list:firstRest (2 (3 5 5))}] - [ a r:Fact; r:gives {(() (2 3 5 5)) list:append (2 3 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3038 a r:Inference; +skolem:lemma2652 a r:Inference; r:gives { (2 3 5 5) :digitsToNumber 2355 . }; @@ -76701,9 +63390,9 @@ skolem:lemma3038 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3039 a r:Inference; +skolem:lemma2653 a r:Inference; r:gives { (5 5 3 2) :digitsToNumber 5532 . }; @@ -76721,9 +63410,9 @@ skolem:lemma3039 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3040 a r:Inference; +skolem:lemma2654 a r:Inference; r:gives { 2356 :numberToDigits (2 3 5 6). }; @@ -76742,32 +63431,9 @@ skolem:lemma3040 a r:Inference; 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:lemma4392. - -skolem:lemma3041 a r:Inference; - r:gives { - (2 3 5 6) :sort (2 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - skolem:lemma4983 - skolem:lemma4395 - skolem:lemma4984 - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - [ a r:Fact; r:gives {(() (2 3 5 6)) list:append (2 3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3042 a r:Inference; +skolem:lemma2655 a r:Inference; r:gives { (2 3 5 6) :digitsToNumber 2356 . }; @@ -76785,9 +63451,9 @@ skolem:lemma3042 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3043 a r:Inference; +skolem:lemma2656 a r:Inference; r:gives { (6 5 3 2) :digitsToNumber 6532 . }; @@ -76805,9 +63471,9 @@ skolem:lemma3043 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3044 a r:Inference; +skolem:lemma2657 a r:Inference; r:gives { 2357 :numberToDigits (2 3 5 7). }; @@ -76826,32 +63492,9 @@ skolem:lemma3044 a r:Inference; 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:lemma4392. - -skolem:lemma3045 a r:Inference; - r:gives { - (2 3 5 7) :sort (2 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - skolem:lemma4985 - skolem:lemma4395 - skolem:lemma4986 - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - [ a r:Fact; r:gives {(() (2 3 5 7)) list:append (2 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3046 a r:Inference; +skolem:lemma2658 a r:Inference; r:gives { (2 3 5 7) :digitsToNumber 2357 . }; @@ -76869,9 +63512,9 @@ skolem:lemma3046 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3047 a r:Inference; +skolem:lemma2659 a r:Inference; r:gives { (7 5 3 2) :digitsToNumber 7532 . }; @@ -76889,9 +63532,70 @@ skolem:lemma3047 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3048 a r:Inference; +skolem:lemma2660 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:lemma3438. + +skolem:lemma2661 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:lemma3439. + +skolem:lemma2662 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:lemma3439. + +skolem:lemma2663 a r:Inference; r:gives { 2359 :numberToDigits (2 3 5 9). }; @@ -76910,32 +63614,9 @@ skolem:lemma3048 a r:Inference; 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:lemma4392. - -skolem:lemma3049 a r:Inference; - r:gives { - (2 3 5 9) :sort (2 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - skolem:lemma4987 - skolem:lemma4395 - skolem:lemma4988 - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - [ a r:Fact; r:gives {(() (2 3 5 9)) list:append (2 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 5 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_2"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3050 a r:Inference; +skolem:lemma2664 a r:Inference; r:gives { (2 3 5 9) :digitsToNumber 2359 . }; @@ -76953,9 +63634,9 @@ skolem:lemma3050 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3051 a r:Inference; +skolem:lemma2665 a r:Inference; r:gives { (9 5 3 2) :digitsToNumber 9532 . }; @@ -76973,9 +63654,9 @@ skolem:lemma3051 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3052 a r:Inference; +skolem:lemma2666 a r:Inference; r:gives { 2360 :numberToDigits (2 3 6 0). }; @@ -76994,32 +63675,9 @@ skolem:lemma3052 a r:Inference; 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:lemma4392. - -skolem:lemma3053 a r:Inference; - r:gives { - (2 3 6 0) :sort (0 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 0) list:firstRest (2 (3 6 0))}] - skolem:lemma4989 - skolem:lemma4506 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((0) (2 3 6)) list:append (0 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 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 (3 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 (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3054 a r:Inference; +skolem:lemma2667 a r:Inference; r:gives { 2361 :numberToDigits (2 3 6 1). }; @@ -77038,32 +63696,9 @@ skolem:lemma3054 a r:Inference; 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:lemma4392. - -skolem:lemma3055 a r:Inference; - r:gives { - (2 3 6 1) :sort (1 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 1) list:firstRest (2 (3 6 1))}] - skolem:lemma4990 - skolem:lemma4705 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((1) (2 3 6)) list:append (1 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 1)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3056 a r:Inference; +skolem:lemma2668 a r:Inference; r:gives { 2362 :numberToDigits (2 3 6 2). }; @@ -77082,34 +63717,11 @@ skolem:lemma3056 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3057 a r:Inference; +skolem:lemma2669 a r:Inference; r:gives { - (2 3 6 2) :sort (2 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 2) list:firstRest (2 (3 6 2))}] - skolem:lemma4991 - skolem:lemma4833 - skolem:lemma4513 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((2) (2 3 6)) list:append (2 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 2)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3058 a r:Inference; - r:gives { - 2363 :numberToDigits (2 3 6 3). + 2363 :numberToDigits (2 3 6 3). }; r:evidence ( [ a r:Fact; r:gives {(2363 1000) math:integerQuotient 2}] @@ -77126,32 +63738,9 @@ skolem:lemma3058 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3059 a r:Inference; - r:gives { - (2 3 6 3) :sort (2 3 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 3) list:firstRest (2 (3 6 3))}] - skolem:lemma4992 - skolem:lemma4395 - skolem:lemma4993 - [ a r:Fact; r:gives {(2 3 3 6) list:firstRest (2 (3 3 6))}] - [ a r:Fact; r:gives {(() (2 3 3 6)) list:append (2 3 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3060 a r:Inference; +skolem:lemma2670 a r:Inference; r:gives { 2364 :numberToDigits (2 3 6 4). }; @@ -77170,32 +63759,9 @@ skolem:lemma3060 a r:Inference; 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:lemma4392. - -skolem:lemma3061 a r:Inference; - r:gives { - (2 3 6 4) :sort (2 3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 4) list:firstRest (2 (3 6 4))}] - skolem:lemma4994 - skolem:lemma4395 - skolem:lemma4995 - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - [ a r:Fact; r:gives {(() (2 3 4 6)) list:append (2 3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3062 a r:Inference; +skolem:lemma2671 a r:Inference; r:gives { 2365 :numberToDigits (2 3 6 5). }; @@ -77214,32 +63780,9 @@ skolem:lemma3062 a r:Inference; 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:lemma4392. - -skolem:lemma3063 a r:Inference; - r:gives { - (2 3 6 5) :sort (2 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 5) list:firstRest (2 (3 6 5))}] - skolem:lemma4996 - skolem:lemma4395 - skolem:lemma4997 - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - [ a r:Fact; r:gives {(() (2 3 5 6)) list:append (2 3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3064 a r:Inference; +skolem:lemma2672 a r:Inference; r:gives { 2366 :numberToDigits (2 3 6 6). }; @@ -77258,32 +63801,9 @@ skolem:lemma3064 a r:Inference; 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:lemma4392. - -skolem:lemma3065 a r:Inference; - r:gives { - (2 3 6 6) :sort (2 3 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 6) list:firstRest (2 (3 6 6))}] - skolem:lemma4998 - skolem:lemma4395 - skolem:lemma4999 - [ a r:Fact; r:gives {(2 3 6 6) list:firstRest (2 (3 6 6))}] - [ a r:Fact; r:gives {(() (2 3 6 6)) list:append (2 3 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3066 a r:Inference; +skolem:lemma2673 a r:Inference; r:gives { (2 3 6 6) :digitsToNumber 2366 . }; @@ -77301,9 +63821,9 @@ skolem:lemma3066 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3067 a r:Inference; +skolem:lemma2674 a r:Inference; r:gives { (6 6 3 2) :digitsToNumber 6632 . }; @@ -77321,9 +63841,9 @@ skolem:lemma3067 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3068 a r:Inference; +skolem:lemma2675 a r:Inference; r:gives { 2367 :numberToDigits (2 3 6 7). }; @@ -77342,32 +63862,9 @@ skolem:lemma3068 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3069 a r:Inference; - r:gives { - (2 3 6 7) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - skolem:lemma5000 - skolem:lemma4395 - skolem:lemma5001 - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - [ a r:Fact; r:gives {(() (2 3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3070 a r:Inference; +skolem:lemma2676 a r:Inference; r:gives { (2 3 6 7) :digitsToNumber 2367 . }; @@ -77385,9 +63882,9 @@ skolem:lemma3070 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3071 a r:Inference; +skolem:lemma2677 a r:Inference; r:gives { (7 6 3 2) :digitsToNumber 7632 . }; @@ -77405,9 +63902,9 @@ skolem:lemma3071 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3072 a r:Inference; +skolem:lemma2678 a r:Inference; r:gives { 2368 :numberToDigits (2 3 6 8). }; @@ -77426,32 +63923,9 @@ skolem:lemma3072 a r:Inference; 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:lemma4392. - -skolem:lemma3073 a r:Inference; - r:gives { - (2 3 6 8) :sort (2 3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - skolem:lemma5002 - skolem:lemma4395 - skolem:lemma5003 - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - [ a r:Fact; r:gives {(() (2 3 6 8)) list:append (2 3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3074 a r:Inference; +skolem:lemma2679 a r:Inference; r:gives { (2 3 6 8) :digitsToNumber 2368 . }; @@ -77469,9 +63943,9 @@ skolem:lemma3074 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3075 a r:Inference; +skolem:lemma2680 a r:Inference; r:gives { (8 6 3 2) :digitsToNumber 8632 . }; @@ -77489,9 +63963,9 @@ skolem:lemma3075 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3076 a r:Inference; +skolem:lemma2681 a r:Inference; r:gives { 2369 :numberToDigits (2 3 6 9). }; @@ -77510,32 +63984,9 @@ skolem:lemma3076 a r:Inference; 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:lemma4392. - -skolem:lemma3077 a r:Inference; - r:gives { - (2 3 6 9) :sort (2 3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - skolem:lemma5004 - skolem:lemma4395 - skolem:lemma5005 - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - [ a r:Fact; r:gives {(() (2 3 6 9)) list:append (2 3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 6 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_2"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3078 a r:Inference; +skolem:lemma2682 a r:Inference; r:gives { (2 3 6 9) :digitsToNumber 2369 . }; @@ -77553,9 +64004,9 @@ skolem:lemma3078 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3079 a r:Inference; +skolem:lemma2683 a r:Inference; r:gives { (9 6 3 2) :digitsToNumber 9632 . }; @@ -77573,9 +64024,9 @@ skolem:lemma3079 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3080 a r:Inference; +skolem:lemma2684 a r:Inference; r:gives { 2370 :numberToDigits (2 3 7 0). }; @@ -77594,32 +64045,9 @@ skolem:lemma3080 a r:Inference; 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:lemma4392. - -skolem:lemma3081 a r:Inference; - r:gives { - (2 3 7 0) :sort (0 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 0) list:firstRest (2 (3 7 0))}] - skolem:lemma5006 - skolem:lemma4506 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((0) (2 3 7)) list:append (0 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 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 (3 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 (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3082 a r:Inference; +skolem:lemma2685 a r:Inference; r:gives { 2371 :numberToDigits (2 3 7 1). }; @@ -77638,32 +64066,9 @@ skolem:lemma3082 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3083 a r:Inference; - r:gives { - (2 3 7 1) :sort (1 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 1) list:firstRest (2 (3 7 1))}] - skolem:lemma5007 - skolem:lemma4705 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((1) (2 3 7)) list:append (1 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 1)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3084 a r:Inference; +skolem:lemma2686 a r:Inference; r:gives { 2372 :numberToDigits (2 3 7 2). }; @@ -77682,32 +64087,9 @@ skolem:lemma3084 a r:Inference; 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:lemma4392. - -skolem:lemma3085 a r:Inference; - r:gives { - (2 3 7 2) :sort (2 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 2) list:firstRest (2 (3 7 2))}] - skolem:lemma5008 - skolem:lemma4833 - skolem:lemma4515 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((2) (2 3 7)) list:append (2 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 2)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3086 a r:Inference; +skolem:lemma2687 a r:Inference; r:gives { 2373 :numberToDigits (2 3 7 3). }; @@ -77726,32 +64108,9 @@ skolem:lemma3086 a r:Inference; 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:lemma4392. - -skolem:lemma3087 a r:Inference; - r:gives { - (2 3 7 3) :sort (2 3 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 3) list:firstRest (2 (3 7 3))}] - skolem:lemma5009 - skolem:lemma4395 - skolem:lemma5010 - [ a r:Fact; r:gives {(2 3 3 7) list:firstRest (2 (3 3 7))}] - [ a r:Fact; r:gives {(() (2 3 3 7)) list:append (2 3 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3088 a r:Inference; +skolem:lemma2688 a r:Inference; r:gives { 2374 :numberToDigits (2 3 7 4). }; @@ -77770,32 +64129,9 @@ skolem:lemma3088 a r:Inference; 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:lemma4392. - -skolem:lemma3089 a r:Inference; - r:gives { - (2 3 7 4) :sort (2 3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 4) list:firstRest (2 (3 7 4))}] - skolem:lemma5011 - skolem:lemma4395 - skolem:lemma5012 - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - [ a r:Fact; r:gives {(() (2 3 4 7)) list:append (2 3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3090 a r:Inference; +skolem:lemma2689 a r:Inference; r:gives { 2375 :numberToDigits (2 3 7 5). }; @@ -77814,32 +64150,9 @@ skolem:lemma3090 a r:Inference; 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:lemma4392. - -skolem:lemma3091 a r:Inference; - r:gives { - (2 3 7 5) :sort (2 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 5) list:firstRest (2 (3 7 5))}] - skolem:lemma5013 - skolem:lemma4395 - skolem:lemma5014 - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - [ a r:Fact; r:gives {(() (2 3 5 7)) list:append (2 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3092 a r:Inference; +skolem:lemma2690 a r:Inference; r:gives { 2376 :numberToDigits (2 3 7 6). }; @@ -77858,32 +64171,9 @@ skolem:lemma3092 a r:Inference; 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:lemma4392. - -skolem:lemma3093 a r:Inference; - r:gives { - (2 3 7 6) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 6) list:firstRest (2 (3 7 6))}] - skolem:lemma5015 - skolem:lemma4395 - skolem:lemma5016 - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - [ a r:Fact; r:gives {(() (2 3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3094 a r:Inference; +skolem:lemma2691 a r:Inference; r:gives { 2377 :numberToDigits (2 3 7 7). }; @@ -77902,32 +64192,9 @@ skolem:lemma3094 a r:Inference; 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:lemma4392. - -skolem:lemma3095 a r:Inference; - r:gives { - (2 3 7 7) :sort (2 3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 7) list:firstRest (2 (3 7 7))}] - skolem:lemma5017 - skolem:lemma4395 - skolem:lemma5018 - [ a r:Fact; r:gives {(2 3 7 7) list:firstRest (2 (3 7 7))}] - [ a r:Fact; r:gives {(() (2 3 7 7)) list:append (2 3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3096 a r:Inference; +skolem:lemma2692 a r:Inference; r:gives { (2 3 7 7) :digitsToNumber 2377 . }; @@ -77945,9 +64212,9 @@ skolem:lemma3096 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3097 a r:Inference; +skolem:lemma2693 a r:Inference; r:gives { (7 7 3 2) :digitsToNumber 7732 . }; @@ -77965,9 +64232,9 @@ skolem:lemma3097 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3098 a r:Inference; +skolem:lemma2694 a r:Inference; r:gives { 2378 :numberToDigits (2 3 7 8). }; @@ -77986,32 +64253,9 @@ skolem:lemma3098 a r:Inference; 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:lemma4392. - -skolem:lemma3099 a r:Inference; - r:gives { - (2 3 7 8) :sort (2 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - skolem:lemma5019 - skolem:lemma4395 - skolem:lemma5020 - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - [ a r:Fact; r:gives {(() (2 3 7 8)) list:append (2 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3100 a r:Inference; +skolem:lemma2695 a r:Inference; r:gives { (2 3 7 8) :digitsToNumber 2378 . }; @@ -78029,9 +64273,9 @@ skolem:lemma3100 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3101 a r:Inference; +skolem:lemma2696 a r:Inference; r:gives { (8 7 3 2) :digitsToNumber 8732 . }; @@ -78049,9 +64293,9 @@ skolem:lemma3101 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3102 a r:Inference; +skolem:lemma2697 a r:Inference; r:gives { 2379 :numberToDigits (2 3 7 9). }; @@ -78070,32 +64314,9 @@ skolem:lemma3102 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3103 a r:Inference; - r:gives { - (2 3 7 9) :sort (2 3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - skolem:lemma5021 - skolem:lemma4395 - skolem:lemma5022 - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - [ a r:Fact; r:gives {(() (2 3 7 9)) list:append (2 3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 7 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_2"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3104 a r:Inference; +skolem:lemma2698 a r:Inference; r:gives { (2 3 7 9) :digitsToNumber 2379 . }; @@ -78113,9 +64334,9 @@ skolem:lemma3104 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3105 a r:Inference; +skolem:lemma2699 a r:Inference; r:gives { (9 7 3 2) :digitsToNumber 9732 . }; @@ -78133,9 +64354,9 @@ skolem:lemma3105 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3106 a r:Inference; +skolem:lemma2700 a r:Inference; r:gives { 2380 :numberToDigits (2 3 8 0). }; @@ -78154,32 +64375,9 @@ skolem:lemma3106 a r:Inference; 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:lemma4392. - -skolem:lemma3107 a r:Inference; - r:gives { - (2 3 8 0) :sort (0 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 0) list:firstRest (2 (3 8 0))}] - skolem:lemma5023 - skolem:lemma4506 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((0) (2 3 8)) list:append (0 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 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 (3 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 (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3108 a r:Inference; +skolem:lemma2701 a r:Inference; r:gives { 2381 :numberToDigits (2 3 8 1). }; @@ -78198,32 +64396,9 @@ skolem:lemma3108 a r:Inference; 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:lemma4392. - -skolem:lemma3109 a r:Inference; - r:gives { - (2 3 8 1) :sort (1 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 1) list:firstRest (2 (3 8 1))}] - skolem:lemma5024 - skolem:lemma4705 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((1) (2 3 8)) list:append (1 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 1)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3110 a r:Inference; +skolem:lemma2702 a r:Inference; r:gives { 2382 :numberToDigits (2 3 8 2). }; @@ -78242,32 +64417,9 @@ skolem:lemma3110 a r:Inference; 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:lemma4392. - -skolem:lemma3111 a r:Inference; - r:gives { - (2 3 8 2) :sort (2 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 2) list:firstRest (2 (3 8 2))}] - skolem:lemma5025 - skolem:lemma4833 - skolem:lemma4517 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((2) (2 3 8)) list:append (2 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 2)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3112 a r:Inference; +skolem:lemma2703 a r:Inference; r:gives { 2383 :numberToDigits (2 3 8 3). }; @@ -78286,32 +64438,9 @@ skolem:lemma3112 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3113 a r:Inference; - r:gives { - (2 3 8 3) :sort (2 3 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 3) list:firstRest (2 (3 8 3))}] - skolem:lemma5026 - skolem:lemma4395 - skolem:lemma5027 - [ a r:Fact; r:gives {(2 3 3 8) list:firstRest (2 (3 3 8))}] - [ a r:Fact; r:gives {(() (2 3 3 8)) list:append (2 3 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3114 a r:Inference; +skolem:lemma2704 a r:Inference; r:gives { 2384 :numberToDigits (2 3 8 4). }; @@ -78330,32 +64459,30 @@ skolem:lemma3114 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3115 a r:Inference; +skolem:lemma2705 a r:Inference; r:gives { - (2 3 8 4) :sort (2 3 4 8). + 2385 :numberToDigits (2 3 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2 3 8 4) list:firstRest (2 (3 8 4))}] - skolem:lemma5028 - skolem:lemma4395 - skolem:lemma5029 - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - [ a r:Fact; r:gives {(() (2 3 4 8)) list:append (2 3 4 8)}] + [ 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_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3116 a r:Inference; +skolem:lemma2706 a r:Inference; r:gives { 2386 :numberToDigits (2 3 8 6). }; @@ -78374,32 +64501,9 @@ skolem:lemma3116 a r:Inference; 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:lemma4392. - -skolem:lemma3117 a r:Inference; - r:gives { - (2 3 8 6) :sort (2 3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 6) list:firstRest (2 (3 8 6))}] - skolem:lemma5030 - skolem:lemma4395 - skolem:lemma5031 - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - [ a r:Fact; r:gives {(() (2 3 6 8)) list:append (2 3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3118 a r:Inference; +skolem:lemma2707 a r:Inference; r:gives { 2387 :numberToDigits (2 3 8 7). }; @@ -78418,32 +64522,9 @@ skolem:lemma3118 a r:Inference; 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:lemma4392. - -skolem:lemma3119 a r:Inference; - r:gives { - (2 3 8 7) :sort (2 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 7) list:firstRest (2 (3 8 7))}] - skolem:lemma5032 - skolem:lemma4395 - skolem:lemma5033 - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - [ a r:Fact; r:gives {(() (2 3 7 8)) list:append (2 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3120 a r:Inference; +skolem:lemma2708 a r:Inference; r:gives { 2388 :numberToDigits (2 3 8 8). }; @@ -78462,32 +64543,9 @@ skolem:lemma3120 a r:Inference; 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:lemma4392. - -skolem:lemma3121 a r:Inference; - r:gives { - (2 3 8 8) :sort (2 3 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 8) list:firstRest (2 (3 8 8))}] - skolem:lemma5034 - skolem:lemma4395 - skolem:lemma5035 - [ a r:Fact; r:gives {(2 3 8 8) list:firstRest (2 (3 8 8))}] - [ a r:Fact; r:gives {(() (2 3 8 8)) list:append (2 3 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3122 a r:Inference; +skolem:lemma2709 a r:Inference; r:gives { (2 3 8 8) :digitsToNumber 2388 . }; @@ -78505,9 +64563,9 @@ skolem:lemma3122 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3123 a r:Inference; +skolem:lemma2710 a r:Inference; r:gives { (8 8 3 2) :digitsToNumber 8832 . }; @@ -78525,9 +64583,9 @@ skolem:lemma3123 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3124 a r:Inference; +skolem:lemma2711 a r:Inference; r:gives { 2389 :numberToDigits (2 3 8 9). }; @@ -78546,32 +64604,9 @@ skolem:lemma3124 a r:Inference; 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:lemma4392. - -skolem:lemma3125 a r:Inference; - r:gives { - (2 3 8 9) :sort (2 3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - skolem:lemma5036 - skolem:lemma4395 - skolem:lemma5037 - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - [ a r:Fact; r:gives {(() (2 3 8 9)) list:append (2 3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 8 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_2"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3126 a r:Inference; +skolem:lemma2712 a r:Inference; r:gives { (2 3 8 9) :digitsToNumber 2389 . }; @@ -78589,9 +64624,9 @@ skolem:lemma3126 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3127 a r:Inference; +skolem:lemma2713 a r:Inference; r:gives { (9 8 3 2) :digitsToNumber 9832 . }; @@ -78609,9 +64644,9 @@ skolem:lemma3127 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3128 a r:Inference; +skolem:lemma2714 a r:Inference; r:gives { 2390 :numberToDigits (2 3 9 0). }; @@ -78630,32 +64665,9 @@ skolem:lemma3128 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3129 a r:Inference; - r:gives { - (2 3 9 0) :sort (0 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 0) list:firstRest (2 (3 9 0))}] - skolem:lemma5038 - skolem:lemma4506 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((0) (2 3 9)) list:append (0 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 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 (3 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 (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3130 a r:Inference; +skolem:lemma2715 a r:Inference; r:gives { 2391 :numberToDigits (2 3 9 1). }; @@ -78674,32 +64686,9 @@ skolem:lemma3130 a r:Inference; 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:lemma4392. - -skolem:lemma3131 a r:Inference; - r:gives { - (2 3 9 1) :sort (1 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 1) list:firstRest (2 (3 9 1))}] - skolem:lemma5039 - skolem:lemma4705 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((1) (2 3 9)) list:append (1 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3132 a r:Inference; +skolem:lemma2716 a r:Inference; r:gives { 2392 :numberToDigits (2 3 9 2). }; @@ -78718,32 +64707,9 @@ skolem:lemma3132 a r:Inference; 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:lemma4392. - -skolem:lemma3133 a r:Inference; - r:gives { - (2 3 9 2) :sort (2 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 2) list:firstRest (2 (3 9 2))}] - skolem:lemma5040 - skolem:lemma4833 - skolem:lemma4519 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((2) (2 3 9)) list:append (2 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3134 a r:Inference; +skolem:lemma2717 a r:Inference; r:gives { 2393 :numberToDigits (2 3 9 3). }; @@ -78762,32 +64728,9 @@ skolem:lemma3134 a r:Inference; 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:lemma4392. - -skolem:lemma3135 a r:Inference; - r:gives { - (2 3 9 3) :sort (2 3 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 3) list:firstRest (2 (3 9 3))}] - skolem:lemma5041 - skolem:lemma4395 - skolem:lemma5042 - [ a r:Fact; r:gives {(2 3 3 9) list:firstRest (2 (3 3 9))}] - [ a r:Fact; r:gives {(() (2 3 3 9)) list:append (2 3 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3136 a r:Inference; +skolem:lemma2718 a r:Inference; r:gives { 2394 :numberToDigits (2 3 9 4). }; @@ -78806,32 +64749,9 @@ skolem:lemma3136 a r:Inference; 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:lemma4392. - -skolem:lemma3137 a r:Inference; - r:gives { - (2 3 9 4) :sort (2 3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 4) list:firstRest (2 (3 9 4))}] - skolem:lemma5043 - skolem:lemma4395 - skolem:lemma5044 - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - [ a r:Fact; r:gives {(() (2 3 4 9)) list:append (2 3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3138 a r:Inference; +skolem:lemma2719 a r:Inference; r:gives { 2395 :numberToDigits (2 3 9 5). }; @@ -78850,32 +64770,9 @@ skolem:lemma3138 a r:Inference; 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:lemma4392. - -skolem:lemma3139 a r:Inference; - r:gives { - (2 3 9 5) :sort (2 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 5) list:firstRest (2 (3 9 5))}] - skolem:lemma5045 - skolem:lemma4395 - skolem:lemma5046 - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - [ a r:Fact; r:gives {(() (2 3 5 9)) list:append (2 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3140 a r:Inference; +skolem:lemma2720 a r:Inference; r:gives { 2396 :numberToDigits (2 3 9 6). }; @@ -78894,32 +64791,9 @@ skolem:lemma3140 a r:Inference; 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:lemma4392. - -skolem:lemma3141 a r:Inference; - r:gives { - (2 3 9 6) :sort (2 3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 6) list:firstRest (2 (3 9 6))}] - skolem:lemma5047 - skolem:lemma4395 - skolem:lemma5048 - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - [ a r:Fact; r:gives {(() (2 3 6 9)) list:append (2 3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3142 a r:Inference; +skolem:lemma2721 a r:Inference; r:gives { 2397 :numberToDigits (2 3 9 7). }; @@ -78938,32 +64812,9 @@ skolem:lemma3142 a r:Inference; 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:lemma4392. - -skolem:lemma3143 a r:Inference; - r:gives { - (2 3 9 7) :sort (2 3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 7) list:firstRest (2 (3 9 7))}] - skolem:lemma5049 - skolem:lemma4395 - skolem:lemma5050 - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - [ a r:Fact; r:gives {(() (2 3 7 9)) list:append (2 3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3144 a r:Inference; +skolem:lemma2722 a r:Inference; r:gives { 2398 :numberToDigits (2 3 9 8). }; @@ -78982,32 +64833,9 @@ skolem:lemma3144 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3145 a r:Inference; - r:gives { - (2 3 9 8) :sort (2 3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 8) list:firstRest (2 (3 9 8))}] - skolem:lemma5051 - skolem:lemma4395 - skolem:lemma5052 - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - [ a r:Fact; r:gives {(() (2 3 8 9)) list:append (2 3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3146 a r:Inference; +skolem:lemma2723 a r:Inference; r:gives { 2399 :numberToDigits (2 3 9 9). }; @@ -79026,32 +64854,9 @@ skolem:lemma3146 a r:Inference; 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:lemma4392. - -skolem:lemma3147 a r:Inference; - r:gives { - (2 3 9 9) :sort (2 3 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9 9) list:firstRest (2 (3 9 9))}] - skolem:lemma5053 - skolem:lemma4395 - skolem:lemma5054 - [ a r:Fact; r:gives {(2 3 9 9) list:firstRest (2 (3 9 9))}] - [ a r:Fact; r:gives {(() (2 3 9 9)) list:append (2 3 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 9 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_2"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3148 a r:Inference; +skolem:lemma2724 a r:Inference; r:gives { (2 3 9 9) :digitsToNumber 2399 . }; @@ -79069,9 +64874,9 @@ skolem:lemma3148 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3149 a r:Inference; +skolem:lemma2725 a r:Inference; r:gives { (9 9 3 2) :digitsToNumber 9932 . }; @@ -79089,9 +64894,9 @@ skolem:lemma3149 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3150 a r:Inference; +skolem:lemma2726 a r:Inference; r:gives { 2400 :numberToDigits (2 4 0 0). }; @@ -79110,32 +64915,9 @@ skolem:lemma3150 a r:Inference; 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:lemma4392. - -skolem:lemma3151 a r:Inference; - r:gives { - (2 4 0 0) :sort (0 0 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 0) list:firstRest (2 (4 0 0))}] - skolem:lemma5055 - skolem:lemma4407 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 0) (2 4)) list:append (0 0 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3152 a r:Inference; +skolem:lemma2727 a r:Inference; r:gives { 2401 :numberToDigits (2 4 0 1). }; @@ -79154,32 +64936,9 @@ skolem:lemma3152 a r:Inference; 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:lemma4392. - -skolem:lemma3153 a r:Inference; - r:gives { - (2 4 0 1) :sort (0 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 1) list:firstRest (2 (4 0 1))}] - skolem:lemma5056 - skolem:lemma4442 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 1) (2 4)) list:append (0 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3154 a r:Inference; +skolem:lemma2728 a r:Inference; r:gives { 2402 :numberToDigits (2 4 0 2). }; @@ -79198,32 +64957,9 @@ skolem:lemma3154 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3155 a r:Inference; - r:gives { - (2 4 0 2) :sort (0 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 2) list:firstRest (2 (4 0 2))}] - skolem:lemma5057 - skolem:lemma4479 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 2) (2 4)) list:append (0 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 4)]; - r:rule skolem:lemma4396. - -skolem:lemma3156 a r:Inference; +skolem:lemma2729 a r:Inference; r:gives { 2403 :numberToDigits (2 4 0 3). }; @@ -79242,32 +64978,9 @@ skolem:lemma3156 a r:Inference; 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:lemma4392. - -skolem:lemma3157 a r:Inference; - r:gives { - (2 4 0 3) :sort (0 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 3) list:firstRest (2 (4 0 3))}] - skolem:lemma5058 - skolem:lemma4506 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((0) (2 3 4)) list:append (0 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 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 (4 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3158 a r:Inference; +skolem:lemma2730 a r:Inference; r:gives { 2404 :numberToDigits (2 4 0 4). }; @@ -79286,32 +64999,9 @@ skolem:lemma3158 a r:Inference; 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:lemma4392. - -skolem:lemma3159 a r:Inference; - r:gives { - (2 4 0 4) :sort (0 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 4) list:firstRest (2 (4 0 4))}] - skolem:lemma5059 - skolem:lemma4506 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((0) (2 4 4)) list:append (0 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 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 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3160 a r:Inference; +skolem:lemma2731 a r:Inference; r:gives { 2405 :numberToDigits (2 4 0 5). }; @@ -79330,32 +65020,30 @@ skolem:lemma3160 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3161 a r:Inference; +skolem:lemma2732 a r:Inference; r:gives { - (2 4 0 5) :sort (0 2 4 5). + 2406 :numberToDigits (2 4 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2 4 0 5) list:firstRest (2 (4 0 5))}] - skolem:lemma5060 - skolem:lemma4506 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((0) (2 4 5)) list:append (0 2 4 5)}] + [ 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_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 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 (4 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 (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 5)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3162 a r:Inference; +skolem:lemma2733 a r:Inference; r:gives { 2407 :numberToDigits (2 4 0 7). }; @@ -79374,32 +65062,9 @@ skolem:lemma3162 a r:Inference; 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:lemma4392. - -skolem:lemma3163 a r:Inference; - r:gives { - (2 4 0 7) :sort (0 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 7) list:firstRest (2 (4 0 7))}] - skolem:lemma5061 - skolem:lemma4506 - skolem:lemma4530 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((0) (2 4 7)) list:append (0 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 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 (4 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 (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3164 a r:Inference; +skolem:lemma2734 a r:Inference; r:gives { 2408 :numberToDigits (2 4 0 8). }; @@ -79418,32 +65083,9 @@ skolem:lemma3164 a r:Inference; 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:lemma4392. - -skolem:lemma3165 a r:Inference; - r:gives { - (2 4 0 8) :sort (0 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 8) list:firstRest (2 (4 0 8))}] - skolem:lemma5062 - skolem:lemma4506 - skolem:lemma4532 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((0) (2 4 8)) list:append (0 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 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 (4 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 (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3166 a r:Inference; +skolem:lemma2735 a r:Inference; r:gives { 2409 :numberToDigits (2 4 0 9). }; @@ -79462,32 +65104,9 @@ skolem:lemma3166 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3167 a r:Inference; - r:gives { - (2 4 0 9) :sort (0 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0 9) list:firstRest (2 (4 0 9))}] - skolem:lemma5063 - skolem:lemma4506 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((0) (2 4 9)) list:append (0 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 0 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_2"]; r:boundTo (4 0 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 (4 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 (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3168 a r:Inference; +skolem:lemma2736 a r:Inference; r:gives { 2410 :numberToDigits (2 4 1 0). }; @@ -79506,32 +65125,9 @@ skolem:lemma3168 a r:Inference; 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:lemma4392. - -skolem:lemma3169 a r:Inference; - r:gives { - (2 4 1 0) :sort (0 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 0) list:firstRest (2 (4 1 0))}] - skolem:lemma5064 - skolem:lemma4660 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 1) (2 4)) list:append (0 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3170 a r:Inference; +skolem:lemma2737 a r:Inference; r:gives { 2411 :numberToDigits (2 4 1 1). }; @@ -79550,32 +65146,9 @@ skolem:lemma3170 a r:Inference; 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:lemma4392. - -skolem:lemma3171 a r:Inference; - r:gives { - (2 4 1 1) :sort (1 1 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 1) list:firstRest (2 (4 1 1))}] - skolem:lemma5065 - skolem:lemma4680 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 1) (2 4)) list:append (1 1 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3172 a r:Inference; +skolem:lemma2738 a r:Inference; r:gives { 2412 :numberToDigits (2 4 1 2). }; @@ -79594,32 +65167,9 @@ skolem:lemma3172 a r:Inference; 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:lemma4392. - -skolem:lemma3173 a r:Inference; - r:gives { - (2 4 1 2) :sort (1 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 2) list:firstRest (2 (4 1 2))}] - skolem:lemma5066 - skolem:lemma4694 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 2) (2 4)) list:append (1 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3174 a r:Inference; +skolem:lemma2739 a r:Inference; r:gives { 2413 :numberToDigits (2 4 1 3). }; @@ -79638,32 +65188,9 @@ skolem:lemma3174 a r:Inference; 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:lemma4392. - -skolem:lemma3175 a r:Inference; - r:gives { - (2 4 1 3) :sort (1 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 3) list:firstRest (2 (4 1 3))}] - skolem:lemma5067 - skolem:lemma4705 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((1) (2 3 4)) list:append (1 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 3)]; - 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 3)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3176 a r:Inference; +skolem:lemma2740 a r:Inference; r:gives { 2414 :numberToDigits (2 4 1 4). }; @@ -79682,32 +65209,9 @@ skolem:lemma3176 a r:Inference; 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:lemma4392. - -skolem:lemma3177 a r:Inference; - r:gives { - (2 4 1 4) :sort (1 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 4) list:firstRest (2 (4 1 4))}] - skolem:lemma5068 - skolem:lemma4705 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((1) (2 4 4)) list:append (1 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3178 a r:Inference; +skolem:lemma2741 a r:Inference; r:gives { 2415 :numberToDigits (2 4 1 5). }; @@ -79726,32 +65230,9 @@ skolem:lemma3178 a r:Inference; 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:lemma4392. - -skolem:lemma3179 a r:Inference; - r:gives { - (2 4 1 5) :sort (1 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 5) list:firstRest (2 (4 1 5))}] - skolem:lemma5069 - skolem:lemma4705 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((1) (2 4 5)) list:append (1 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3180 a r:Inference; +skolem:lemma2742 a r:Inference; r:gives { 2416 :numberToDigits (2 4 1 6). }; @@ -79770,32 +65251,30 @@ skolem:lemma3180 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3181 a r:Inference; +skolem:lemma2743 a r:Inference; r:gives { - (2 4 1 6) :sort (1 2 4 6). + 2417 :numberToDigits (2 4 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2 4 1 6) list:firstRest (2 (4 1 6))}] - skolem:lemma5070 - skolem:lemma4705 - skolem:lemma4719 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((1) (2 4 6)) list:append (1 2 4 6)}] + [ 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_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 6)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3182 a r:Inference; +skolem:lemma2744 a r:Inference; r:gives { 2418 :numberToDigits (2 4 1 8). }; @@ -79814,32 +65293,9 @@ skolem:lemma3182 a r:Inference; 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:lemma4392. - -skolem:lemma3183 a r:Inference; - r:gives { - (2 4 1 8) :sort (1 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 8) list:firstRest (2 (4 1 8))}] - skolem:lemma5071 - skolem:lemma4705 - skolem:lemma4532 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((1) (2 4 8)) list:append (1 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3184 a r:Inference; +skolem:lemma2745 a r:Inference; r:gives { 2419 :numberToDigits (2 4 1 9). }; @@ -79858,32 +65314,9 @@ skolem:lemma3184 a r:Inference; 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:lemma4392. - -skolem:lemma3185 a r:Inference; - r:gives { - (2 4 1 9) :sort (1 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1 9) list:firstRest (2 (4 1 9))}] - skolem:lemma5072 - skolem:lemma4705 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((1) (2 4 9)) list:append (1 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 1 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_2"]; r:boundTo (4 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3186 a r:Inference; +skolem:lemma2746 a r:Inference; r:gives { 2420 :numberToDigits (2 4 2 0). }; @@ -79902,32 +65335,9 @@ skolem:lemma3186 a r:Inference; 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:lemma4392. - -skolem:lemma3187 a r:Inference; - r:gives { - (2 4 2 0) :sort (0 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 0) list:firstRest (2 (4 2 0))}] - skolem:lemma5073 - skolem:lemma4793 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((0 2) (2 4)) list:append (0 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3188 a r:Inference; +skolem:lemma2747 a r:Inference; r:gives { 2421 :numberToDigits (2 4 2 1). }; @@ -79946,32 +65356,9 @@ skolem:lemma3188 a r:Inference; 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:lemma4392. - -skolem:lemma3189 a r:Inference; - r:gives { - (2 4 2 1) :sort (1 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 1) list:firstRest (2 (4 2 1))}] - skolem:lemma5074 - skolem:lemma4807 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((1 2) (2 4)) list:append (1 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3190 a r:Inference; +skolem:lemma2748 a r:Inference; r:gives { 2422 :numberToDigits (2 4 2 2). }; @@ -79990,32 +65377,9 @@ skolem:lemma3190 a r:Inference; 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:lemma4392. - -skolem:lemma3191 a r:Inference; - r:gives { - (2 4 2 2) :sort (2 2 2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 2) list:firstRest (2 (4 2 2))}] - skolem:lemma5075 - skolem:lemma4822 - skolem:lemma4414 - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {((2 2) (2 4)) list:append (2 2 2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3192 a r:Inference; +skolem:lemma2749 a r:Inference; r:gives { 2423 :numberToDigits (2 4 2 3). }; @@ -80034,32 +65398,9 @@ skolem:lemma3192 a r:Inference; 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:lemma4392. - -skolem:lemma3193 a r:Inference; - r:gives { - (2 4 2 3) :sort (2 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 3) list:firstRest (2 (4 2 3))}] - skolem:lemma5076 - skolem:lemma4833 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((2) (2 3 4)) list:append (2 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 3)]; - 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 3)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3194 a r:Inference; +skolem:lemma2750 a r:Inference; r:gives { 2424 :numberToDigits (2 4 2 4). }; @@ -80078,32 +65419,9 @@ skolem:lemma3194 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3195 a r:Inference; - r:gives { - (2 4 2 4) :sort (2 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 4) list:firstRest (2 (4 2 4))}] - skolem:lemma5077 - skolem:lemma4833 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((2) (2 4 4)) list:append (2 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 4)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma3196 a r:Inference; +skolem:lemma2751 a r:Inference; r:gives { 2425 :numberToDigits (2 4 2 5). }; @@ -80122,32 +65440,9 @@ skolem:lemma3196 a r:Inference; 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:lemma4392. - -skolem:lemma3197 a r:Inference; - r:gives { - (2 4 2 5) :sort (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 5) list:firstRest (2 (4 2 5))}] - skolem:lemma5078 - skolem:lemma4833 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((2) (2 4 5)) list:append (2 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3198 a r:Inference; +skolem:lemma2752 a r:Inference; r:gives { 2426 :numberToDigits (2 4 2 6). }; @@ -80166,32 +65461,9 @@ skolem:lemma3198 a r:Inference; 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:lemma4392. - -skolem:lemma3199 a r:Inference; - r:gives { - (2 4 2 6) :sort (2 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 6) list:firstRest (2 (4 2 6))}] - skolem:lemma5079 - skolem:lemma4833 - skolem:lemma4719 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((2) (2 4 6)) list:append (2 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3200 a r:Inference; +skolem:lemma2753 a r:Inference; r:gives { 2427 :numberToDigits (2 4 2 7). }; @@ -80210,32 +65482,30 @@ skolem:lemma3200 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3201 a r:Inference; +skolem:lemma2754 a r:Inference; r:gives { - (2 4 2 7) :sort (2 2 4 7). + 2428 :numberToDigits (2 4 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 4 2 7) list:firstRest (2 (4 2 7))}] - skolem:lemma5080 - skolem:lemma4833 - skolem:lemma4530 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((2) (2 4 7)) list:append (2 2 4 7)}] + [ 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_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3202 a r:Inference; +skolem:lemma2755 a r:Inference; r:gives { 2429 :numberToDigits (2 4 2 9). }; @@ -80254,32 +65524,9 @@ skolem:lemma3202 a r:Inference; 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:lemma4392. - -skolem:lemma3203 a r:Inference; - r:gives { - (2 4 2 9) :sort (2 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2 9) list:firstRest (2 (4 2 9))}] - skolem:lemma5081 - skolem:lemma4833 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((2) (2 4 9)) list:append (2 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 2 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_2"]; r:boundTo (4 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3204 a r:Inference; +skolem:lemma2756 a r:Inference; r:gives { 2430 :numberToDigits (2 4 3 0). }; @@ -80298,32 +65545,9 @@ skolem:lemma3204 a r:Inference; 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:lemma4392. - -skolem:lemma3205 a r:Inference; - r:gives { - (2 4 3 0) :sort (0 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 0) list:firstRest (2 (4 3 0))}] - skolem:lemma5082 - skolem:lemma4506 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((0) (2 3 4)) list:append (0 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 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 (4 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3206 a r:Inference; +skolem:lemma2757 a r:Inference; r:gives { 2431 :numberToDigits (2 4 3 1). }; @@ -80342,32 +65566,9 @@ skolem:lemma3206 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3207 a r:Inference; - r:gives { - (2 4 3 1) :sort (1 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 1) list:firstRest (2 (4 3 1))}] - skolem:lemma5083 - skolem:lemma4705 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((1) (2 3 4)) list:append (1 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 1)]; - 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 3)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma3208 a r:Inference; +skolem:lemma2758 a r:Inference; r:gives { 2432 :numberToDigits (2 4 3 2). }; @@ -80386,32 +65587,9 @@ skolem:lemma3208 a r:Inference; 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:lemma4392. - -skolem:lemma3209 a r:Inference; - r:gives { - (2 4 3 2) :sort (2 2 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 2) list:firstRest (2 (4 3 2))}] - skolem:lemma5084 - skolem:lemma4833 - skolem:lemma4524 - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {((2) (2 3 4)) list:append (2 2 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 2)]; - 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 3)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3210 a r:Inference; +skolem:lemma2759 a r:Inference; r:gives { 2433 :numberToDigits (2 4 3 3). }; @@ -80430,32 +65608,9 @@ skolem:lemma3210 a r:Inference; 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:lemma4392. - -skolem:lemma3211 a r:Inference; - r:gives { - (2 4 3 3) :sort (2 3 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 3) list:firstRest (2 (4 3 3))}] - skolem:lemma5085 - skolem:lemma4395 - skolem:lemma5086 - [ a r:Fact; r:gives {(2 3 3 4) list:firstRest (2 (3 3 4))}] - [ a r:Fact; r:gives {(() (2 3 3 4)) list:append (2 3 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3212 a r:Inference; +skolem:lemma2760 a r:Inference; r:gives { 2434 :numberToDigits (2 4 3 4). }; @@ -80474,32 +65629,9 @@ skolem:lemma3212 a r:Inference; 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:lemma4392. - -skolem:lemma3213 a r:Inference; - r:gives { - (2 4 3 4) :sort (2 3 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 4) list:firstRest (2 (4 3 4))}] - skolem:lemma5087 - skolem:lemma4395 - skolem:lemma5088 - [ a r:Fact; r:gives {(2 3 4 4) list:firstRest (2 (3 4 4))}] - [ a r:Fact; r:gives {(() (2 3 4 4)) list:append (2 3 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3214 a r:Inference; +skolem:lemma2761 a r:Inference; r:gives { 2435 :numberToDigits (2 4 3 5). }; @@ -80518,32 +65650,9 @@ skolem:lemma3214 a r:Inference; 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:lemma4392. - -skolem:lemma3215 a r:Inference; - r:gives { - (2 4 3 5) :sort (2 3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 5) list:firstRest (2 (4 3 5))}] - skolem:lemma5089 - skolem:lemma4395 - skolem:lemma5090 - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - [ a r:Fact; r:gives {(() (2 3 4 5)) list:append (2 3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3216 a r:Inference; +skolem:lemma2762 a r:Inference; r:gives { 2436 :numberToDigits (2 4 3 6). }; @@ -80562,32 +65671,9 @@ skolem:lemma3216 a r:Inference; 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:lemma4392. - -skolem:lemma3217 a r:Inference; - r:gives { - (2 4 3 6) :sort (2 3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 6) list:firstRest (2 (4 3 6))}] - skolem:lemma5091 - skolem:lemma4395 - skolem:lemma5092 - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - [ a r:Fact; r:gives {(() (2 3 4 6)) list:append (2 3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3218 a r:Inference; +skolem:lemma2763 a r:Inference; r:gives { 2437 :numberToDigits (2 4 3 7). }; @@ -80606,32 +65692,9 @@ skolem:lemma3218 a r:Inference; 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:lemma4392. - -skolem:lemma3219 a r:Inference; - r:gives { - (2 4 3 7) :sort (2 3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 7) list:firstRest (2 (4 3 7))}] - skolem:lemma5093 - skolem:lemma4395 - skolem:lemma5094 - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - [ a r:Fact; r:gives {(() (2 3 4 7)) list:append (2 3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3220 a r:Inference; +skolem:lemma2764 a r:Inference; r:gives { 2438 :numberToDigits (2 4 3 8). }; @@ -80650,32 +65713,9 @@ skolem:lemma3220 a r:Inference; 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:lemma4392. - -skolem:lemma3221 a r:Inference; - r:gives { - (2 4 3 8) :sort (2 3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 8) list:firstRest (2 (4 3 8))}] - skolem:lemma5095 - skolem:lemma4395 - skolem:lemma5096 - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - [ a r:Fact; r:gives {(() (2 3 4 8)) list:append (2 3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3222 a r:Inference; +skolem:lemma2765 a r:Inference; r:gives { 2439 :numberToDigits (2 4 3 9). }; @@ -80694,32 +65734,9 @@ skolem:lemma3222 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3223 a r:Inference; - r:gives { - (2 4 3 9) :sort (2 3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3 9) list:firstRest (2 (4 3 9))}] - skolem:lemma5097 - skolem:lemma4395 - skolem:lemma5098 - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - [ a r:Fact; r:gives {(() (2 3 4 9)) list:append (2 3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 3 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_2"]; r:boundTo (4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3224 a r:Inference; +skolem:lemma2766 a r:Inference; r:gives { 2440 :numberToDigits (2 4 4 0). }; @@ -80738,32 +65755,9 @@ skolem:lemma3224 a r:Inference; 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:lemma4392. - -skolem:lemma3225 a r:Inference; - r:gives { - (2 4 4 0) :sort (0 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 0) list:firstRest (2 (4 4 0))}] - skolem:lemma5099 - skolem:lemma4506 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((0) (2 4 4)) list:append (0 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 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 (4 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3226 a r:Inference; +skolem:lemma2767 a r:Inference; r:gives { 2441 :numberToDigits (2 4 4 1). }; @@ -80782,32 +65776,9 @@ skolem:lemma3226 a r:Inference; 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:lemma4392. - -skolem:lemma3227 a r:Inference; - r:gives { - (2 4 4 1) :sort (1 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 1) list:firstRest (2 (4 4 1))}] - skolem:lemma5100 - skolem:lemma4705 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((1) (2 4 4)) list:append (1 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 1)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3228 a r:Inference; +skolem:lemma2768 a r:Inference; r:gives { 2442 :numberToDigits (2 4 4 2). }; @@ -80826,32 +65797,9 @@ skolem:lemma3228 a r:Inference; 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:lemma4392. - -skolem:lemma3229 a r:Inference; - r:gives { - (2 4 4 2) :sort (2 2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 2) list:firstRest (2 (4 4 2))}] - skolem:lemma5101 - skolem:lemma4833 - skolem:lemma4526 - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {((2) (2 4 4)) list:append (2 2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 2)]; - 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 4)]; - 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3230 a r:Inference; +skolem:lemma2769 a r:Inference; r:gives { 2443 :numberToDigits (2 4 4 3). }; @@ -80870,32 +65818,9 @@ skolem:lemma3230 a r:Inference; 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:lemma4392. - -skolem:lemma3231 a r:Inference; - r:gives { - (2 4 4 3) :sort (2 3 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 3) list:firstRest (2 (4 4 3))}] - skolem:lemma5102 - skolem:lemma4395 - skolem:lemma5103 - [ a r:Fact; r:gives {(2 3 4 4) list:firstRest (2 (3 4 4))}] - [ a r:Fact; r:gives {(() (2 3 4 4)) list:append (2 3 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3232 a r:Inference; +skolem:lemma2770 a r:Inference; r:gives { 2444 :numberToDigits (2 4 4 4). }; @@ -80914,32 +65839,9 @@ skolem:lemma3232 a r:Inference; 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:lemma4392. - -skolem:lemma3233 a r:Inference; - r:gives { - (2 4 4 4) :sort (2 4 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 4) list:firstRest (2 (4 4 4))}] - skolem:lemma5104 - skolem:lemma4395 - skolem:lemma5105 - [ a r:Fact; r:gives {(2 4 4 4) list:firstRest (2 (4 4 4))}] - [ a r:Fact; r:gives {(() (2 4 4 4)) list:append (2 4 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 4)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3234 a r:Inference; +skolem:lemma2771 a r:Inference; r:gives { (2 4 4 4) :digitsToNumber 2444 . }; @@ -80957,9 +65859,9 @@ skolem:lemma3234 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3235 a r:Inference; +skolem:lemma2772 a r:Inference; r:gives { (4 4 4 2) :digitsToNumber 4442 . }; @@ -80977,9 +65879,9 @@ skolem:lemma3235 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3236 a r:Inference; +skolem:lemma2773 a r:Inference; r:gives { 2445 :numberToDigits (2 4 4 5). }; @@ -80998,32 +65900,9 @@ skolem:lemma3236 a r:Inference; 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:lemma4392. - -skolem:lemma3237 a r:Inference; - r:gives { - (2 4 4 5) :sort (2 4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 5) list:firstRest (2 (4 4 5))}] - skolem:lemma5106 - skolem:lemma4395 - skolem:lemma5107 - [ a r:Fact; r:gives {(2 4 4 5) list:firstRest (2 (4 4 5))}] - [ a r:Fact; r:gives {(() (2 4 4 5)) list:append (2 4 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3238 a r:Inference; +skolem:lemma2774 a r:Inference; r:gives { (2 4 4 5) :digitsToNumber 2445 . }; @@ -81041,9 +65920,9 @@ skolem:lemma3238 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3239 a r:Inference; +skolem:lemma2775 a r:Inference; r:gives { (5 4 4 2) :digitsToNumber 5442 . }; @@ -81061,9 +65940,9 @@ skolem:lemma3239 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3240 a r:Inference; +skolem:lemma2776 a r:Inference; r:gives { 2446 :numberToDigits (2 4 4 6). }; @@ -81082,32 +65961,9 @@ skolem:lemma3240 a r:Inference; 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:lemma4392. - -skolem:lemma3241 a r:Inference; - r:gives { - (2 4 4 6) :sort (2 4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 6) list:firstRest (2 (4 4 6))}] - skolem:lemma5108 - skolem:lemma4395 - skolem:lemma5109 - [ a r:Fact; r:gives {(2 4 4 6) list:firstRest (2 (4 4 6))}] - [ a r:Fact; r:gives {(() (2 4 4 6)) list:append (2 4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3242 a r:Inference; +skolem:lemma2777 a r:Inference; r:gives { (2 4 4 6) :digitsToNumber 2446 . }; @@ -81125,9 +65981,9 @@ skolem:lemma3242 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3243 a r:Inference; +skolem:lemma2778 a r:Inference; r:gives { (6 4 4 2) :digitsToNumber 6442 . }; @@ -81145,9 +66001,9 @@ skolem:lemma3243 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3244 a r:Inference; +skolem:lemma2779 a r:Inference; r:gives { 2447 :numberToDigits (2 4 4 7). }; @@ -81166,32 +66022,9 @@ skolem:lemma3244 a r:Inference; 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:lemma4392. - -skolem:lemma3245 a r:Inference; - r:gives { - (2 4 4 7) :sort (2 4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 7) list:firstRest (2 (4 4 7))}] - skolem:lemma5110 - skolem:lemma4395 - skolem:lemma5111 - [ a r:Fact; r:gives {(2 4 4 7) list:firstRest (2 (4 4 7))}] - [ a r:Fact; r:gives {(() (2 4 4 7)) list:append (2 4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3246 a r:Inference; +skolem:lemma2780 a r:Inference; r:gives { (2 4 4 7) :digitsToNumber 2447 . }; @@ -81209,9 +66042,9 @@ skolem:lemma3246 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3247 a r:Inference; +skolem:lemma2781 a r:Inference; r:gives { (7 4 4 2) :digitsToNumber 7442 . }; @@ -81229,9 +66062,9 @@ skolem:lemma3247 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3248 a r:Inference; +skolem:lemma2782 a r:Inference; r:gives { 2448 :numberToDigits (2 4 4 8). }; @@ -81250,32 +66083,9 @@ skolem:lemma3248 a r:Inference; 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:lemma4392. - -skolem:lemma3249 a r:Inference; - r:gives { - (2 4 4 8) :sort (2 4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 8) list:firstRest (2 (4 4 8))}] - skolem:lemma5112 - skolem:lemma4395 - skolem:lemma5113 - [ a r:Fact; r:gives {(2 4 4 8) list:firstRest (2 (4 4 8))}] - [ a r:Fact; r:gives {(() (2 4 4 8)) list:append (2 4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3250 a r:Inference; +skolem:lemma2783 a r:Inference; r:gives { (2 4 4 8) :digitsToNumber 2448 . }; @@ -81293,9 +66103,9 @@ skolem:lemma3250 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3251 a r:Inference; +skolem:lemma2784 a r:Inference; r:gives { (8 4 4 2) :digitsToNumber 8442 . }; @@ -81313,9 +66123,9 @@ skolem:lemma3251 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3252 a r:Inference; +skolem:lemma2785 a r:Inference; r:gives { 2449 :numberToDigits (2 4 4 9). }; @@ -81334,32 +66144,9 @@ skolem:lemma3252 a r:Inference; 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:lemma4392. - -skolem:lemma3253 a r:Inference; - r:gives { - (2 4 4 9) :sort (2 4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4 9) list:firstRest (2 (4 4 9))}] - skolem:lemma5114 - skolem:lemma4395 - skolem:lemma5115 - [ a r:Fact; r:gives {(2 4 4 9) list:firstRest (2 (4 4 9))}] - [ a r:Fact; r:gives {(() (2 4 4 9)) list:append (2 4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 4 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_2"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3254 a r:Inference; +skolem:lemma2786 a r:Inference; r:gives { (2 4 4 9) :digitsToNumber 2449 . }; @@ -81377,9 +66164,9 @@ skolem:lemma3254 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3255 a r:Inference; +skolem:lemma2787 a r:Inference; r:gives { (9 4 4 2) :digitsToNumber 9442 . }; @@ -81397,9 +66184,9 @@ skolem:lemma3255 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3256 a r:Inference; +skolem:lemma2788 a r:Inference; r:gives { 2450 :numberToDigits (2 4 5 0). }; @@ -81418,32 +66205,9 @@ skolem:lemma3256 a r:Inference; 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:lemma4392. - -skolem:lemma3257 a r:Inference; - r:gives { - (2 4 5 0) :sort (0 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 0) list:firstRest (2 (4 5 0))}] - skolem:lemma5116 - skolem:lemma4506 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((0) (2 4 5)) list:append (0 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 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 (4 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 (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3258 a r:Inference; +skolem:lemma2789 a r:Inference; r:gives { 2451 :numberToDigits (2 4 5 1). }; @@ -81462,32 +66226,9 @@ skolem:lemma3258 a r:Inference; 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:lemma4392. - -skolem:lemma3259 a r:Inference; - r:gives { - (2 4 5 1) :sort (1 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 1) list:firstRest (2 (4 5 1))}] - skolem:lemma5117 - skolem:lemma4705 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((1) (2 4 5)) list:append (1 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 1)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3260 a r:Inference; +skolem:lemma2790 a r:Inference; r:gives { 2452 :numberToDigits (2 4 5 2). }; @@ -81506,32 +66247,9 @@ skolem:lemma3260 a r:Inference; 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:lemma4392. - -skolem:lemma3261 a r:Inference; - r:gives { - (2 4 5 2) :sort (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 2) list:firstRest (2 (4 5 2))}] - skolem:lemma5118 - skolem:lemma4833 - skolem:lemma4528 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((2) (2 4 5)) list:append (2 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 2)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3262 a r:Inference; +skolem:lemma2791 a r:Inference; r:gives { 2453 :numberToDigits (2 4 5 3). }; @@ -81550,32 +66268,9 @@ skolem:lemma3262 a r:Inference; 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:lemma4392. - -skolem:lemma3263 a r:Inference; - r:gives { - (2 4 5 3) :sort (2 3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 3) list:firstRest (2 (4 5 3))}] - skolem:lemma5119 - skolem:lemma4395 - skolem:lemma5120 - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - [ a r:Fact; r:gives {(() (2 3 4 5)) list:append (2 3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3264 a r:Inference; +skolem:lemma2792 a r:Inference; r:gives { 2454 :numberToDigits (2 4 5 4). }; @@ -81594,32 +66289,9 @@ skolem:lemma3264 a r:Inference; 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:lemma4392. - -skolem:lemma3265 a r:Inference; - r:gives { - (2 4 5 4) :sort (2 4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 4) list:firstRest (2 (4 5 4))}] - skolem:lemma5121 - skolem:lemma4395 - skolem:lemma5122 - [ a r:Fact; r:gives {(2 4 4 5) list:firstRest (2 (4 4 5))}] - [ a r:Fact; r:gives {(() (2 4 4 5)) list:append (2 4 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3266 a r:Inference; +skolem:lemma2793 a r:Inference; r:gives { 2455 :numberToDigits (2 4 5 5). }; @@ -81638,32 +66310,9 @@ skolem:lemma3266 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3267 a r:Inference; - r:gives { - (2 4 5 5) :sort (2 4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 5) list:firstRest (2 (4 5 5))}] - skolem:lemma5123 - skolem:lemma4395 - skolem:lemma5124 - [ a r:Fact; r:gives {(2 4 5 5) list:firstRest (2 (4 5 5))}] - [ a r:Fact; r:gives {(() (2 4 5 5)) list:append (2 4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3268 a r:Inference; +skolem:lemma2794 a r:Inference; r:gives { (2 4 5 5) :digitsToNumber 2455 . }; @@ -81681,9 +66330,9 @@ skolem:lemma3268 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3269 a r:Inference; +skolem:lemma2795 a r:Inference; r:gives { (5 5 4 2) :digitsToNumber 5542 . }; @@ -81701,9 +66350,9 @@ skolem:lemma3269 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3270 a r:Inference; +skolem:lemma2796 a r:Inference; r:gives { 2456 :numberToDigits (2 4 5 6). }; @@ -81722,32 +66371,9 @@ skolem:lemma3270 a r:Inference; 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:lemma4392. - -skolem:lemma3271 a r:Inference; - r:gives { - (2 4 5 6) :sort (2 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - skolem:lemma5125 - skolem:lemma4395 - skolem:lemma5126 - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - [ a r:Fact; r:gives {(() (2 4 5 6)) list:append (2 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3272 a r:Inference; +skolem:lemma2797 a r:Inference; r:gives { (2 4 5 6) :digitsToNumber 2456 . }; @@ -81765,9 +66391,9 @@ skolem:lemma3272 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3273 a r:Inference; +skolem:lemma2798 a r:Inference; r:gives { (6 5 4 2) :digitsToNumber 6542 . }; @@ -81785,9 +66411,9 @@ skolem:lemma3273 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3274 a r:Inference; +skolem:lemma2799 a r:Inference; r:gives { 2457 :numberToDigits (2 4 5 7). }; @@ -81806,32 +66432,9 @@ skolem:lemma3274 a r:Inference; 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:lemma4392. - -skolem:lemma3275 a r:Inference; - r:gives { - (2 4 5 7) :sort (2 4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - skolem:lemma5127 - skolem:lemma4395 - skolem:lemma5128 - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - [ a r:Fact; r:gives {(() (2 4 5 7)) list:append (2 4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3276 a r:Inference; +skolem:lemma2800 a r:Inference; r:gives { (2 4 5 7) :digitsToNumber 2457 . }; @@ -81849,9 +66452,9 @@ skolem:lemma3276 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3277 a r:Inference; +skolem:lemma2801 a r:Inference; r:gives { (7 5 4 2) :digitsToNumber 7542 . }; @@ -81869,9 +66472,9 @@ skolem:lemma3277 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3278 a r:Inference; +skolem:lemma2802 a r:Inference; r:gives { 2458 :numberToDigits (2 4 5 8). }; @@ -81890,32 +66493,9 @@ skolem:lemma3278 a r:Inference; 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:lemma4392. - -skolem:lemma3279 a r:Inference; - r:gives { - (2 4 5 8) :sort (2 4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - skolem:lemma5129 - skolem:lemma4395 - skolem:lemma5130 - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - [ a r:Fact; r:gives {(() (2 4 5 8)) list:append (2 4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3280 a r:Inference; +skolem:lemma2803 a r:Inference; r:gives { (2 4 5 8) :digitsToNumber 2458 . }; @@ -81933,9 +66513,9 @@ skolem:lemma3280 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3281 a r:Inference; +skolem:lemma2804 a r:Inference; r:gives { (8 5 4 2) :digitsToNumber 8542 . }; @@ -81953,9 +66533,9 @@ skolem:lemma3281 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3282 a r:Inference; +skolem:lemma2805 a r:Inference; r:gives { 2459 :numberToDigits (2 4 5 9). }; @@ -81974,32 +66554,9 @@ skolem:lemma3282 a r:Inference; 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:lemma4392. - -skolem:lemma3283 a r:Inference; - r:gives { - (2 4 5 9) :sort (2 4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - skolem:lemma5131 - skolem:lemma4395 - skolem:lemma5132 - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - [ a r:Fact; r:gives {(() (2 4 5 9)) list:append (2 4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 5 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_2"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3284 a r:Inference; +skolem:lemma2806 a r:Inference; r:gives { (2 4 5 9) :digitsToNumber 2459 . }; @@ -82017,9 +66574,9 @@ skolem:lemma3284 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3285 a r:Inference; +skolem:lemma2807 a r:Inference; r:gives { (9 5 4 2) :digitsToNumber 9542 . }; @@ -82037,9 +66594,30 @@ skolem:lemma3285 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3286 a r:Inference; +skolem:lemma2808 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:lemma3438. + +skolem:lemma2809 a r:Inference; r:gives { 2461 :numberToDigits (2 4 6 1). }; @@ -82058,32 +66636,9 @@ skolem:lemma3286 a r:Inference; 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:lemma4392. - -skolem:lemma3287 a r:Inference; - r:gives { - (2 4 6 1) :sort (1 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 1) list:firstRest (2 (4 6 1))}] - skolem:lemma5133 - skolem:lemma4705 - skolem:lemma4719 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((1) (2 4 6)) list:append (1 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 1)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3288 a r:Inference; +skolem:lemma2810 a r:Inference; r:gives { 2462 :numberToDigits (2 4 6 2). }; @@ -82102,32 +66657,9 @@ skolem:lemma3288 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3289 a r:Inference; - r:gives { - (2 4 6 2) :sort (2 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 2) list:firstRest (2 (4 6 2))}] - skolem:lemma5134 - skolem:lemma4833 - skolem:lemma4719 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((2) (2 4 6)) list:append (2 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 2)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3290 a r:Inference; +skolem:lemma2811 a r:Inference; r:gives { 2463 :numberToDigits (2 4 6 3). }; @@ -82146,32 +66678,9 @@ skolem:lemma3290 a r:Inference; 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:lemma4392. - -skolem:lemma3291 a r:Inference; - r:gives { - (2 4 6 3) :sort (2 3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 3) list:firstRest (2 (4 6 3))}] - skolem:lemma5135 - skolem:lemma4395 - skolem:lemma5136 - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - [ a r:Fact; r:gives {(() (2 3 4 6)) list:append (2 3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3292 a r:Inference; +skolem:lemma2812 a r:Inference; r:gives { 2464 :numberToDigits (2 4 6 4). }; @@ -82190,32 +66699,9 @@ skolem:lemma3292 a r:Inference; 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:lemma4392. - -skolem:lemma3293 a r:Inference; - r:gives { - (2 4 6 4) :sort (2 4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 4) list:firstRest (2 (4 6 4))}] - skolem:lemma5137 - skolem:lemma4395 - skolem:lemma5138 - [ a r:Fact; r:gives {(2 4 4 6) list:firstRest (2 (4 4 6))}] - [ a r:Fact; r:gives {(() (2 4 4 6)) list:append (2 4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3294 a r:Inference; +skolem:lemma2813 a r:Inference; r:gives { 2465 :numberToDigits (2 4 6 5). }; @@ -82234,32 +66720,9 @@ skolem:lemma3294 a r:Inference; 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:lemma4392. - -skolem:lemma3295 a r:Inference; - r:gives { - (2 4 6 5) :sort (2 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 5) list:firstRest (2 (4 6 5))}] - skolem:lemma5139 - skolem:lemma4395 - skolem:lemma5140 - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - [ a r:Fact; r:gives {(() (2 4 5 6)) list:append (2 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3296 a r:Inference; +skolem:lemma2814 a r:Inference; r:gives { 2466 :numberToDigits (2 4 6 6). }; @@ -82278,32 +66741,9 @@ skolem:lemma3296 a r:Inference; 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:lemma4392. - -skolem:lemma3297 a r:Inference; - r:gives { - (2 4 6 6) :sort (2 4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 6) list:firstRest (2 (4 6 6))}] - skolem:lemma5141 - skolem:lemma4395 - skolem:lemma5142 - [ a r:Fact; r:gives {(2 4 6 6) list:firstRest (2 (4 6 6))}] - [ a r:Fact; r:gives {(() (2 4 6 6)) list:append (2 4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3298 a r:Inference; +skolem:lemma2815 a r:Inference; r:gives { (2 4 6 6) :digitsToNumber 2466 . }; @@ -82321,9 +66761,9 @@ skolem:lemma3298 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3299 a r:Inference; +skolem:lemma2816 a r:Inference; r:gives { (6 6 4 2) :digitsToNumber 6642 . }; @@ -82341,9 +66781,9 @@ skolem:lemma3299 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3300 a r:Inference; +skolem:lemma2817 a r:Inference; r:gives { 2467 :numberToDigits (2 4 6 7). }; @@ -82362,32 +66802,9 @@ skolem:lemma3300 a r:Inference; 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:lemma4392. - -skolem:lemma3301 a r:Inference; - r:gives { - (2 4 6 7) :sort (2 4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - skolem:lemma5143 - skolem:lemma4395 - skolem:lemma5144 - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - [ a r:Fact; r:gives {(() (2 4 6 7)) list:append (2 4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3302 a r:Inference; +skolem:lemma2818 a r:Inference; r:gives { (2 4 6 7) :digitsToNumber 2467 . }; @@ -82405,9 +66822,9 @@ skolem:lemma3302 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3303 a r:Inference; +skolem:lemma2819 a r:Inference; r:gives { (7 6 4 2) :digitsToNumber 7642 . }; @@ -82425,14 +66842,75 @@ skolem:lemma3303 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3304 a r:Inference; +skolem:lemma2820 a r:Inference; r:gives { - 2469 :numberToDigits (2 4 6 9). + 2468 :numberToDigits (2 4 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2469 1000) math:integerQuotient 2}] + [ 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:lemma3438. + +skolem:lemma2821 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:lemma3439. + +skolem:lemma2822 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:lemma3439. + +skolem:lemma2823 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}] @@ -82446,32 +66924,9 @@ skolem:lemma3304 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3305 a r:Inference; - r:gives { - (2 4 6 9) :sort (2 4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - skolem:lemma5145 - skolem:lemma4395 - skolem:lemma5146 - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - [ a r:Fact; r:gives {(() (2 4 6 9)) list:append (2 4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 6 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_2"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3306 a r:Inference; +skolem:lemma2824 a r:Inference; r:gives { (2 4 6 9) :digitsToNumber 2469 . }; @@ -82489,9 +66944,9 @@ skolem:lemma3306 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3307 a r:Inference; +skolem:lemma2825 a r:Inference; r:gives { (9 6 4 2) :digitsToNumber 9642 . }; @@ -82509,9 +66964,9 @@ skolem:lemma3307 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3308 a r:Inference; +skolem:lemma2826 a r:Inference; r:gives { 2470 :numberToDigits (2 4 7 0). }; @@ -82530,32 +66985,30 @@ skolem:lemma3308 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3309 a r:Inference; +skolem:lemma2827 a r:Inference; r:gives { - (2 4 7 0) :sort (0 2 4 7). + 2471 :numberToDigits (2 4 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2 4 7 0) list:firstRest (2 (4 7 0))}] - skolem:lemma5147 - skolem:lemma4506 - skolem:lemma4530 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((0) (2 4 7)) list:append (0 2 4 7)}] + [ 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_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 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 (4 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 (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3310 a r:Inference; +skolem:lemma2828 a r:Inference; r:gives { 2472 :numberToDigits (2 4 7 2). }; @@ -82574,32 +67027,9 @@ skolem:lemma3310 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3311 a r:Inference; - r:gives { - (2 4 7 2) :sort (2 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 2) list:firstRest (2 (4 7 2))}] - skolem:lemma5148 - skolem:lemma4833 - skolem:lemma4530 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((2) (2 4 7)) list:append (2 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 2)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3312 a r:Inference; +skolem:lemma2829 a r:Inference; r:gives { 2473 :numberToDigits (2 4 7 3). }; @@ -82618,32 +67048,9 @@ skolem:lemma3312 a r:Inference; 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:lemma4392. - -skolem:lemma3313 a r:Inference; - r:gives { - (2 4 7 3) :sort (2 3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 3) list:firstRest (2 (4 7 3))}] - skolem:lemma5149 - skolem:lemma4395 - skolem:lemma5150 - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - [ a r:Fact; r:gives {(() (2 3 4 7)) list:append (2 3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3314 a r:Inference; +skolem:lemma2830 a r:Inference; r:gives { 2474 :numberToDigits (2 4 7 4). }; @@ -82662,32 +67069,9 @@ skolem:lemma3314 a r:Inference; 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:lemma4392. - -skolem:lemma3315 a r:Inference; - r:gives { - (2 4 7 4) :sort (2 4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 4) list:firstRest (2 (4 7 4))}] - skolem:lemma5151 - skolem:lemma4395 - skolem:lemma5152 - [ a r:Fact; r:gives {(2 4 4 7) list:firstRest (2 (4 4 7))}] - [ a r:Fact; r:gives {(() (2 4 4 7)) list:append (2 4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3316 a r:Inference; +skolem:lemma2831 a r:Inference; r:gives { 2475 :numberToDigits (2 4 7 5). }; @@ -82706,32 +67090,9 @@ skolem:lemma3316 a r:Inference; 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:lemma4392. - -skolem:lemma3317 a r:Inference; - r:gives { - (2 4 7 5) :sort (2 4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 5) list:firstRest (2 (4 7 5))}] - skolem:lemma5153 - skolem:lemma4395 - skolem:lemma5154 - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - [ a r:Fact; r:gives {(() (2 4 5 7)) list:append (2 4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3318 a r:Inference; +skolem:lemma2832 a r:Inference; r:gives { 2476 :numberToDigits (2 4 7 6). }; @@ -82750,32 +67111,9 @@ skolem:lemma3318 a r:Inference; 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:lemma4392. - -skolem:lemma3319 a r:Inference; - r:gives { - (2 4 7 6) :sort (2 4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 6) list:firstRest (2 (4 7 6))}] - skolem:lemma5155 - skolem:lemma4395 - skolem:lemma5156 - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - [ a r:Fact; r:gives {(() (2 4 6 7)) list:append (2 4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3320 a r:Inference; +skolem:lemma2833 a r:Inference; r:gives { 2477 :numberToDigits (2 4 7 7). }; @@ -82794,32 +67132,9 @@ skolem:lemma3320 a r:Inference; 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:lemma4392. - -skolem:lemma3321 a r:Inference; - r:gives { - (2 4 7 7) :sort (2 4 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 7) list:firstRest (2 (4 7 7))}] - skolem:lemma5157 - skolem:lemma4395 - skolem:lemma5158 - [ a r:Fact; r:gives {(2 4 7 7) list:firstRest (2 (4 7 7))}] - [ a r:Fact; r:gives {(() (2 4 7 7)) list:append (2 4 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3322 a r:Inference; +skolem:lemma2834 a r:Inference; r:gives { (2 4 7 7) :digitsToNumber 2477 . }; @@ -82837,9 +67152,9 @@ skolem:lemma3322 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3323 a r:Inference; +skolem:lemma2835 a r:Inference; r:gives { (7 7 4 2) :digitsToNumber 7742 . }; @@ -82857,9 +67172,9 @@ skolem:lemma3323 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3324 a r:Inference; +skolem:lemma2836 a r:Inference; r:gives { 2478 :numberToDigits (2 4 7 8). }; @@ -82878,32 +67193,9 @@ skolem:lemma3324 a r:Inference; 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:lemma4392. - -skolem:lemma3325 a r:Inference; - r:gives { - (2 4 7 8) :sort (2 4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - skolem:lemma5159 - skolem:lemma4395 - skolem:lemma5160 - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - [ a r:Fact; r:gives {(() (2 4 7 8)) list:append (2 4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3326 a r:Inference; +skolem:lemma2837 a r:Inference; r:gives { (2 4 7 8) :digitsToNumber 2478 . }; @@ -82921,9 +67213,9 @@ skolem:lemma3326 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3327 a r:Inference; +skolem:lemma2838 a r:Inference; r:gives { (8 7 4 2) :digitsToNumber 8742 . }; @@ -82941,9 +67233,9 @@ skolem:lemma3327 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3328 a r:Inference; +skolem:lemma2839 a r:Inference; r:gives { 2479 :numberToDigits (2 4 7 9). }; @@ -82962,32 +67254,9 @@ skolem:lemma3328 a r:Inference; 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:lemma4392. - -skolem:lemma3329 a r:Inference; - r:gives { - (2 4 7 9) :sort (2 4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - skolem:lemma5161 - skolem:lemma4395 - skolem:lemma5162 - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - [ a r:Fact; r:gives {(() (2 4 7 9)) list:append (2 4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 7 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_2"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3330 a r:Inference; +skolem:lemma2840 a r:Inference; r:gives { (2 4 7 9) :digitsToNumber 2479 . }; @@ -83005,9 +67274,9 @@ skolem:lemma3330 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3331 a r:Inference; +skolem:lemma2841 a r:Inference; r:gives { (9 7 4 2) :digitsToNumber 9742 . }; @@ -83025,9 +67294,9 @@ skolem:lemma3331 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3332 a r:Inference; +skolem:lemma2842 a r:Inference; r:gives { 2480 :numberToDigits (2 4 8 0). }; @@ -83046,32 +67315,9 @@ skolem:lemma3332 a r:Inference; 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:lemma4392. - -skolem:lemma3333 a r:Inference; - r:gives { - (2 4 8 0) :sort (0 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 8 0) list:firstRest (2 (4 8 0))}] - skolem:lemma5163 - skolem:lemma4506 - skolem:lemma4532 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((0) (2 4 8)) list:append (0 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 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 (4 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 (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3334 a r:Inference; +skolem:lemma2843 a r:Inference; r:gives { 2481 :numberToDigits (2 4 8 1). }; @@ -83090,32 +67336,30 @@ skolem:lemma3334 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3335 a r:Inference; +skolem:lemma2844 a r:Inference; r:gives { - (2 4 8 1) :sort (1 2 4 8). + 2482 :numberToDigits (2 4 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2 4 8 1) list:firstRest (2 (4 8 1))}] - skolem:lemma5164 - skolem:lemma4705 - skolem:lemma4532 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((1) (2 4 8)) list:append (1 2 4 8)}] + [ 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_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 1)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3336 a r:Inference; +skolem:lemma2845 a r:Inference; r:gives { 2483 :numberToDigits (2 4 8 3). }; @@ -83134,32 +67378,9 @@ skolem:lemma3336 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3337 a r:Inference; - r:gives { - (2 4 8 3) :sort (2 3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 8 3) list:firstRest (2 (4 8 3))}] - skolem:lemma5165 - skolem:lemma4395 - skolem:lemma5166 - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - [ a r:Fact; r:gives {(() (2 3 4 8)) list:append (2 3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3338 a r:Inference; +skolem:lemma2846 a r:Inference; r:gives { 2484 :numberToDigits (2 4 8 4). }; @@ -83178,32 +67399,9 @@ skolem:lemma3338 a r:Inference; 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:lemma4392. - -skolem:lemma3339 a r:Inference; - r:gives { - (2 4 8 4) :sort (2 4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 8 4) list:firstRest (2 (4 8 4))}] - skolem:lemma5167 - skolem:lemma4395 - skolem:lemma5168 - [ a r:Fact; r:gives {(2 4 4 8) list:firstRest (2 (4 4 8))}] - [ a r:Fact; r:gives {(() (2 4 4 8)) list:append (2 4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3340 a r:Inference; +skolem:lemma2847 a r:Inference; r:gives { 2485 :numberToDigits (2 4 8 5). }; @@ -83222,32 +67420,30 @@ skolem:lemma3340 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3341 a r:Inference; +skolem:lemma2848 a r:Inference; r:gives { - (2 4 8 5) :sort (2 4 5 8). + 2486 :numberToDigits (2 4 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2 4 8 5) list:firstRest (2 (4 8 5))}] - skolem:lemma5169 - skolem:lemma4395 - skolem:lemma5170 - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - [ a r:Fact; r:gives {(() (2 4 5 8)) list:append (2 4 5 8)}] + [ 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_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3342 a r:Inference; +skolem:lemma2849 a r:Inference; r:gives { 2487 :numberToDigits (2 4 8 7). }; @@ -83266,32 +67462,9 @@ skolem:lemma3342 a r:Inference; 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:lemma4392. - -skolem:lemma3343 a r:Inference; - r:gives { - (2 4 8 7) :sort (2 4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 8 7) list:firstRest (2 (4 8 7))}] - skolem:lemma5171 - skolem:lemma4395 - skolem:lemma5172 - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - [ a r:Fact; r:gives {(() (2 4 7 8)) list:append (2 4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3344 a r:Inference; +skolem:lemma2850 a r:Inference; r:gives { 2488 :numberToDigits (2 4 8 8). }; @@ -83310,32 +67483,9 @@ skolem:lemma3344 a r:Inference; 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:lemma4392. - -skolem:lemma3345 a r:Inference; - r:gives { - (2 4 8 8) :sort (2 4 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 8 8) list:firstRest (2 (4 8 8))}] - skolem:lemma5173 - skolem:lemma4395 - skolem:lemma5174 - [ a r:Fact; r:gives {(2 4 8 8) list:firstRest (2 (4 8 8))}] - [ a r:Fact; r:gives {(() (2 4 8 8)) list:append (2 4 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3346 a r:Inference; +skolem:lemma2851 a r:Inference; r:gives { (2 4 8 8) :digitsToNumber 2488 . }; @@ -83353,9 +67503,9 @@ skolem:lemma3346 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3347 a r:Inference; +skolem:lemma2852 a r:Inference; r:gives { (8 8 4 2) :digitsToNumber 8842 . }; @@ -83373,9 +67523,9 @@ skolem:lemma3347 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3348 a r:Inference; +skolem:lemma2853 a r:Inference; r:gives { 2489 :numberToDigits (2 4 8 9). }; @@ -83394,32 +67544,9 @@ skolem:lemma3348 a r:Inference; 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:lemma4392. - -skolem:lemma3349 a r:Inference; - r:gives { - (2 4 8 9) :sort (2 4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - skolem:lemma5175 - skolem:lemma4395 - skolem:lemma5176 - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - [ a r:Fact; r:gives {(() (2 4 8 9)) list:append (2 4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 8 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_2"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3350 a r:Inference; +skolem:lemma2854 a r:Inference; r:gives { (2 4 8 9) :digitsToNumber 2489 . }; @@ -83437,9 +67564,9 @@ skolem:lemma3350 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3351 a r:Inference; +skolem:lemma2855 a r:Inference; r:gives { (9 8 4 2) :digitsToNumber 9842 . }; @@ -83457,9 +67584,9 @@ skolem:lemma3351 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3352 a r:Inference; +skolem:lemma2856 a r:Inference; r:gives { 2490 :numberToDigits (2 4 9 0). }; @@ -83478,32 +67605,9 @@ skolem:lemma3352 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3353 a r:Inference; - r:gives { - (2 4 9 0) :sort (0 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 0) list:firstRest (2 (4 9 0))}] - skolem:lemma5177 - skolem:lemma4506 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((0) (2 4 9)) list:append (0 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 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 (4 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 (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3354 a r:Inference; +skolem:lemma2857 a r:Inference; r:gives { 2491 :numberToDigits (2 4 9 1). }; @@ -83522,32 +67626,9 @@ skolem:lemma3354 a r:Inference; 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:lemma4392. - -skolem:lemma3355 a r:Inference; - r:gives { - (2 4 9 1) :sort (1 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 1) list:firstRest (2 (4 9 1))}] - skolem:lemma5178 - skolem:lemma4705 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((1) (2 4 9)) list:append (1 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3356 a r:Inference; +skolem:lemma2858 a r:Inference; r:gives { 2492 :numberToDigits (2 4 9 2). }; @@ -83566,32 +67647,9 @@ skolem:lemma3356 a r:Inference; 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:lemma4392. - -skolem:lemma3357 a r:Inference; - r:gives { - (2 4 9 2) :sort (2 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 2) list:firstRest (2 (4 9 2))}] - skolem:lemma5179 - skolem:lemma4833 - skolem:lemma4534 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((2) (2 4 9)) list:append (2 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3358 a r:Inference; +skolem:lemma2859 a r:Inference; r:gives { 2493 :numberToDigits (2 4 9 3). }; @@ -83610,32 +67668,9 @@ skolem:lemma3358 a r:Inference; 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:lemma4392. - -skolem:lemma3359 a r:Inference; - r:gives { - (2 4 9 3) :sort (2 3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 3) list:firstRest (2 (4 9 3))}] - skolem:lemma5180 - skolem:lemma4395 - skolem:lemma5181 - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - [ a r:Fact; r:gives {(() (2 3 4 9)) list:append (2 3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3360 a r:Inference; +skolem:lemma2860 a r:Inference; r:gives { 2494 :numberToDigits (2 4 9 4). }; @@ -83654,32 +67689,9 @@ skolem:lemma3360 a r:Inference; 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:lemma4392. - -skolem:lemma3361 a r:Inference; - r:gives { - (2 4 9 4) :sort (2 4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 4) list:firstRest (2 (4 9 4))}] - skolem:lemma5182 - skolem:lemma4395 - skolem:lemma5183 - [ a r:Fact; r:gives {(2 4 4 9) list:firstRest (2 (4 4 9))}] - [ a r:Fact; r:gives {(() (2 4 4 9)) list:append (2 4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3362 a r:Inference; +skolem:lemma2861 a r:Inference; r:gives { 2495 :numberToDigits (2 4 9 5). }; @@ -83698,32 +67710,9 @@ skolem:lemma3362 a r:Inference; 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:lemma4392. - -skolem:lemma3363 a r:Inference; - r:gives { - (2 4 9 5) :sort (2 4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 5) list:firstRest (2 (4 9 5))}] - skolem:lemma5184 - skolem:lemma4395 - skolem:lemma5185 - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - [ a r:Fact; r:gives {(() (2 4 5 9)) list:append (2 4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3364 a r:Inference; +skolem:lemma2862 a r:Inference; r:gives { 2496 :numberToDigits (2 4 9 6). }; @@ -83742,32 +67731,9 @@ skolem:lemma3364 a r:Inference; 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:lemma4392. - -skolem:lemma3365 a r:Inference; - r:gives { - (2 4 9 6) :sort (2 4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 6) list:firstRest (2 (4 9 6))}] - skolem:lemma5186 - skolem:lemma4395 - skolem:lemma5187 - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - [ a r:Fact; r:gives {(() (2 4 6 9)) list:append (2 4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3366 a r:Inference; +skolem:lemma2863 a r:Inference; r:gives { 2497 :numberToDigits (2 4 9 7). }; @@ -83786,32 +67752,9 @@ skolem:lemma3366 a r:Inference; 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:lemma4392. - -skolem:lemma3367 a r:Inference; - r:gives { - (2 4 9 7) :sort (2 4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 7) list:firstRest (2 (4 9 7))}] - skolem:lemma5188 - skolem:lemma4395 - skolem:lemma5189 - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - [ a r:Fact; r:gives {(() (2 4 7 9)) list:append (2 4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3368 a r:Inference; +skolem:lemma2864 a r:Inference; r:gives { 2498 :numberToDigits (2 4 9 8). }; @@ -83830,32 +67773,9 @@ skolem:lemma3368 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3369 a r:Inference; - r:gives { - (2 4 9 8) :sort (2 4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 8) list:firstRest (2 (4 9 8))}] - skolem:lemma5190 - skolem:lemma4395 - skolem:lemma5191 - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - [ a r:Fact; r:gives {(() (2 4 8 9)) list:append (2 4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3370 a r:Inference; +skolem:lemma2865 a r:Inference; r:gives { 2499 :numberToDigits (2 4 9 9). }; @@ -83874,32 +67794,9 @@ skolem:lemma3370 a r:Inference; 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:lemma4392. - -skolem:lemma3371 a r:Inference; - r:gives { - (2 4 9 9) :sort (2 4 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9 9) list:firstRest (2 (4 9 9))}] - skolem:lemma5192 - skolem:lemma4395 - skolem:lemma5193 - [ a r:Fact; r:gives {(2 4 9 9) list:firstRest (2 (4 9 9))}] - [ a r:Fact; r:gives {(() (2 4 9 9)) list:append (2 4 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 9 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_2"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3372 a r:Inference; +skolem:lemma2866 a r:Inference; r:gives { (2 4 9 9) :digitsToNumber 2499 . }; @@ -83917,9 +67814,9 @@ skolem:lemma3372 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3373 a r:Inference; +skolem:lemma2867 a r:Inference; r:gives { (9 9 4 2) :digitsToNumber 9942 . }; @@ -83937,9 +67834,9 @@ skolem:lemma3373 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3374 a r:Inference; +skolem:lemma2868 a r:Inference; r:gives { 2500 :numberToDigits (2 5 0 0). }; @@ -83958,32 +67855,9 @@ skolem:lemma3374 a r:Inference; 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:lemma4392. - -skolem:lemma3375 a r:Inference; - r:gives { - (2 5 0 0) :sort (0 0 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 0) list:firstRest (2 (5 0 0))}] - skolem:lemma5194 - skolem:lemma4407 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 0) (2 5)) list:append (0 0 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3376 a r:Inference; +skolem:lemma2869 a r:Inference; r:gives { 2501 :numberToDigits (2 5 0 1). }; @@ -84002,32 +67876,9 @@ skolem:lemma3376 a r:Inference; 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:lemma4392. - -skolem:lemma3377 a r:Inference; - r:gives { - (2 5 0 1) :sort (0 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 1) list:firstRest (2 (5 0 1))}] - skolem:lemma5195 - skolem:lemma4442 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 1) (2 5)) list:append (0 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3378 a r:Inference; +skolem:lemma2870 a r:Inference; r:gives { 2502 :numberToDigits (2 5 0 2). }; @@ -84046,32 +67897,9 @@ skolem:lemma3378 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3379 a r:Inference; - r:gives { - (2 5 0 2) :sort (0 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 2) list:firstRest (2 (5 0 2))}] - skolem:lemma5196 - skolem:lemma4479 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 2) (2 5)) list:append (0 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3380 a r:Inference; +skolem:lemma2871 a r:Inference; r:gives { 2503 :numberToDigits (2 5 0 3). }; @@ -84090,32 +67918,9 @@ skolem:lemma3380 a r:Inference; 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:lemma4392. - -skolem:lemma3381 a r:Inference; - r:gives { - (2 5 0 3) :sort (0 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 3) list:firstRest (2 (5 0 3))}] - skolem:lemma5197 - skolem:lemma4506 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((0) (2 3 5)) list:append (0 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3382 a r:Inference; +skolem:lemma2872 a r:Inference; r:gives { 2504 :numberToDigits (2 5 0 4). }; @@ -84134,32 +67939,9 @@ skolem:lemma3382 a r:Inference; 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:lemma4392. - -skolem:lemma3383 a r:Inference; - r:gives { - (2 5 0 4) :sort (0 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 4) list:firstRest (2 (5 0 4))}] - skolem:lemma5198 - skolem:lemma4506 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((0) (2 4 5)) list:append (0 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3384 a r:Inference; +skolem:lemma2873 a r:Inference; r:gives { 2505 :numberToDigits (2 5 0 5). }; @@ -84178,32 +67960,9 @@ skolem:lemma3384 a r:Inference; 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:lemma4392. - -skolem:lemma3385 a r:Inference; - r:gives { - (2 5 0 5) :sort (0 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 5) list:firstRest (2 (5 0 5))}] - skolem:lemma5199 - skolem:lemma4506 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((0) (2 5 5)) list:append (0 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3386 a r:Inference; +skolem:lemma2874 a r:Inference; r:gives { 2506 :numberToDigits (2 5 0 6). }; @@ -84222,32 +67981,9 @@ skolem:lemma3386 a r:Inference; 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:lemma4392. - -skolem:lemma3387 a r:Inference; - r:gives { - (2 5 0 6) :sort (0 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 6) list:firstRest (2 (5 0 6))}] - skolem:lemma5200 - skolem:lemma4506 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((0) (2 5 6)) list:append (0 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 (5 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 (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3388 a r:Inference; +skolem:lemma2875 a r:Inference; r:gives { 2507 :numberToDigits (2 5 0 7). }; @@ -84266,32 +68002,9 @@ skolem:lemma3388 a r:Inference; 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:lemma4392. - -skolem:lemma3389 a r:Inference; - r:gives { - (2 5 0 7) :sort (0 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 7) list:firstRest (2 (5 0 7))}] - skolem:lemma5201 - skolem:lemma4506 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((0) (2 5 7)) list:append (0 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 (5 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 (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3390 a r:Inference; +skolem:lemma2876 a r:Inference; r:gives { 2508 :numberToDigits (2 5 0 8). }; @@ -84310,32 +68023,9 @@ skolem:lemma3390 a r:Inference; 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:lemma4392. - -skolem:lemma3391 a r:Inference; - r:gives { - (2 5 0 8) :sort (0 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 8) list:firstRest (2 (5 0 8))}] - skolem:lemma5202 - skolem:lemma4506 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((0) (2 5 8)) list:append (0 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 (5 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 (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3392 a r:Inference; +skolem:lemma2877 a r:Inference; r:gives { 2509 :numberToDigits (2 5 0 9). }; @@ -84354,32 +68044,9 @@ skolem:lemma3392 a r:Inference; 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:lemma4392. - -skolem:lemma3393 a r:Inference; - r:gives { - (2 5 0 9) :sort (0 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0 9) list:firstRest (2 (5 0 9))}] - skolem:lemma5203 - skolem:lemma4506 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((0) (2 5 9)) list:append (0 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 0 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_2"]; r:boundTo (5 0 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 (5 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 (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3394 a r:Inference; +skolem:lemma2878 a r:Inference; r:gives { 2510 :numberToDigits (2 5 1 0). }; @@ -84398,32 +68065,9 @@ skolem:lemma3394 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3395 a r:Inference; - r:gives { - (2 5 1 0) :sort (0 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 0) list:firstRest (2 (5 1 0))}] - skolem:lemma5204 - skolem:lemma4660 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 1) (2 5)) list:append (0 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3396 a r:Inference; +skolem:lemma2879 a r:Inference; r:gives { 2511 :numberToDigits (2 5 1 1). }; @@ -84442,32 +68086,9 @@ skolem:lemma3396 a r:Inference; 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:lemma4392. - -skolem:lemma3397 a r:Inference; - r:gives { - (2 5 1 1) :sort (1 1 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 1) list:firstRest (2 (5 1 1))}] - skolem:lemma5205 - skolem:lemma4680 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 1) (2 5)) list:append (1 1 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3398 a r:Inference; +skolem:lemma2880 a r:Inference; r:gives { 2512 :numberToDigits (2 5 1 2). }; @@ -84486,32 +68107,9 @@ skolem:lemma3398 a r:Inference; 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:lemma4392. - -skolem:lemma3399 a r:Inference; - r:gives { - (2 5 1 2) :sort (1 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 2) list:firstRest (2 (5 1 2))}] - skolem:lemma5206 - skolem:lemma4694 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 2) (2 5)) list:append (1 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3400 a r:Inference; +skolem:lemma2881 a r:Inference; r:gives { 2513 :numberToDigits (2 5 1 3). }; @@ -84530,32 +68128,9 @@ skolem:lemma3400 a r:Inference; 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:lemma4392. - -skolem:lemma3401 a r:Inference; - r:gives { - (2 5 1 3) :sort (1 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 3) list:firstRest (2 (5 1 3))}] - skolem:lemma5207 - skolem:lemma4705 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((1) (2 3 5)) list:append (1 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 3)]; - 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 3)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3402 a r:Inference; +skolem:lemma2882 a r:Inference; r:gives { 2514 :numberToDigits (2 5 1 4). }; @@ -84574,32 +68149,9 @@ skolem:lemma3402 a r:Inference; 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:lemma4392. - -skolem:lemma3403 a r:Inference; - r:gives { - (2 5 1 4) :sort (1 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 4) list:firstRest (2 (5 1 4))}] - skolem:lemma5208 - skolem:lemma4705 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((1) (2 4 5)) list:append (1 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 4)]; - 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 4)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3404 a r:Inference; +skolem:lemma2883 a r:Inference; r:gives { 2515 :numberToDigits (2 5 1 5). }; @@ -84618,32 +68170,9 @@ skolem:lemma3404 a r:Inference; 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:lemma4392. - -skolem:lemma3405 a r:Inference; - r:gives { - (2 5 1 5) :sort (1 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 5) list:firstRest (2 (5 1 5))}] - skolem:lemma5209 - skolem:lemma4705 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((1) (2 5 5)) list:append (1 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3406 a r:Inference; +skolem:lemma2884 a r:Inference; r:gives { 2516 :numberToDigits (2 5 1 6). }; @@ -84662,32 +68191,9 @@ skolem:lemma3406 a r:Inference; 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:lemma4392. - -skolem:lemma3407 a r:Inference; - r:gives { - (2 5 1 6) :sort (1 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 6) list:firstRest (2 (5 1 6))}] - skolem:lemma5210 - skolem:lemma4705 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((1) (2 5 6)) list:append (1 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3408 a r:Inference; +skolem:lemma2885 a r:Inference; r:gives { 2517 :numberToDigits (2 5 1 7). }; @@ -84706,32 +68212,9 @@ skolem:lemma3408 a r:Inference; 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:lemma4392. - -skolem:lemma3409 a r:Inference; - r:gives { - (2 5 1 7) :sort (1 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 7) list:firstRest (2 (5 1 7))}] - skolem:lemma5211 - skolem:lemma4705 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((1) (2 5 7)) list:append (1 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3410 a r:Inference; +skolem:lemma2886 a r:Inference; r:gives { 2518 :numberToDigits (2 5 1 8). }; @@ -84750,32 +68233,9 @@ skolem:lemma3410 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3411 a r:Inference; - r:gives { - (2 5 1 8) :sort (1 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 8) list:firstRest (2 (5 1 8))}] - skolem:lemma5212 - skolem:lemma4705 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((1) (2 5 8)) list:append (1 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3412 a r:Inference; +skolem:lemma2887 a r:Inference; r:gives { 2519 :numberToDigits (2 5 1 9). }; @@ -84794,34 +68254,11 @@ skolem:lemma3412 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3413 a r:Inference; +skolem:lemma2888 a r:Inference; r:gives { - (2 5 1 9) :sort (1 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1 9) list:firstRest (2 (5 1 9))}] - skolem:lemma5213 - skolem:lemma4705 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((1) (2 5 9)) list:append (1 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 1 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_2"]; r:boundTo (5 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3414 a r:Inference; - r:gives { - 2520 :numberToDigits (2 5 2 0). + 2520 :numberToDigits (2 5 2 0). }; r:evidence ( [ a r:Fact; r:gives {(2520 1000) math:integerQuotient 2}] @@ -84838,32 +68275,9 @@ skolem:lemma3414 a r:Inference; 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:lemma4392. - -skolem:lemma3415 a r:Inference; - r:gives { - (2 5 2 0) :sort (0 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 0) list:firstRest (2 (5 2 0))}] - skolem:lemma5214 - skolem:lemma4793 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((0 2) (2 5)) list:append (0 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3416 a r:Inference; +skolem:lemma2889 a r:Inference; r:gives { 2521 :numberToDigits (2 5 2 1). }; @@ -84882,32 +68296,9 @@ skolem:lemma3416 a r:Inference; 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:lemma4392. - -skolem:lemma3417 a r:Inference; - r:gives { - (2 5 2 1) :sort (1 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 1) list:firstRest (2 (5 2 1))}] - skolem:lemma5215 - skolem:lemma4807 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((1 2) (2 5)) list:append (1 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3418 a r:Inference; +skolem:lemma2890 a r:Inference; r:gives { 2522 :numberToDigits (2 5 2 2). }; @@ -84926,32 +68317,9 @@ skolem:lemma3418 a r:Inference; 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:lemma4392. - -skolem:lemma3419 a r:Inference; - r:gives { - (2 5 2 2) :sort (2 2 2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 2) list:firstRest (2 (5 2 2))}] - skolem:lemma5216 - skolem:lemma4822 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {((2 2) (2 5)) list:append (2 2 2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3420 a r:Inference; +skolem:lemma2891 a r:Inference; r:gives { 2523 :numberToDigits (2 5 2 3). }; @@ -84970,32 +68338,9 @@ skolem:lemma3420 a r:Inference; 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:lemma4392. - -skolem:lemma3421 a r:Inference; - r:gives { - (2 5 2 3) :sort (2 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 3) list:firstRest (2 (5 2 3))}] - skolem:lemma5217 - skolem:lemma4833 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((2) (2 3 5)) list:append (2 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 3)]; - 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 3)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3422 a r:Inference; +skolem:lemma2892 a r:Inference; r:gives { 2524 :numberToDigits (2 5 2 4). }; @@ -85014,32 +68359,9 @@ skolem:lemma3422 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3423 a r:Inference; - r:gives { - (2 5 2 4) :sort (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 4) list:firstRest (2 (5 2 4))}] - skolem:lemma5218 - skolem:lemma4833 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((2) (2 4 5)) list:append (2 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 4)]; - 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 4)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3424 a r:Inference; +skolem:lemma2893 a r:Inference; r:gives { 2525 :numberToDigits (2 5 2 5). }; @@ -85058,32 +68380,9 @@ skolem:lemma3424 a r:Inference; 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:lemma4392. - -skolem:lemma3425 a r:Inference; - r:gives { - (2 5 2 5) :sort (2 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 5) list:firstRest (2 (5 2 5))}] - skolem:lemma5219 - skolem:lemma4833 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((2) (2 5 5)) list:append (2 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 5)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3426 a r:Inference; +skolem:lemma2894 a r:Inference; r:gives { 2526 :numberToDigits (2 5 2 6). }; @@ -85102,32 +68401,9 @@ skolem:lemma3426 a r:Inference; 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:lemma4392. - -skolem:lemma3427 a r:Inference; - r:gives { - (2 5 2 6) :sort (2 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 6) list:firstRest (2 (5 2 6))}] - skolem:lemma5220 - skolem:lemma4833 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((2) (2 5 6)) list:append (2 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3428 a r:Inference; +skolem:lemma2895 a r:Inference; r:gives { 2527 :numberToDigits (2 5 2 7). }; @@ -85146,32 +68422,9 @@ skolem:lemma3428 a r:Inference; 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:lemma4392. - -skolem:lemma3429 a r:Inference; - r:gives { - (2 5 2 7) :sort (2 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 7) list:firstRest (2 (5 2 7))}] - skolem:lemma5221 - skolem:lemma4833 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((2) (2 5 7)) list:append (2 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3430 a r:Inference; +skolem:lemma2896 a r:Inference; r:gives { 2528 :numberToDigits (2 5 2 8). }; @@ -85190,32 +68443,9 @@ skolem:lemma3430 a r:Inference; 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:lemma4392. - -skolem:lemma3431 a r:Inference; - r:gives { - (2 5 2 8) :sort (2 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 8) list:firstRest (2 (5 2 8))}] - skolem:lemma5222 - skolem:lemma4833 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((2) (2 5 8)) list:append (2 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3432 a r:Inference; +skolem:lemma2897 a r:Inference; r:gives { 2529 :numberToDigits (2 5 2 9). }; @@ -85234,32 +68464,9 @@ skolem:lemma3432 a r:Inference; 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:lemma4392. - -skolem:lemma3433 a r:Inference; - r:gives { - (2 5 2 9) :sort (2 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2 9) list:firstRest (2 (5 2 9))}] - skolem:lemma5223 - skolem:lemma4833 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((2) (2 5 9)) list:append (2 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 2 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_2"]; r:boundTo (5 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3434 a r:Inference; +skolem:lemma2898 a r:Inference; r:gives { 2530 :numberToDigits (2 5 3 0). }; @@ -85278,32 +68485,9 @@ skolem:lemma3434 a r:Inference; 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:lemma4392. - -skolem:lemma3435 a r:Inference; - r:gives { - (2 5 3 0) :sort (0 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 0) list:firstRest (2 (5 3 0))}] - skolem:lemma5224 - skolem:lemma4506 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((0) (2 3 5)) list:append (0 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3436 a r:Inference; +skolem:lemma2899 a r:Inference; r:gives { 2531 :numberToDigits (2 5 3 1). }; @@ -85322,32 +68506,9 @@ skolem:lemma3436 a r:Inference; 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:lemma4392. - -skolem:lemma3437 a r:Inference; - r:gives { - (2 5 3 1) :sort (1 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 1) list:firstRest (2 (5 3 1))}] - skolem:lemma5225 - skolem:lemma4705 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((1) (2 3 5)) list:append (1 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 1)]; - 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 3)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3438 a r:Inference; +skolem:lemma2900 a r:Inference; r:gives { 2532 :numberToDigits (2 5 3 2). }; @@ -85366,32 +68527,9 @@ skolem:lemma3438 a r:Inference; 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:lemma4392. - -skolem:lemma3439 a r:Inference; - r:gives { - (2 5 3 2) :sort (2 2 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 2) list:firstRest (2 (5 3 2))}] - skolem:lemma5226 - skolem:lemma4833 - skolem:lemma4539 - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {((2) (2 3 5)) list:append (2 2 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 2)]; - 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 3)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3440 a r:Inference; +skolem:lemma2901 a r:Inference; r:gives { 2533 :numberToDigits (2 5 3 3). }; @@ -85410,32 +68548,9 @@ skolem:lemma3440 a r:Inference; 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:lemma4392. - -skolem:lemma3441 a r:Inference; - r:gives { - (2 5 3 3) :sort (2 3 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 3) list:firstRest (2 (5 3 3))}] - skolem:lemma5227 - skolem:lemma4395 - skolem:lemma5228 - [ a r:Fact; r:gives {(2 3 3 5) list:firstRest (2 (3 3 5))}] - [ a r:Fact; r:gives {(() (2 3 3 5)) list:append (2 3 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3442 a r:Inference; +skolem:lemma2902 a r:Inference; r:gives { 2534 :numberToDigits (2 5 3 4). }; @@ -85454,32 +68569,9 @@ skolem:lemma3442 a r:Inference; 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:lemma4392. - -skolem:lemma3443 a r:Inference; - r:gives { - (2 5 3 4) :sort (2 3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 4) list:firstRest (2 (5 3 4))}] - skolem:lemma5229 - skolem:lemma4395 - skolem:lemma5230 - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - [ a r:Fact; r:gives {(() (2 3 4 5)) list:append (2 3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3444 a r:Inference; +skolem:lemma2903 a r:Inference; r:gives { 2535 :numberToDigits (2 5 3 5). }; @@ -85498,32 +68590,9 @@ skolem:lemma3444 a r:Inference; 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:lemma4392. - -skolem:lemma3445 a r:Inference; - r:gives { - (2 5 3 5) :sort (2 3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 5) list:firstRest (2 (5 3 5))}] - skolem:lemma5231 - skolem:lemma4395 - skolem:lemma5232 - [ a r:Fact; r:gives {(2 3 5 5) list:firstRest (2 (3 5 5))}] - [ a r:Fact; r:gives {(() (2 3 5 5)) list:append (2 3 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3446 a r:Inference; +skolem:lemma2904 a r:Inference; r:gives { 2536 :numberToDigits (2 5 3 6). }; @@ -85542,32 +68611,9 @@ skolem:lemma3446 a r:Inference; 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:lemma4392. - -skolem:lemma3447 a r:Inference; - r:gives { - (2 5 3 6) :sort (2 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 6) list:firstRest (2 (5 3 6))}] - skolem:lemma5233 - skolem:lemma4395 - skolem:lemma5234 - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - [ a r:Fact; r:gives {(() (2 3 5 6)) list:append (2 3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3448 a r:Inference; +skolem:lemma2905 a r:Inference; r:gives { 2537 :numberToDigits (2 5 3 7). }; @@ -85586,32 +68632,30 @@ skolem:lemma3448 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3449 a r:Inference; +skolem:lemma2906 a r:Inference; r:gives { - (2 5 3 7) :sort (2 3 5 7). + 2538 :numberToDigits (2 5 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 5 3 7) list:firstRest (2 (5 3 7))}] - skolem:lemma5235 - skolem:lemma4395 - skolem:lemma5236 - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - [ a r:Fact; r:gives {(() (2 3 5 7)) list:append (2 3 5 7)}] + [ 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_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3450 a r:Inference; +skolem:lemma2907 a r:Inference; r:gives { 2539 :numberToDigits (2 5 3 9). }; @@ -85630,32 +68674,9 @@ skolem:lemma3450 a r:Inference; 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:lemma4392. - -skolem:lemma3451 a r:Inference; - r:gives { - (2 5 3 9) :sort (2 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3 9) list:firstRest (2 (5 3 9))}] - skolem:lemma5237 - skolem:lemma4395 - skolem:lemma5238 - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - [ a r:Fact; r:gives {(() (2 3 5 9)) list:append (2 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 3 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_2"]; r:boundTo (5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3452 a r:Inference; +skolem:lemma2908 a r:Inference; r:gives { 2540 :numberToDigits (2 5 4 0). }; @@ -85674,32 +68695,9 @@ skolem:lemma3452 a r:Inference; 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:lemma4392. - -skolem:lemma3453 a r:Inference; - r:gives { - (2 5 4 0) :sort (0 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 0) list:firstRest (2 (5 4 0))}] - skolem:lemma5239 - skolem:lemma4506 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((0) (2 4 5)) list:append (0 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3454 a r:Inference; +skolem:lemma2909 a r:Inference; r:gives { 2541 :numberToDigits (2 5 4 1). }; @@ -85718,32 +68716,9 @@ skolem:lemma3454 a r:Inference; 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:lemma4392. - -skolem:lemma3455 a r:Inference; - r:gives { - (2 5 4 1) :sort (1 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 1) list:firstRest (2 (5 4 1))}] - skolem:lemma5240 - skolem:lemma4705 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((1) (2 4 5)) list:append (1 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 1)]; - 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 4)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3456 a r:Inference; +skolem:lemma2910 a r:Inference; r:gives { 2542 :numberToDigits (2 5 4 2). }; @@ -85762,32 +68737,9 @@ skolem:lemma3456 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3457 a r:Inference; - r:gives { - (2 5 4 2) :sort (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 2) list:firstRest (2 (5 4 2))}] - skolem:lemma5241 - skolem:lemma4833 - skolem:lemma4541 - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {((2) (2 4 5)) list:append (2 2 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 2)]; - 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 4)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3458 a r:Inference; +skolem:lemma2911 a r:Inference; r:gives { 2543 :numberToDigits (2 5 4 3). }; @@ -85806,32 +68758,9 @@ skolem:lemma3458 a r:Inference; 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:lemma4392. - -skolem:lemma3459 a r:Inference; - r:gives { - (2 5 4 3) :sort (2 3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 3) list:firstRest (2 (5 4 3))}] - skolem:lemma5242 - skolem:lemma4395 - skolem:lemma5243 - [ a r:Fact; r:gives {(2 3 4 5) list:firstRest (2 (3 4 5))}] - [ a r:Fact; r:gives {(() (2 3 4 5)) list:append (2 3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3460 a r:Inference; +skolem:lemma2912 a r:Inference; r:gives { 2544 :numberToDigits (2 5 4 4). }; @@ -85850,32 +68779,9 @@ skolem:lemma3460 a r:Inference; 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:lemma4392. - -skolem:lemma3461 a r:Inference; - r:gives { - (2 5 4 4) :sort (2 4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 4) list:firstRest (2 (5 4 4))}] - skolem:lemma5244 - skolem:lemma4395 - skolem:lemma5245 - [ a r:Fact; r:gives {(2 4 4 5) list:firstRest (2 (4 4 5))}] - [ a r:Fact; r:gives {(() (2 4 4 5)) list:append (2 4 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3462 a r:Inference; +skolem:lemma2913 a r:Inference; r:gives { 2545 :numberToDigits (2 5 4 5). }; @@ -85894,32 +68800,9 @@ skolem:lemma3462 a r:Inference; 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:lemma4392. - -skolem:lemma3463 a r:Inference; - r:gives { - (2 5 4 5) :sort (2 4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 5) list:firstRest (2 (5 4 5))}] - skolem:lemma5246 - skolem:lemma4395 - skolem:lemma5247 - [ a r:Fact; r:gives {(2 4 5 5) list:firstRest (2 (4 5 5))}] - [ a r:Fact; r:gives {(() (2 4 5 5)) list:append (2 4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3464 a r:Inference; +skolem:lemma2914 a r:Inference; r:gives { 2546 :numberToDigits (2 5 4 6). }; @@ -85938,32 +68821,9 @@ skolem:lemma3464 a r:Inference; 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:lemma4392. - -skolem:lemma3465 a r:Inference; - r:gives { - (2 5 4 6) :sort (2 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 6) list:firstRest (2 (5 4 6))}] - skolem:lemma5248 - skolem:lemma4395 - skolem:lemma5249 - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - [ a r:Fact; r:gives {(() (2 4 5 6)) list:append (2 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3466 a r:Inference; +skolem:lemma2915 a r:Inference; r:gives { 2547 :numberToDigits (2 5 4 7). }; @@ -85982,32 +68842,9 @@ skolem:lemma3466 a r:Inference; 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:lemma4392. - -skolem:lemma3467 a r:Inference; - r:gives { - (2 5 4 7) :sort (2 4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 7) list:firstRest (2 (5 4 7))}] - skolem:lemma5250 - skolem:lemma4395 - skolem:lemma5251 - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - [ a r:Fact; r:gives {(() (2 4 5 7)) list:append (2 4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3468 a r:Inference; +skolem:lemma2916 a r:Inference; r:gives { 2548 :numberToDigits (2 5 4 8). }; @@ -86026,32 +68863,9 @@ skolem:lemma3468 a r:Inference; 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:lemma4392. - -skolem:lemma3469 a r:Inference; - r:gives { - (2 5 4 8) :sort (2 4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 8) list:firstRest (2 (5 4 8))}] - skolem:lemma5252 - skolem:lemma4395 - skolem:lemma5253 - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - [ a r:Fact; r:gives {(() (2 4 5 8)) list:append (2 4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3470 a r:Inference; +skolem:lemma2917 a r:Inference; r:gives { 2549 :numberToDigits (2 5 4 9). }; @@ -86070,32 +68884,9 @@ skolem:lemma3470 a r:Inference; 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:lemma4392. - -skolem:lemma3471 a r:Inference; - r:gives { - (2 5 4 9) :sort (2 4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4 9) list:firstRest (2 (5 4 9))}] - skolem:lemma5254 - skolem:lemma4395 - skolem:lemma5255 - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - [ a r:Fact; r:gives {(() (2 4 5 9)) list:append (2 4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 4 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_2"]; r:boundTo (5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3472 a r:Inference; +skolem:lemma2918 a r:Inference; r:gives { 2550 :numberToDigits (2 5 5 0). }; @@ -86114,32 +68905,9 @@ skolem:lemma3472 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3473 a r:Inference; - r:gives { - (2 5 5 0) :sort (0 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 0) list:firstRest (2 (5 5 0))}] - skolem:lemma5256 - skolem:lemma4506 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((0) (2 5 5)) list:append (0 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 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 (5 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma3474 a r:Inference; +skolem:lemma2919 a r:Inference; r:gives { 2551 :numberToDigits (2 5 5 1). }; @@ -86158,32 +68926,9 @@ skolem:lemma3474 a r:Inference; 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:lemma4392. - -skolem:lemma3475 a r:Inference; - r:gives { - (2 5 5 1) :sort (1 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 1) list:firstRest (2 (5 5 1))}] - skolem:lemma5257 - skolem:lemma4705 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((1) (2 5 5)) list:append (1 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 1)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3476 a r:Inference; +skolem:lemma2920 a r:Inference; r:gives { 2552 :numberToDigits (2 5 5 2). }; @@ -86202,32 +68947,9 @@ skolem:lemma3476 a r:Inference; 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:lemma4392. - -skolem:lemma3477 a r:Inference; - r:gives { - (2 5 5 2) :sort (2 2 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 2) list:firstRest (2 (5 5 2))}] - skolem:lemma5258 - skolem:lemma4833 - skolem:lemma4543 - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {((2) (2 5 5)) list:append (2 2 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 2)]; - 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 5)]; - 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3478 a r:Inference; +skolem:lemma2921 a r:Inference; r:gives { 2553 :numberToDigits (2 5 5 3). }; @@ -86246,32 +68968,9 @@ skolem:lemma3478 a r:Inference; 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:lemma4392. - -skolem:lemma3479 a r:Inference; - r:gives { - (2 5 5 3) :sort (2 3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 3) list:firstRest (2 (5 5 3))}] - skolem:lemma5259 - skolem:lemma4395 - skolem:lemma5260 - [ a r:Fact; r:gives {(2 3 5 5) list:firstRest (2 (3 5 5))}] - [ a r:Fact; r:gives {(() (2 3 5 5)) list:append (2 3 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3480 a r:Inference; +skolem:lemma2922 a r:Inference; r:gives { 2554 :numberToDigits (2 5 5 4). }; @@ -86290,32 +68989,9 @@ skolem:lemma3480 a r:Inference; 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:lemma4392. - -skolem:lemma3481 a r:Inference; - r:gives { - (2 5 5 4) :sort (2 4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 4) list:firstRest (2 (5 5 4))}] - skolem:lemma5261 - skolem:lemma4395 - skolem:lemma5262 - [ a r:Fact; r:gives {(2 4 5 5) list:firstRest (2 (4 5 5))}] - [ a r:Fact; r:gives {(() (2 4 5 5)) list:append (2 4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3482 a r:Inference; +skolem:lemma2923 a r:Inference; r:gives { 2555 :numberToDigits (2 5 5 5). }; @@ -86334,32 +69010,9 @@ skolem:lemma3482 a r:Inference; 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:lemma4392. - -skolem:lemma3483 a r:Inference; - r:gives { - (2 5 5 5) :sort (2 5 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 5) list:firstRest (2 (5 5 5))}] - skolem:lemma5263 - skolem:lemma4395 - skolem:lemma5264 - [ a r:Fact; r:gives {(2 5 5 5) list:firstRest (2 (5 5 5))}] - [ a r:Fact; r:gives {(() (2 5 5 5)) list:append (2 5 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 5)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3484 a r:Inference; +skolem:lemma2924 a r:Inference; r:gives { (2 5 5 5) :digitsToNumber 2555 . }; @@ -86377,9 +69030,9 @@ skolem:lemma3484 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3485 a r:Inference; +skolem:lemma2925 a r:Inference; r:gives { (5 5 5 2) :digitsToNumber 5552 . }; @@ -86397,9 +69050,9 @@ skolem:lemma3485 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3486 a r:Inference; +skolem:lemma2926 a r:Inference; r:gives { 2556 :numberToDigits (2 5 5 6). }; @@ -86418,32 +69071,9 @@ skolem:lemma3486 a r:Inference; 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:lemma4392. - -skolem:lemma3487 a r:Inference; - r:gives { - (2 5 5 6) :sort (2 5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 6) list:firstRest (2 (5 5 6))}] - skolem:lemma5265 - skolem:lemma4395 - skolem:lemma5266 - [ a r:Fact; r:gives {(2 5 5 6) list:firstRest (2 (5 5 6))}] - [ a r:Fact; r:gives {(() (2 5 5 6)) list:append (2 5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3488 a r:Inference; +skolem:lemma2927 a r:Inference; r:gives { (2 5 5 6) :digitsToNumber 2556 . }; @@ -86461,9 +69091,9 @@ skolem:lemma3488 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3489 a r:Inference; +skolem:lemma2928 a r:Inference; r:gives { (6 5 5 2) :digitsToNumber 6552 . }; @@ -86481,9 +69111,9 @@ skolem:lemma3489 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3490 a r:Inference; +skolem:lemma2929 a r:Inference; r:gives { 2557 :numberToDigits (2 5 5 7). }; @@ -86502,32 +69132,9 @@ skolem:lemma3490 a r:Inference; 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:lemma4392. - -skolem:lemma3491 a r:Inference; - r:gives { - (2 5 5 7) :sort (2 5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 7) list:firstRest (2 (5 5 7))}] - skolem:lemma5267 - skolem:lemma4395 - skolem:lemma5268 - [ a r:Fact; r:gives {(2 5 5 7) list:firstRest (2 (5 5 7))}] - [ a r:Fact; r:gives {(() (2 5 5 7)) list:append (2 5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3492 a r:Inference; +skolem:lemma2930 a r:Inference; r:gives { (2 5 5 7) :digitsToNumber 2557 . }; @@ -86545,9 +69152,9 @@ skolem:lemma3492 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3493 a r:Inference; +skolem:lemma2931 a r:Inference; r:gives { (7 5 5 2) :digitsToNumber 7552 . }; @@ -86565,9 +69172,9 @@ skolem:lemma3493 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3494 a r:Inference; +skolem:lemma2932 a r:Inference; r:gives { 2558 :numberToDigits (2 5 5 8). }; @@ -86586,32 +69193,9 @@ skolem:lemma3494 a r:Inference; 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:lemma4392. - -skolem:lemma3495 a r:Inference; - r:gives { - (2 5 5 8) :sort (2 5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 8) list:firstRest (2 (5 5 8))}] - skolem:lemma5269 - skolem:lemma4395 - skolem:lemma5270 - [ a r:Fact; r:gives {(2 5 5 8) list:firstRest (2 (5 5 8))}] - [ a r:Fact; r:gives {(() (2 5 5 8)) list:append (2 5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3496 a r:Inference; +skolem:lemma2933 a r:Inference; r:gives { (2 5 5 8) :digitsToNumber 2558 . }; @@ -86629,9 +69213,9 @@ skolem:lemma3496 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3497 a r:Inference; +skolem:lemma2934 a r:Inference; r:gives { (8 5 5 2) :digitsToNumber 8552 . }; @@ -86649,9 +69233,9 @@ skolem:lemma3497 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3498 a r:Inference; +skolem:lemma2935 a r:Inference; r:gives { 2559 :numberToDigits (2 5 5 9). }; @@ -86670,32 +69254,9 @@ skolem:lemma3498 a r:Inference; 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:lemma4392. - -skolem:lemma3499 a r:Inference; - r:gives { - (2 5 5 9) :sort (2 5 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5 9) list:firstRest (2 (5 5 9))}] - skolem:lemma5271 - skolem:lemma4395 - skolem:lemma5272 - [ a r:Fact; r:gives {(2 5 5 9) list:firstRest (2 (5 5 9))}] - [ a r:Fact; r:gives {(() (2 5 5 9)) list:append (2 5 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 5 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_2"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3500 a r:Inference; +skolem:lemma2936 a r:Inference; r:gives { (2 5 5 9) :digitsToNumber 2559 . }; @@ -86713,9 +69274,9 @@ skolem:lemma3500 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3501 a r:Inference; +skolem:lemma2937 a r:Inference; r:gives { (9 5 5 2) :digitsToNumber 9552 . }; @@ -86733,9 +69294,9 @@ skolem:lemma3501 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3502 a r:Inference; +skolem:lemma2938 a r:Inference; r:gives { 2560 :numberToDigits (2 5 6 0). }; @@ -86754,32 +69315,9 @@ skolem:lemma3502 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3503 a r:Inference; - r:gives { - (2 5 6 0) :sort (0 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 0) list:firstRest (2 (5 6 0))}] - skolem:lemma5273 - skolem:lemma4506 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((0) (2 5 6)) list:append (0 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 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 (5 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 (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3504 a r:Inference; +skolem:lemma2939 a r:Inference; r:gives { 2561 :numberToDigits (2 5 6 1). }; @@ -86798,32 +69336,9 @@ skolem:lemma3504 a r:Inference; 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:lemma4392. - -skolem:lemma3505 a r:Inference; - r:gives { - (2 5 6 1) :sort (1 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 1) list:firstRest (2 (5 6 1))}] - skolem:lemma5274 - skolem:lemma4705 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((1) (2 5 6)) list:append (1 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 1)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3506 a r:Inference; +skolem:lemma2940 a r:Inference; r:gives { 2562 :numberToDigits (2 5 6 2). }; @@ -86842,32 +69357,9 @@ skolem:lemma3506 a r:Inference; 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:lemma4392. - -skolem:lemma3507 a r:Inference; - r:gives { - (2 5 6 2) :sort (2 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 2) list:firstRest (2 (5 6 2))}] - skolem:lemma5275 - skolem:lemma4833 - skolem:lemma4547 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((2) (2 5 6)) list:append (2 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 2)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3508 a r:Inference; +skolem:lemma2941 a r:Inference; r:gives { 2563 :numberToDigits (2 5 6 3). }; @@ -86886,32 +69378,9 @@ skolem:lemma3508 a r:Inference; 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:lemma4392. - -skolem:lemma3509 a r:Inference; - r:gives { - (2 5 6 3) :sort (2 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 3) list:firstRest (2 (5 6 3))}] - skolem:lemma5276 - skolem:lemma4395 - skolem:lemma5277 - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - [ a r:Fact; r:gives {(() (2 3 5 6)) list:append (2 3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3510 a r:Inference; +skolem:lemma2942 a r:Inference; r:gives { 2564 :numberToDigits (2 5 6 4). }; @@ -86930,32 +69399,9 @@ skolem:lemma3510 a r:Inference; 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:lemma4392. - -skolem:lemma3511 a r:Inference; - r:gives { - (2 5 6 4) :sort (2 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 4) list:firstRest (2 (5 6 4))}] - skolem:lemma5278 - skolem:lemma4395 - skolem:lemma5279 - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - [ a r:Fact; r:gives {(() (2 4 5 6)) list:append (2 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3512 a r:Inference; +skolem:lemma2943 a r:Inference; r:gives { 2565 :numberToDigits (2 5 6 5). }; @@ -86974,32 +69420,9 @@ skolem:lemma3512 a r:Inference; 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:lemma4392. - -skolem:lemma3513 a r:Inference; - r:gives { - (2 5 6 5) :sort (2 5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 5) list:firstRest (2 (5 6 5))}] - skolem:lemma5280 - skolem:lemma4395 - skolem:lemma5281 - [ a r:Fact; r:gives {(2 5 5 6) list:firstRest (2 (5 5 6))}] - [ a r:Fact; r:gives {(() (2 5 5 6)) list:append (2 5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3514 a r:Inference; +skolem:lemma2944 a r:Inference; r:gives { 2566 :numberToDigits (2 5 6 6). }; @@ -87018,32 +69441,9 @@ skolem:lemma3514 a r:Inference; 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:lemma4392. - -skolem:lemma3515 a r:Inference; - r:gives { - (2 5 6 6) :sort (2 5 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 6) list:firstRest (2 (5 6 6))}] - skolem:lemma5282 - skolem:lemma4395 - skolem:lemma5283 - [ a r:Fact; r:gives {(2 5 6 6) list:firstRest (2 (5 6 6))}] - [ a r:Fact; r:gives {(() (2 5 6 6)) list:append (2 5 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3516 a r:Inference; +skolem:lemma2945 a r:Inference; r:gives { (2 5 6 6) :digitsToNumber 2566 . }; @@ -87061,9 +69461,9 @@ skolem:lemma3516 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3517 a r:Inference; +skolem:lemma2946 a r:Inference; r:gives { (6 6 5 2) :digitsToNumber 6652 . }; @@ -87081,9 +69481,9 @@ skolem:lemma3517 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3518 a r:Inference; +skolem:lemma2947 a r:Inference; r:gives { 2567 :numberToDigits (2 5 6 7). }; @@ -87102,32 +69502,9 @@ skolem:lemma3518 a r:Inference; 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:lemma4392. - -skolem:lemma3519 a r:Inference; - r:gives { - (2 5 6 7) :sort (2 5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - skolem:lemma5284 - skolem:lemma4395 - skolem:lemma5285 - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - [ a r:Fact; r:gives {(() (2 5 6 7)) list:append (2 5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3520 a r:Inference; +skolem:lemma2948 a r:Inference; r:gives { (2 5 6 7) :digitsToNumber 2567 . }; @@ -87145,9 +69522,9 @@ skolem:lemma3520 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3521 a r:Inference; +skolem:lemma2949 a r:Inference; r:gives { (7 6 5 2) :digitsToNumber 7652 . }; @@ -87165,9 +69542,9 @@ skolem:lemma3521 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3522 a r:Inference; +skolem:lemma2950 a r:Inference; r:gives { 2568 :numberToDigits (2 5 6 8). }; @@ -87186,32 +69563,9 @@ skolem:lemma3522 a r:Inference; 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:lemma4392. - -skolem:lemma3523 a r:Inference; - r:gives { - (2 5 6 8) :sort (2 5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - skolem:lemma5286 - skolem:lemma4395 - skolem:lemma5287 - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - [ a r:Fact; r:gives {(() (2 5 6 8)) list:append (2 5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3524 a r:Inference; +skolem:lemma2951 a r:Inference; r:gives { (2 5 6 8) :digitsToNumber 2568 . }; @@ -87229,9 +69583,9 @@ skolem:lemma3524 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3525 a r:Inference; +skolem:lemma2952 a r:Inference; r:gives { (8 6 5 2) :digitsToNumber 8652 . }; @@ -87249,9 +69603,9 @@ skolem:lemma3525 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3526 a r:Inference; +skolem:lemma2953 a r:Inference; r:gives { 2569 :numberToDigits (2 5 6 9). }; @@ -87270,32 +69624,9 @@ skolem:lemma3526 a r:Inference; 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:lemma4392. - -skolem:lemma3527 a r:Inference; - r:gives { - (2 5 6 9) :sort (2 5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - skolem:lemma5288 - skolem:lemma4395 - skolem:lemma5289 - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - [ a r:Fact; r:gives {(() (2 5 6 9)) list:append (2 5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 6 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_2"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3528 a r:Inference; +skolem:lemma2954 a r:Inference; r:gives { (2 5 6 9) :digitsToNumber 2569 . }; @@ -87313,9 +69644,9 @@ skolem:lemma3528 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3529 a r:Inference; +skolem:lemma2955 a r:Inference; r:gives { (9 6 5 2) :digitsToNumber 9652 . }; @@ -87333,9 +69664,9 @@ skolem:lemma3529 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3530 a r:Inference; +skolem:lemma2956 a r:Inference; r:gives { 2570 :numberToDigits (2 5 7 0). }; @@ -87354,32 +69685,9 @@ skolem:lemma3530 a r:Inference; 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:lemma4392. - -skolem:lemma3531 a r:Inference; - r:gives { - (2 5 7 0) :sort (0 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 0) list:firstRest (2 (5 7 0))}] - skolem:lemma5290 - skolem:lemma4506 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((0) (2 5 7)) list:append (0 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 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 (5 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 (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3532 a r:Inference; +skolem:lemma2957 a r:Inference; r:gives { 2571 :numberToDigits (2 5 7 1). }; @@ -87398,32 +69706,9 @@ skolem:lemma3532 a r:Inference; 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:lemma4392. - -skolem:lemma3533 a r:Inference; - r:gives { - (2 5 7 1) :sort (1 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 1) list:firstRest (2 (5 7 1))}] - skolem:lemma5291 - skolem:lemma4705 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((1) (2 5 7)) list:append (1 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 1)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3534 a r:Inference; +skolem:lemma2958 a r:Inference; r:gives { 2572 :numberToDigits (2 5 7 2). }; @@ -87442,32 +69727,9 @@ skolem:lemma3534 a r:Inference; 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:lemma4392. - -skolem:lemma3535 a r:Inference; - r:gives { - (2 5 7 2) :sort (2 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 2) list:firstRest (2 (5 7 2))}] - skolem:lemma5292 - skolem:lemma4833 - skolem:lemma4551 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((2) (2 5 7)) list:append (2 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 2)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3536 a r:Inference; +skolem:lemma2959 a r:Inference; r:gives { 2573 :numberToDigits (2 5 7 3). }; @@ -87486,32 +69748,9 @@ skolem:lemma3536 a r:Inference; 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:lemma4392. - -skolem:lemma3537 a r:Inference; - r:gives { - (2 5 7 3) :sort (2 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 3) list:firstRest (2 (5 7 3))}] - skolem:lemma5293 - skolem:lemma4395 - skolem:lemma5294 - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - [ a r:Fact; r:gives {(() (2 3 5 7)) list:append (2 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3538 a r:Inference; +skolem:lemma2960 a r:Inference; r:gives { 2574 :numberToDigits (2 5 7 4). }; @@ -87530,32 +69769,9 @@ skolem:lemma3538 a r:Inference; 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:lemma4392. - -skolem:lemma3539 a r:Inference; - r:gives { - (2 5 7 4) :sort (2 4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 4) list:firstRest (2 (5 7 4))}] - skolem:lemma5295 - skolem:lemma4395 - skolem:lemma5296 - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - [ a r:Fact; r:gives {(() (2 4 5 7)) list:append (2 4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3540 a r:Inference; +skolem:lemma2961 a r:Inference; r:gives { 2575 :numberToDigits (2 5 7 5). }; @@ -87574,32 +69790,9 @@ skolem:lemma3540 a r:Inference; 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:lemma4392. - -skolem:lemma3541 a r:Inference; - r:gives { - (2 5 7 5) :sort (2 5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 5) list:firstRest (2 (5 7 5))}] - skolem:lemma5297 - skolem:lemma4395 - skolem:lemma5298 - [ a r:Fact; r:gives {(2 5 5 7) list:firstRest (2 (5 5 7))}] - [ a r:Fact; r:gives {(() (2 5 5 7)) list:append (2 5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3542 a r:Inference; +skolem:lemma2962 a r:Inference; r:gives { 2576 :numberToDigits (2 5 7 6). }; @@ -87618,32 +69811,9 @@ skolem:lemma3542 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3543 a r:Inference; - r:gives { - (2 5 7 6) :sort (2 5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 6) list:firstRest (2 (5 7 6))}] - skolem:lemma5299 - skolem:lemma4395 - skolem:lemma5300 - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - [ a r:Fact; r:gives {(() (2 5 6 7)) list:append (2 5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3544 a r:Inference; +skolem:lemma2963 a r:Inference; r:gives { 2577 :numberToDigits (2 5 7 7). }; @@ -87662,32 +69832,9 @@ skolem:lemma3544 a r:Inference; 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:lemma4392. - -skolem:lemma3545 a r:Inference; - r:gives { - (2 5 7 7) :sort (2 5 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 7) list:firstRest (2 (5 7 7))}] - skolem:lemma5301 - skolem:lemma4395 - skolem:lemma5302 - [ a r:Fact; r:gives {(2 5 7 7) list:firstRest (2 (5 7 7))}] - [ a r:Fact; r:gives {(() (2 5 7 7)) list:append (2 5 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3546 a r:Inference; +skolem:lemma2964 a r:Inference; r:gives { (2 5 7 7) :digitsToNumber 2577 . }; @@ -87705,9 +69852,9 @@ skolem:lemma3546 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3547 a r:Inference; +skolem:lemma2965 a r:Inference; r:gives { (7 7 5 2) :digitsToNumber 7752 . }; @@ -87725,9 +69872,70 @@ skolem:lemma3547 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. + +skolem:lemma2966 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:lemma3438. + +skolem:lemma2967 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:lemma3439. + +skolem:lemma2968 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:lemma3439. -skolem:lemma3548 a r:Inference; +skolem:lemma2969 a r:Inference; r:gives { 2579 :numberToDigits (2 5 7 9). }; @@ -87746,32 +69954,9 @@ skolem:lemma3548 a r:Inference; 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:lemma4392. - -skolem:lemma3549 a r:Inference; - r:gives { - (2 5 7 9) :sort (2 5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - skolem:lemma5303 - skolem:lemma4395 - skolem:lemma5304 - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - [ a r:Fact; r:gives {(() (2 5 7 9)) list:append (2 5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 7 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_2"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3550 a r:Inference; +skolem:lemma2970 a r:Inference; r:gives { (2 5 7 9) :digitsToNumber 2579 . }; @@ -87789,9 +69974,9 @@ skolem:lemma3550 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3551 a r:Inference; +skolem:lemma2971 a r:Inference; r:gives { (9 7 5 2) :digitsToNumber 9752 . }; @@ -87809,9 +69994,9 @@ skolem:lemma3551 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3552 a r:Inference; +skolem:lemma2972 a r:Inference; r:gives { 2580 :numberToDigits (2 5 8 0). }; @@ -87830,32 +70015,9 @@ skolem:lemma3552 a r:Inference; 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:lemma4392. - -skolem:lemma3553 a r:Inference; - r:gives { - (2 5 8 0) :sort (0 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8 0) list:firstRest (2 (5 8 0))}] - skolem:lemma5305 - skolem:lemma4506 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((0) (2 5 8)) list:append (0 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 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 (5 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 (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3554 a r:Inference; +skolem:lemma2973 a r:Inference; r:gives { 2581 :numberToDigits (2 5 8 1). }; @@ -87874,34 +70036,11 @@ skolem:lemma3554 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3555 a r:Inference; +skolem:lemma2974 a r:Inference; r:gives { - (2 5 8 1) :sort (1 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8 1) list:firstRest (2 (5 8 1))}] - skolem:lemma5306 - skolem:lemma4705 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((1) (2 5 8)) list:append (1 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 1)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3556 a r:Inference; - r:gives { - 2582 :numberToDigits (2 5 8 2). + 2582 :numberToDigits (2 5 8 2). }; r:evidence ( [ a r:Fact; r:gives {(2582 1000) math:integerQuotient 2}] @@ -87918,32 +70057,30 @@ skolem:lemma3556 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3557 a r:Inference; +skolem:lemma2975 a r:Inference; r:gives { - (2 5 8 2) :sort (2 2 5 8). + 2583 :numberToDigits (2 5 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2 5 8 2) list:firstRest (2 (5 8 2))}] - skolem:lemma5307 - skolem:lemma4833 - skolem:lemma4555 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((2) (2 5 8)) list:append (2 2 5 8)}] + [ 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_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 2)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3558 a r:Inference; +skolem:lemma2976 a r:Inference; r:gives { 2584 :numberToDigits (2 5 8 4). }; @@ -87962,32 +70099,9 @@ skolem:lemma3558 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3559 a r:Inference; - r:gives { - (2 5 8 4) :sort (2 4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8 4) list:firstRest (2 (5 8 4))}] - skolem:lemma5308 - skolem:lemma4395 - skolem:lemma5309 - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - [ a r:Fact; r:gives {(() (2 4 5 8)) list:append (2 4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3560 a r:Inference; +skolem:lemma2977 a r:Inference; r:gives { 2585 :numberToDigits (2 5 8 5). }; @@ -88006,32 +70120,9 @@ skolem:lemma3560 a r:Inference; 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:lemma4392. - -skolem:lemma3561 a r:Inference; - r:gives { - (2 5 8 5) :sort (2 5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8 5) list:firstRest (2 (5 8 5))}] - skolem:lemma5310 - skolem:lemma4395 - skolem:lemma5311 - [ a r:Fact; r:gives {(2 5 5 8) list:firstRest (2 (5 5 8))}] - [ a r:Fact; r:gives {(() (2 5 5 8)) list:append (2 5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3562 a r:Inference; +skolem:lemma2978 a r:Inference; r:gives { 2586 :numberToDigits (2 5 8 6). }; @@ -88050,32 +70141,30 @@ skolem:lemma3562 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3563 a r:Inference; +skolem:lemma2979 a r:Inference; r:gives { - (2 5 8 6) :sort (2 5 6 8). + 2587 :numberToDigits (2 5 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2 5 8 6) list:firstRest (2 (5 8 6))}] - skolem:lemma5312 - skolem:lemma4395 - skolem:lemma5313 - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - [ a r:Fact; r:gives {(() (2 5 6 8)) list:append (2 5 6 8)}] + [ 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_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3564 a r:Inference; +skolem:lemma2980 a r:Inference; r:gives { 2588 :numberToDigits (2 5 8 8). }; @@ -88094,32 +70183,9 @@ skolem:lemma3564 a r:Inference; 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:lemma4392. - -skolem:lemma3565 a r:Inference; - r:gives { - (2 5 8 8) :sort (2 5 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8 8) list:firstRest (2 (5 8 8))}] - skolem:lemma5314 - skolem:lemma4395 - skolem:lemma5315 - [ a r:Fact; r:gives {(2 5 8 8) list:firstRest (2 (5 8 8))}] - [ a r:Fact; r:gives {(() (2 5 8 8)) list:append (2 5 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3566 a r:Inference; +skolem:lemma2981 a r:Inference; r:gives { (2 5 8 8) :digitsToNumber 2588 . }; @@ -88137,9 +70203,9 @@ skolem:lemma3566 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3567 a r:Inference; +skolem:lemma2982 a r:Inference; r:gives { (8 8 5 2) :digitsToNumber 8852 . }; @@ -88157,9 +70223,9 @@ skolem:lemma3567 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3568 a r:Inference; +skolem:lemma2983 a r:Inference; r:gives { 2589 :numberToDigits (2 5 8 9). }; @@ -88178,32 +70244,9 @@ skolem:lemma3568 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3569 a r:Inference; - r:gives { - (2 5 8 9) :sort (2 5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - skolem:lemma5316 - skolem:lemma4395 - skolem:lemma5317 - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - [ a r:Fact; r:gives {(() (2 5 8 9)) list:append (2 5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 8 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_2"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3570 a r:Inference; +skolem:lemma2984 a r:Inference; r:gives { (2 5 8 9) :digitsToNumber 2589 . }; @@ -88221,9 +70264,9 @@ skolem:lemma3570 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3571 a r:Inference; +skolem:lemma2985 a r:Inference; r:gives { (9 8 5 2) :digitsToNumber 9852 . }; @@ -88241,9 +70284,9 @@ skolem:lemma3571 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3572 a r:Inference; +skolem:lemma2986 a r:Inference; r:gives { 2590 :numberToDigits (2 5 9 0). }; @@ -88262,32 +70305,9 @@ skolem:lemma3572 a r:Inference; 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:lemma4392. - -skolem:lemma3573 a r:Inference; - r:gives { - (2 5 9 0) :sort (0 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 0) list:firstRest (2 (5 9 0))}] - skolem:lemma5318 - skolem:lemma4506 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((0) (2 5 9)) list:append (0 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 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 (5 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 (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3574 a r:Inference; +skolem:lemma2987 a r:Inference; r:gives { 2591 :numberToDigits (2 5 9 1). }; @@ -88306,32 +70326,9 @@ skolem:lemma3574 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3575 a r:Inference; - r:gives { - (2 5 9 1) :sort (1 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 1) list:firstRest (2 (5 9 1))}] - skolem:lemma5319 - skolem:lemma4705 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((1) (2 5 9)) list:append (1 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3576 a r:Inference; +skolem:lemma2988 a r:Inference; r:gives { 2592 :numberToDigits (2 5 9 2). }; @@ -88350,32 +70347,9 @@ skolem:lemma3576 a r:Inference; 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:lemma4392. - -skolem:lemma3577 a r:Inference; - r:gives { - (2 5 9 2) :sort (2 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 2) list:firstRest (2 (5 9 2))}] - skolem:lemma5320 - skolem:lemma4833 - skolem:lemma4559 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((2) (2 5 9)) list:append (2 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3578 a r:Inference; +skolem:lemma2989 a r:Inference; r:gives { 2593 :numberToDigits (2 5 9 3). }; @@ -88394,32 +70368,9 @@ skolem:lemma3578 a r:Inference; 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:lemma4392. - -skolem:lemma3579 a r:Inference; - r:gives { - (2 5 9 3) :sort (2 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 3) list:firstRest (2 (5 9 3))}] - skolem:lemma5321 - skolem:lemma4395 - skolem:lemma5322 - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - [ a r:Fact; r:gives {(() (2 3 5 9)) list:append (2 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3580 a r:Inference; +skolem:lemma2990 a r:Inference; r:gives { 2594 :numberToDigits (2 5 9 4). }; @@ -88438,32 +70389,9 @@ skolem:lemma3580 a r:Inference; 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:lemma4392. - -skolem:lemma3581 a r:Inference; - r:gives { - (2 5 9 4) :sort (2 4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 4) list:firstRest (2 (5 9 4))}] - skolem:lemma5323 - skolem:lemma4395 - skolem:lemma5324 - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - [ a r:Fact; r:gives {(() (2 4 5 9)) list:append (2 4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3582 a r:Inference; +skolem:lemma2991 a r:Inference; r:gives { 2595 :numberToDigits (2 5 9 5). }; @@ -88482,32 +70410,9 @@ skolem:lemma3582 a r:Inference; 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:lemma4392. - -skolem:lemma3583 a r:Inference; - r:gives { - (2 5 9 5) :sort (2 5 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 5) list:firstRest (2 (5 9 5))}] - skolem:lemma5325 - skolem:lemma4395 - skolem:lemma5326 - [ a r:Fact; r:gives {(2 5 5 9) list:firstRest (2 (5 5 9))}] - [ a r:Fact; r:gives {(() (2 5 5 9)) list:append (2 5 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3584 a r:Inference; +skolem:lemma2992 a r:Inference; r:gives { 2596 :numberToDigits (2 5 9 6). }; @@ -88526,32 +70431,9 @@ skolem:lemma3584 a r:Inference; 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:lemma4392. - -skolem:lemma3585 a r:Inference; - r:gives { - (2 5 9 6) :sort (2 5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 6) list:firstRest (2 (5 9 6))}] - skolem:lemma5327 - skolem:lemma4395 - skolem:lemma5328 - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - [ a r:Fact; r:gives {(() (2 5 6 9)) list:append (2 5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3586 a r:Inference; +skolem:lemma2993 a r:Inference; r:gives { 2597 :numberToDigits (2 5 9 7). }; @@ -88570,32 +70452,9 @@ skolem:lemma3586 a r:Inference; 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:lemma4392. - -skolem:lemma3587 a r:Inference; - r:gives { - (2 5 9 7) :sort (2 5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 7) list:firstRest (2 (5 9 7))}] - skolem:lemma5329 - skolem:lemma4395 - skolem:lemma5330 - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - [ a r:Fact; r:gives {(() (2 5 7 9)) list:append (2 5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3588 a r:Inference; +skolem:lemma2994 a r:Inference; r:gives { 2598 :numberToDigits (2 5 9 8). }; @@ -88614,32 +70473,9 @@ skolem:lemma3588 a r:Inference; 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:lemma4392. - -skolem:lemma3589 a r:Inference; - r:gives { - (2 5 9 8) :sort (2 5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 8) list:firstRest (2 (5 9 8))}] - skolem:lemma5331 - skolem:lemma4395 - skolem:lemma5332 - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - [ a r:Fact; r:gives {(() (2 5 8 9)) list:append (2 5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3590 a r:Inference; +skolem:lemma2995 a r:Inference; r:gives { 2599 :numberToDigits (2 5 9 9). }; @@ -88658,32 +70494,9 @@ skolem:lemma3590 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3591 a r:Inference; - r:gives { - (2 5 9 9) :sort (2 5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9 9) list:firstRest (2 (5 9 9))}] - skolem:lemma5333 - skolem:lemma4395 - skolem:lemma5334 - [ a r:Fact; r:gives {(2 5 9 9) list:firstRest (2 (5 9 9))}] - [ a r:Fact; r:gives {(() (2 5 9 9)) list:append (2 5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 9 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_2"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3592 a r:Inference; +skolem:lemma2996 a r:Inference; r:gives { (2 5 9 9) :digitsToNumber 2599 . }; @@ -88701,9 +70514,9 @@ skolem:lemma3592 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3593 a r:Inference; +skolem:lemma2997 a r:Inference; r:gives { (9 9 5 2) :digitsToNumber 9952 . }; @@ -88721,9 +70534,30 @@ skolem:lemma3593 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3594 a r:Inference; +skolem:lemma2998 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:lemma3438. + +skolem:lemma2999 a r:Inference; r:gives { 2601 :numberToDigits (2 6 0 1). }; @@ -88742,32 +70576,9 @@ skolem:lemma3594 a r:Inference; 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:lemma4392. - -skolem:lemma3595 a r:Inference; - r:gives { - (2 6 0 1) :sort (0 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 1) list:firstRest (2 (6 0 1))}] - skolem:lemma5335 - skolem:lemma4442 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 1) (2 6)) list:append (0 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3596 a r:Inference; +skolem:lemma3000 a r:Inference; r:gives { 2602 :numberToDigits (2 6 0 2). }; @@ -88786,32 +70597,9 @@ skolem:lemma3596 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma3597 a r:Inference; - r:gives { - (2 6 0 2) :sort (0 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 2) list:firstRest (2 (6 0 2))}] - skolem:lemma5336 - skolem:lemma4479 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 2) (2 6)) list:append (0 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3598 a r:Inference; +skolem:lemma3001 a r:Inference; r:gives { 2603 :numberToDigits (2 6 0 3). }; @@ -88830,32 +70618,30 @@ skolem:lemma3598 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3599 a r:Inference; +skolem:lemma3002 a r:Inference; r:gives { - (2 6 0 3) :sort (0 2 3 6). + 2604 :numberToDigits (2 6 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 6 0 3) list:firstRest (2 (6 0 3))}] - skolem:lemma5337 - skolem:lemma4506 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((0) (2 3 6)) list:append (0 2 3 6)}] + [ 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_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 6)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3600 a r:Inference; +skolem:lemma3003 a r:Inference; r:gives { 2605 :numberToDigits (2 6 0 5). }; @@ -88874,32 +70660,9 @@ skolem:lemma3600 a r:Inference; 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:lemma4392. - -skolem:lemma3601 a r:Inference; - r:gives { - (2 6 0 5) :sort (0 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 5) list:firstRest (2 (6 0 5))}] - skolem:lemma5338 - skolem:lemma4506 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((0) (2 5 6)) list:append (0 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3602 a r:Inference; +skolem:lemma3004 a r:Inference; r:gives { 2606 :numberToDigits (2 6 0 6). }; @@ -88918,32 +70681,9 @@ skolem:lemma3602 a r:Inference; 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:lemma4392. - -skolem:lemma3603 a r:Inference; - r:gives { - (2 6 0 6) :sort (0 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 6) list:firstRest (2 (6 0 6))}] - skolem:lemma5339 - skolem:lemma4506 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((0) (2 6 6)) list:append (0 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 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 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3604 a r:Inference; +skolem:lemma3005 a r:Inference; r:gives { 2607 :numberToDigits (2 6 0 7). }; @@ -88962,32 +70702,9 @@ skolem:lemma3604 a r:Inference; 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:lemma4392. - -skolem:lemma3605 a r:Inference; - r:gives { - (2 6 0 7) :sort (0 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 7) list:firstRest (2 (6 0 7))}] - skolem:lemma5340 - skolem:lemma4506 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((0) (2 6 7)) list:append (0 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 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 (6 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 (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3606 a r:Inference; +skolem:lemma3006 a r:Inference; r:gives { 2608 :numberToDigits (2 6 0 8). }; @@ -89006,32 +70723,9 @@ skolem:lemma3606 a r:Inference; 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:lemma4392. - -skolem:lemma3607 a r:Inference; - r:gives { - (2 6 0 8) :sort (0 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 8) list:firstRest (2 (6 0 8))}] - skolem:lemma5341 - skolem:lemma4506 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((0) (2 6 8)) list:append (0 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 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 (6 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 (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3608 a r:Inference; +skolem:lemma3007 a r:Inference; r:gives { 2609 :numberToDigits (2 6 0 9). }; @@ -89050,32 +70744,9 @@ skolem:lemma3608 a r:Inference; 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:lemma4392. - -skolem:lemma3609 a r:Inference; - r:gives { - (2 6 0 9) :sort (0 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0 9) list:firstRest (2 (6 0 9))}] - skolem:lemma5342 - skolem:lemma4506 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((0) (2 6 9)) list:append (0 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 0 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_2"]; r:boundTo (6 0 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 (6 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 (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3610 a r:Inference; +skolem:lemma3008 a r:Inference; r:gives { 2610 :numberToDigits (2 6 1 0). }; @@ -89094,32 +70765,9 @@ skolem:lemma3610 a r:Inference; 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:lemma4392. - -skolem:lemma3611 a r:Inference; - r:gives { - (2 6 1 0) :sort (0 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 0) list:firstRest (2 (6 1 0))}] - skolem:lemma5343 - skolem:lemma4660 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 1) (2 6)) list:append (0 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3612 a r:Inference; +skolem:lemma3009 a r:Inference; r:gives { 2611 :numberToDigits (2 6 1 1). }; @@ -89138,32 +70786,9 @@ skolem:lemma3612 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3613 a r:Inference; - r:gives { - (2 6 1 1) :sort (1 1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 1) list:firstRest (2 (6 1 1))}] - skolem:lemma5344 - skolem:lemma4680 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 1) (2 6)) list:append (1 1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3614 a r:Inference; +skolem:lemma3010 a r:Inference; r:gives { 2612 :numberToDigits (2 6 1 2). }; @@ -89182,32 +70807,9 @@ skolem:lemma3614 a r:Inference; 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:lemma4392. - -skolem:lemma3615 a r:Inference; - r:gives { - (2 6 1 2) :sort (1 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 2) list:firstRest (2 (6 1 2))}] - skolem:lemma5345 - skolem:lemma4694 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 2) (2 6)) list:append (1 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3616 a r:Inference; +skolem:lemma3011 a r:Inference; r:gives { 2613 :numberToDigits (2 6 1 3). }; @@ -89226,32 +70828,9 @@ skolem:lemma3616 a r:Inference; 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:lemma4392. - -skolem:lemma3617 a r:Inference; - r:gives { - (2 6 1 3) :sort (1 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 3) list:firstRest (2 (6 1 3))}] - skolem:lemma5346 - skolem:lemma4705 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((1) (2 3 6)) list:append (1 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 3)]; - 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 3)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3618 a r:Inference; +skolem:lemma3012 a r:Inference; r:gives { 2614 :numberToDigits (2 6 1 4). }; @@ -89270,32 +70849,9 @@ skolem:lemma3618 a r:Inference; 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:lemma4392. - -skolem:lemma3619 a r:Inference; - r:gives { - (2 6 1 4) :sort (1 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 4) list:firstRest (2 (6 1 4))}] - skolem:lemma5347 - skolem:lemma4705 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((1) (2 4 6)) list:append (1 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 4)]; - 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 4)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3620 a r:Inference; +skolem:lemma3013 a r:Inference; r:gives { 2615 :numberToDigits (2 6 1 5). }; @@ -89314,32 +70870,9 @@ skolem:lemma3620 a r:Inference; 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:lemma4392. - -skolem:lemma3621 a r:Inference; - r:gives { - (2 6 1 5) :sort (1 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 5) list:firstRest (2 (6 1 5))}] - skolem:lemma5348 - skolem:lemma4705 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((1) (2 5 6)) list:append (1 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 5)]; - 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 5)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3622 a r:Inference; +skolem:lemma3014 a r:Inference; r:gives { 2616 :numberToDigits (2 6 1 6). }; @@ -89358,32 +70891,9 @@ skolem:lemma3622 a r:Inference; 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:lemma4392. - -skolem:lemma3623 a r:Inference; - r:gives { - (2 6 1 6) :sort (1 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 6) list:firstRest (2 (6 1 6))}] - skolem:lemma5349 - skolem:lemma4705 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((1) (2 6 6)) list:append (1 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3624 a r:Inference; +skolem:lemma3015 a r:Inference; r:gives { 2617 :numberToDigits (2 6 1 7). }; @@ -89402,32 +70912,9 @@ skolem:lemma3624 a r:Inference; 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:lemma4392. - -skolem:lemma3625 a r:Inference; - r:gives { - (2 6 1 7) :sort (1 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 7) list:firstRest (2 (6 1 7))}] - skolem:lemma5350 - skolem:lemma4705 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((1) (2 6 7)) list:append (1 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3626 a r:Inference; +skolem:lemma3016 a r:Inference; r:gives { 2618 :numberToDigits (2 6 1 8). }; @@ -89446,32 +70933,9 @@ skolem:lemma3626 a r:Inference; 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:lemma4392. - -skolem:lemma3627 a r:Inference; - r:gives { - (2 6 1 8) :sort (1 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 8) list:firstRest (2 (6 1 8))}] - skolem:lemma5351 - skolem:lemma4705 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((1) (2 6 8)) list:append (1 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3628 a r:Inference; +skolem:lemma3017 a r:Inference; r:gives { 2619 :numberToDigits (2 6 1 9). }; @@ -89490,32 +70954,9 @@ skolem:lemma3628 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3629 a r:Inference; - r:gives { - (2 6 1 9) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1 9) list:firstRest (2 (6 1 9))}] - skolem:lemma5352 - skolem:lemma4705 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((1) (2 6 9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 1 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_2"]; r:boundTo (6 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3630 a r:Inference; +skolem:lemma3018 a r:Inference; r:gives { 2620 :numberToDigits (2 6 2 0). }; @@ -89534,32 +70975,9 @@ skolem:lemma3630 a r:Inference; 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:lemma4392. - -skolem:lemma3631 a r:Inference; - r:gives { - (2 6 2 0) :sort (0 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 0) list:firstRest (2 (6 2 0))}] - skolem:lemma5353 - skolem:lemma4793 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((0 2) (2 6)) list:append (0 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3632 a r:Inference; +skolem:lemma3019 a r:Inference; r:gives { 2621 :numberToDigits (2 6 2 1). }; @@ -89578,32 +70996,9 @@ skolem:lemma3632 a r:Inference; 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:lemma4392. - -skolem:lemma3633 a r:Inference; - r:gives { - (2 6 2 1) :sort (1 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 1) list:firstRest (2 (6 2 1))}] - skolem:lemma5354 - skolem:lemma4807 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1 2) (2 6)) list:append (1 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3634 a r:Inference; +skolem:lemma3020 a r:Inference; r:gives { 2622 :numberToDigits (2 6 2 2). }; @@ -89622,32 +71017,9 @@ skolem:lemma3634 a r:Inference; 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:lemma4392. - -skolem:lemma3635 a r:Inference; - r:gives { - (2 6 2 2) :sort (2 2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 2) list:firstRest (2 (6 2 2))}] - skolem:lemma5355 - skolem:lemma4822 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((2 2) (2 6)) list:append (2 2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3636 a r:Inference; +skolem:lemma3021 a r:Inference; r:gives { 2623 :numberToDigits (2 6 2 3). }; @@ -89666,32 +71038,9 @@ skolem:lemma3636 a r:Inference; 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:lemma4392. - -skolem:lemma3637 a r:Inference; - r:gives { - (2 6 2 3) :sort (2 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 3) list:firstRest (2 (6 2 3))}] - skolem:lemma5356 - skolem:lemma4833 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((2) (2 3 6)) list:append (2 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 3)]; - 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 3)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3638 a r:Inference; +skolem:lemma3022 a r:Inference; r:gives { 2624 :numberToDigits (2 6 2 4). }; @@ -89710,32 +71059,9 @@ skolem:lemma3638 a r:Inference; 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:lemma4392. - -skolem:lemma3639 a r:Inference; - r:gives { - (2 6 2 4) :sort (2 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 4) list:firstRest (2 (6 2 4))}] - skolem:lemma5357 - skolem:lemma4833 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((2) (2 4 6)) list:append (2 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 4)]; - 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 4)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3640 a r:Inference; +skolem:lemma3023 a r:Inference; r:gives { 2625 :numberToDigits (2 6 2 5). }; @@ -89754,32 +71080,9 @@ skolem:lemma3640 a r:Inference; 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:lemma4392. - -skolem:lemma3641 a r:Inference; - r:gives { - (2 6 2 5) :sort (2 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 5) list:firstRest (2 (6 2 5))}] - skolem:lemma5358 - skolem:lemma4833 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((2) (2 5 6)) list:append (2 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 5)]; - 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 5)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3642 a r:Inference; +skolem:lemma3024 a r:Inference; r:gives { 2626 :numberToDigits (2 6 2 6). }; @@ -89798,32 +71101,9 @@ skolem:lemma3642 a r:Inference; 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:lemma4392. - -skolem:lemma3643 a r:Inference; - r:gives { - (2 6 2 6) :sort (2 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 6) list:firstRest (2 (6 2 6))}] - skolem:lemma5359 - skolem:lemma4833 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((2) (2 6 6)) list:append (2 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3644 a r:Inference; +skolem:lemma3025 a r:Inference; r:gives { 2627 :numberToDigits (2 6 2 7). }; @@ -89842,32 +71122,9 @@ skolem:lemma3644 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3645 a r:Inference; - r:gives { - (2 6 2 7) :sort (2 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 7) list:firstRest (2 (6 2 7))}] - skolem:lemma5360 - skolem:lemma4833 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((2) (2 6 7)) list:append (2 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3646 a r:Inference; +skolem:lemma3026 a r:Inference; r:gives { 2628 :numberToDigits (2 6 2 8). }; @@ -89886,32 +71143,9 @@ skolem:lemma3646 a r:Inference; 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:lemma4392. - -skolem:lemma3647 a r:Inference; - r:gives { - (2 6 2 8) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 8) list:firstRest (2 (6 2 8))}] - skolem:lemma5361 - skolem:lemma4833 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((2) (2 6 8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3648 a r:Inference; +skolem:lemma3027 a r:Inference; r:gives { 2629 :numberToDigits (2 6 2 9). }; @@ -89930,32 +71164,9 @@ skolem:lemma3648 a r:Inference; 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:lemma4392. - -skolem:lemma3649 a r:Inference; - r:gives { - (2 6 2 9) :sort (2 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2 9) list:firstRest (2 (6 2 9))}] - skolem:lemma5362 - skolem:lemma4833 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((2) (2 6 9)) list:append (2 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 2 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_2"]; r:boundTo (6 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3650 a r:Inference; +skolem:lemma3028 a r:Inference; r:gives { 2630 :numberToDigits (2 6 3 0). }; @@ -89974,32 +71185,9 @@ skolem:lemma3650 a r:Inference; 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:lemma4392. - -skolem:lemma3651 a r:Inference; - r:gives { - (2 6 3 0) :sort (0 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 0) list:firstRest (2 (6 3 0))}] - skolem:lemma5363 - skolem:lemma4506 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((0) (2 3 6)) list:append (0 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3652 a r:Inference; +skolem:lemma3029 a r:Inference; r:gives { 2631 :numberToDigits (2 6 3 1). }; @@ -90018,32 +71206,9 @@ skolem:lemma3652 a r:Inference; 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:lemma4392. - -skolem:lemma3653 a r:Inference; - r:gives { - (2 6 3 1) :sort (1 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 1) list:firstRest (2 (6 3 1))}] - skolem:lemma5364 - skolem:lemma4705 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((1) (2 3 6)) list:append (1 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 1)]; - 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 3)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3654 a r:Inference; +skolem:lemma3030 a r:Inference; r:gives { 2632 :numberToDigits (2 6 3 2). }; @@ -90062,32 +71227,9 @@ skolem:lemma3654 a r:Inference; 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:lemma4392. - -skolem:lemma3655 a r:Inference; - r:gives { - (2 6 3 2) :sort (2 2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 2) list:firstRest (2 (6 3 2))}] - skolem:lemma5365 - skolem:lemma4833 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {((2) (2 3 6)) list:append (2 2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 2)]; - 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 3)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3656 a r:Inference; +skolem:lemma3031 a r:Inference; r:gives { 2633 :numberToDigits (2 6 3 3). }; @@ -90106,32 +71248,9 @@ skolem:lemma3656 a r:Inference; 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:lemma4392. - -skolem:lemma3657 a r:Inference; - r:gives { - (2 6 3 3) :sort (2 3 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 3) list:firstRest (2 (6 3 3))}] - skolem:lemma5366 - skolem:lemma4395 - skolem:lemma5367 - [ a r:Fact; r:gives {(2 3 3 6) list:firstRest (2 (3 3 6))}] - [ a r:Fact; r:gives {(() (2 3 3 6)) list:append (2 3 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3658 a r:Inference; +skolem:lemma3032 a r:Inference; r:gives { 2634 :numberToDigits (2 6 3 4). }; @@ -90150,32 +71269,9 @@ skolem:lemma3658 a r:Inference; 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:lemma4392. - -skolem:lemma3659 a r:Inference; - r:gives { - (2 6 3 4) :sort (2 3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 4) list:firstRest (2 (6 3 4))}] - skolem:lemma5368 - skolem:lemma4395 - skolem:lemma5369 - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - [ a r:Fact; r:gives {(() (2 3 4 6)) list:append (2 3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3660 a r:Inference; +skolem:lemma3033 a r:Inference; r:gives { 2635 :numberToDigits (2 6 3 5). }; @@ -90194,32 +71290,9 @@ skolem:lemma3660 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3661 a r:Inference; - r:gives { - (2 6 3 5) :sort (2 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 5) list:firstRest (2 (6 3 5))}] - skolem:lemma5370 - skolem:lemma4395 - skolem:lemma5371 - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - [ a r:Fact; r:gives {(() (2 3 5 6)) list:append (2 3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3662 a r:Inference; +skolem:lemma3034 a r:Inference; r:gives { 2636 :numberToDigits (2 6 3 6). }; @@ -90238,32 +71311,9 @@ skolem:lemma3662 a r:Inference; 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:lemma4392. - -skolem:lemma3663 a r:Inference; - r:gives { - (2 6 3 6) :sort (2 3 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 6) list:firstRest (2 (6 3 6))}] - skolem:lemma5372 - skolem:lemma4395 - skolem:lemma5373 - [ a r:Fact; r:gives {(2 3 6 6) list:firstRest (2 (3 6 6))}] - [ a r:Fact; r:gives {(() (2 3 6 6)) list:append (2 3 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3664 a r:Inference; +skolem:lemma3035 a r:Inference; r:gives { 2637 :numberToDigits (2 6 3 7). }; @@ -90282,32 +71332,9 @@ skolem:lemma3664 a r:Inference; 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:lemma4392. - -skolem:lemma3665 a r:Inference; - r:gives { - (2 6 3 7) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 7) list:firstRest (2 (6 3 7))}] - skolem:lemma5374 - skolem:lemma4395 - skolem:lemma5375 - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - [ a r:Fact; r:gives {(() (2 3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3666 a r:Inference; +skolem:lemma3036 a r:Inference; r:gives { 2638 :numberToDigits (2 6 3 8). }; @@ -90326,32 +71353,9 @@ skolem:lemma3666 a r:Inference; 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:lemma4392. - -skolem:lemma3667 a r:Inference; - r:gives { - (2 6 3 8) :sort (2 3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3 8) list:firstRest (2 (6 3 8))}] - skolem:lemma5376 - skolem:lemma4395 - skolem:lemma5377 - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - [ a r:Fact; r:gives {(() (2 3 6 8)) list:append (2 3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3668 a r:Inference; +skolem:lemma3037 a r:Inference; r:gives { 2639 :numberToDigits (2 6 3 9). }; @@ -90370,32 +71374,30 @@ skolem:lemma3668 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3669 a r:Inference; +skolem:lemma3038 a r:Inference; r:gives { - (2 6 3 9) :sort (2 3 6 9). + 2640 :numberToDigits (2 6 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2 6 3 9) list:firstRest (2 (6 3 9))}] - skolem:lemma5378 - skolem:lemma4395 - skolem:lemma5379 - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - [ a r:Fact; r:gives {(() (2 3 6 9)) list:append (2 3 6 9)}] + [ 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_0"]; r:boundTo (2 6 3 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_2"]; r:boundTo (6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 9)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3670 a r:Inference; +skolem:lemma3039 a r:Inference; r:gives { 2641 :numberToDigits (2 6 4 1). }; @@ -90414,32 +71416,9 @@ skolem:lemma3670 a r:Inference; 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:lemma4392. - -skolem:lemma3671 a r:Inference; - r:gives { - (2 6 4 1) :sort (1 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 1) list:firstRest (2 (6 4 1))}] - skolem:lemma5380 - skolem:lemma4705 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((1) (2 4 6)) list:append (1 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 1)]; - 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 4)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3672 a r:Inference; +skolem:lemma3040 a r:Inference; r:gives { 2642 :numberToDigits (2 6 4 2). }; @@ -90458,32 +71437,9 @@ skolem:lemma3672 a r:Inference; 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:lemma4392. - -skolem:lemma3673 a r:Inference; - r:gives { - (2 6 4 2) :sort (2 2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 2) list:firstRest (2 (6 4 2))}] - skolem:lemma5381 - skolem:lemma4833 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {((2) (2 4 6)) list:append (2 2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 2)]; - 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 4)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3674 a r:Inference; +skolem:lemma3041 a r:Inference; r:gives { 2643 :numberToDigits (2 6 4 3). }; @@ -90502,32 +71458,9 @@ skolem:lemma3674 a r:Inference; 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:lemma4392. - -skolem:lemma3675 a r:Inference; - r:gives { - (2 6 4 3) :sort (2 3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 3) list:firstRest (2 (6 4 3))}] - skolem:lemma5382 - skolem:lemma4395 - skolem:lemma5383 - [ a r:Fact; r:gives {(2 3 4 6) list:firstRest (2 (3 4 6))}] - [ a r:Fact; r:gives {(() (2 3 4 6)) list:append (2 3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3676 a r:Inference; +skolem:lemma3042 a r:Inference; r:gives { 2644 :numberToDigits (2 6 4 4). }; @@ -90546,32 +71479,9 @@ skolem:lemma3676 a r:Inference; 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:lemma4392. - -skolem:lemma3677 a r:Inference; - r:gives { - (2 6 4 4) :sort (2 4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 4) list:firstRest (2 (6 4 4))}] - skolem:lemma5384 - skolem:lemma4395 - skolem:lemma5385 - [ a r:Fact; r:gives {(2 4 4 6) list:firstRest (2 (4 4 6))}] - [ a r:Fact; r:gives {(() (2 4 4 6)) list:append (2 4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3678 a r:Inference; +skolem:lemma3043 a r:Inference; r:gives { 2645 :numberToDigits (2 6 4 5). }; @@ -90590,32 +71500,9 @@ skolem:lemma3678 a r:Inference; 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:lemma4392. - -skolem:lemma3679 a r:Inference; - r:gives { - (2 6 4 5) :sort (2 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 5) list:firstRest (2 (6 4 5))}] - skolem:lemma5386 - skolem:lemma4395 - skolem:lemma5387 - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - [ a r:Fact; r:gives {(() (2 4 5 6)) list:append (2 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3680 a r:Inference; +skolem:lemma3044 a r:Inference; r:gives { 2646 :numberToDigits (2 6 4 6). }; @@ -90634,32 +71521,9 @@ skolem:lemma3680 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3681 a r:Inference; - r:gives { - (2 6 4 6) :sort (2 4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 6) list:firstRest (2 (6 4 6))}] - skolem:lemma5388 - skolem:lemma4395 - skolem:lemma5389 - [ a r:Fact; r:gives {(2 4 6 6) list:firstRest (2 (4 6 6))}] - [ a r:Fact; r:gives {(() (2 4 6 6)) list:append (2 4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3682 a r:Inference; +skolem:lemma3045 a r:Inference; r:gives { 2647 :numberToDigits (2 6 4 7). }; @@ -90678,32 +71542,30 @@ skolem:lemma3682 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3683 a r:Inference; +skolem:lemma3046 a r:Inference; r:gives { - (2 6 4 7) :sort (2 4 6 7). + 2648 :numberToDigits (2 6 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 6 4 7) list:firstRest (2 (6 4 7))}] - skolem:lemma5390 - skolem:lemma4395 - skolem:lemma5391 - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - [ a r:Fact; r:gives {(() (2 4 6 7)) list:append (2 4 6 7)}] + [ 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_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3684 a r:Inference; +skolem:lemma3047 a r:Inference; r:gives { 2649 :numberToDigits (2 6 4 9). }; @@ -90722,32 +71584,9 @@ skolem:lemma3684 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3685 a r:Inference; - r:gives { - (2 6 4 9) :sort (2 4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4 9) list:firstRest (2 (6 4 9))}] - skolem:lemma5392 - skolem:lemma4395 - skolem:lemma5393 - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - [ a r:Fact; r:gives {(() (2 4 6 9)) list:append (2 4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 4 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_2"]; r:boundTo (6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3686 a r:Inference; +skolem:lemma3048 a r:Inference; r:gives { 2650 :numberToDigits (2 6 5 0). }; @@ -90766,32 +71605,9 @@ skolem:lemma3686 a r:Inference; 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:lemma4392. - -skolem:lemma3687 a r:Inference; - r:gives { - (2 6 5 0) :sort (0 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 0) list:firstRest (2 (6 5 0))}] - skolem:lemma5394 - skolem:lemma4506 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((0) (2 5 6)) list:append (0 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3688 a r:Inference; +skolem:lemma3049 a r:Inference; r:gives { 2651 :numberToDigits (2 6 5 1). }; @@ -90810,32 +71626,9 @@ skolem:lemma3688 a r:Inference; 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:lemma4392. - -skolem:lemma3689 a r:Inference; - r:gives { - (2 6 5 1) :sort (1 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 1) list:firstRest (2 (6 5 1))}] - skolem:lemma5395 - skolem:lemma4705 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((1) (2 5 6)) list:append (1 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 1)]; - 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 5)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3690 a r:Inference; +skolem:lemma3050 a r:Inference; r:gives { 2652 :numberToDigits (2 6 5 2). }; @@ -90854,32 +71647,9 @@ skolem:lemma3690 a r:Inference; 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:lemma4392. - -skolem:lemma3691 a r:Inference; - r:gives { - (2 6 5 2) :sort (2 2 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 2) list:firstRest (2 (6 5 2))}] - skolem:lemma5396 - skolem:lemma4833 - skolem:lemma4567 - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {((2) (2 5 6)) list:append (2 2 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 2)]; - 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 5)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3692 a r:Inference; +skolem:lemma3051 a r:Inference; r:gives { 2653 :numberToDigits (2 6 5 3). }; @@ -90898,32 +71668,9 @@ skolem:lemma3692 a r:Inference; 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:lemma4392. - -skolem:lemma3693 a r:Inference; - r:gives { - (2 6 5 3) :sort (2 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 3) list:firstRest (2 (6 5 3))}] - skolem:lemma5397 - skolem:lemma4395 - skolem:lemma5398 - [ a r:Fact; r:gives {(2 3 5 6) list:firstRest (2 (3 5 6))}] - [ a r:Fact; r:gives {(() (2 3 5 6)) list:append (2 3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3694 a r:Inference; +skolem:lemma3052 a r:Inference; r:gives { 2654 :numberToDigits (2 6 5 4). }; @@ -90942,32 +71689,9 @@ skolem:lemma3694 a r:Inference; 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:lemma4392. - -skolem:lemma3695 a r:Inference; - r:gives { - (2 6 5 4) :sort (2 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 4) list:firstRest (2 (6 5 4))}] - skolem:lemma5399 - skolem:lemma4395 - skolem:lemma5400 - [ a r:Fact; r:gives {(2 4 5 6) list:firstRest (2 (4 5 6))}] - [ a r:Fact; r:gives {(() (2 4 5 6)) list:append (2 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3696 a r:Inference; +skolem:lemma3053 a r:Inference; r:gives { 2655 :numberToDigits (2 6 5 5). }; @@ -90986,34 +71710,11 @@ skolem:lemma3696 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3697 a r:Inference; +skolem:lemma3054 a r:Inference; r:gives { - (2 6 5 5) :sort (2 5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 5) list:firstRest (2 (6 5 5))}] - skolem:lemma5401 - skolem:lemma4395 - skolem:lemma5402 - [ a r:Fact; r:gives {(2 5 5 6) list:firstRest (2 (5 5 6))}] - [ a r:Fact; r:gives {(() (2 5 5 6)) list:append (2 5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma3698 a r:Inference; - r:gives { - 2656 :numberToDigits (2 6 5 6). + 2656 :numberToDigits (2 6 5 6). }; r:evidence ( [ a r:Fact; r:gives {(2656 1000) math:integerQuotient 2}] @@ -91030,32 +71731,9 @@ skolem:lemma3698 a r:Inference; 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:lemma4392. - -skolem:lemma3699 a r:Inference; - r:gives { - (2 6 5 6) :sort (2 5 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 6) list:firstRest (2 (6 5 6))}] - skolem:lemma5403 - skolem:lemma4395 - skolem:lemma5404 - [ a r:Fact; r:gives {(2 5 6 6) list:firstRest (2 (5 6 6))}] - [ a r:Fact; r:gives {(() (2 5 6 6)) list:append (2 5 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3700 a r:Inference; +skolem:lemma3055 a r:Inference; r:gives { 2657 :numberToDigits (2 6 5 7). }; @@ -91074,32 +71752,9 @@ skolem:lemma3700 a r:Inference; 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:lemma4392. - -skolem:lemma3701 a r:Inference; - r:gives { - (2 6 5 7) :sort (2 5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 7) list:firstRest (2 (6 5 7))}] - skolem:lemma5405 - skolem:lemma4395 - skolem:lemma5406 - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - [ a r:Fact; r:gives {(() (2 5 6 7)) list:append (2 5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3702 a r:Inference; +skolem:lemma3056 a r:Inference; r:gives { 2658 :numberToDigits (2 6 5 8). }; @@ -91118,32 +71773,9 @@ skolem:lemma3702 a r:Inference; 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:lemma4392. - -skolem:lemma3703 a r:Inference; - r:gives { - (2 6 5 8) :sort (2 5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 8) list:firstRest (2 (6 5 8))}] - skolem:lemma5407 - skolem:lemma4395 - skolem:lemma5408 - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - [ a r:Fact; r:gives {(() (2 5 6 8)) list:append (2 5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3704 a r:Inference; +skolem:lemma3057 a r:Inference; r:gives { 2659 :numberToDigits (2 6 5 9). }; @@ -91162,32 +71794,9 @@ skolem:lemma3704 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3705 a r:Inference; - r:gives { - (2 6 5 9) :sort (2 5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5 9) list:firstRest (2 (6 5 9))}] - skolem:lemma5409 - skolem:lemma4395 - skolem:lemma5410 - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - [ a r:Fact; r:gives {(() (2 5 6 9)) list:append (2 5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 5 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_2"]; r:boundTo (6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3706 a r:Inference; +skolem:lemma3058 a r:Inference; r:gives { 2660 :numberToDigits (2 6 6 0). }; @@ -91206,32 +71815,9 @@ skolem:lemma3706 a r:Inference; 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:lemma4392. - -skolem:lemma3707 a r:Inference; - r:gives { - (2 6 6 0) :sort (0 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 0) list:firstRest (2 (6 6 0))}] - skolem:lemma5411 - skolem:lemma4506 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((0) (2 6 6)) list:append (0 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 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 (6 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3708 a r:Inference; +skolem:lemma3059 a r:Inference; r:gives { 2661 :numberToDigits (2 6 6 1). }; @@ -91250,32 +71836,9 @@ skolem:lemma3708 a r:Inference; 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:lemma4392. - -skolem:lemma3709 a r:Inference; - r:gives { - (2 6 6 1) :sort (1 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 1) list:firstRest (2 (6 6 1))}] - skolem:lemma5412 - skolem:lemma4705 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((1) (2 6 6)) list:append (1 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 1)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3710 a r:Inference; +skolem:lemma3060 a r:Inference; r:gives { 2662 :numberToDigits (2 6 6 2). }; @@ -91294,32 +71857,9 @@ skolem:lemma3710 a r:Inference; 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:lemma4392. - -skolem:lemma3711 a r:Inference; - r:gives { - (2 6 6 2) :sort (2 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 2) list:firstRest (2 (6 6 2))}] - skolem:lemma5413 - skolem:lemma4833 - skolem:lemma4569 - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {((2) (2 6 6)) list:append (2 2 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 2)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3712 a r:Inference; +skolem:lemma3061 a r:Inference; r:gives { 2663 :numberToDigits (2 6 6 3). }; @@ -91338,32 +71878,9 @@ skolem:lemma3712 a r:Inference; 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:lemma4392. - -skolem:lemma3713 a r:Inference; - r:gives { - (2 6 6 3) :sort (2 3 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 3) list:firstRest (2 (6 6 3))}] - skolem:lemma5414 - skolem:lemma4395 - skolem:lemma5415 - [ a r:Fact; r:gives {(2 3 6 6) list:firstRest (2 (3 6 6))}] - [ a r:Fact; r:gives {(() (2 3 6 6)) list:append (2 3 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3714 a r:Inference; +skolem:lemma3062 a r:Inference; r:gives { 2664 :numberToDigits (2 6 6 4). }; @@ -91382,32 +71899,9 @@ skolem:lemma3714 a r:Inference; 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:lemma4392. - -skolem:lemma3715 a r:Inference; - r:gives { - (2 6 6 4) :sort (2 4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 4) list:firstRest (2 (6 6 4))}] - skolem:lemma5416 - skolem:lemma4395 - skolem:lemma5417 - [ a r:Fact; r:gives {(2 4 6 6) list:firstRest (2 (4 6 6))}] - [ a r:Fact; r:gives {(() (2 4 6 6)) list:append (2 4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3716 a r:Inference; +skolem:lemma3063 a r:Inference; r:gives { 2665 :numberToDigits (2 6 6 5). }; @@ -91426,32 +71920,9 @@ skolem:lemma3716 a r:Inference; 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:lemma4392. - -skolem:lemma3717 a r:Inference; - r:gives { - (2 6 6 5) :sort (2 5 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 5) list:firstRest (2 (6 6 5))}] - skolem:lemma5418 - skolem:lemma4395 - skolem:lemma5419 - [ a r:Fact; r:gives {(2 5 6 6) list:firstRest (2 (5 6 6))}] - [ a r:Fact; r:gives {(() (2 5 6 6)) list:append (2 5 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3718 a r:Inference; +skolem:lemma3064 a r:Inference; r:gives { 2666 :numberToDigits (2 6 6 6). }; @@ -91470,32 +71941,9 @@ skolem:lemma3718 a r:Inference; 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:lemma4392. - -skolem:lemma3719 a r:Inference; - r:gives { - (2 6 6 6) :sort (2 6 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 6) list:firstRest (2 (6 6 6))}] - skolem:lemma5420 - skolem:lemma4395 - skolem:lemma5421 - [ a r:Fact; r:gives {(2 6 6 6) list:firstRest (2 (6 6 6))}] - [ a r:Fact; r:gives {(() (2 6 6 6)) list:append (2 6 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 6)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3720 a r:Inference; +skolem:lemma3065 a r:Inference; r:gives { (2 6 6 6) :digitsToNumber 2666 . }; @@ -91513,9 +71961,9 @@ skolem:lemma3720 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3721 a r:Inference; +skolem:lemma3066 a r:Inference; r:gives { (6 6 6 2) :digitsToNumber 6662 . }; @@ -91533,9 +71981,9 @@ skolem:lemma3721 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3722 a r:Inference; +skolem:lemma3067 a r:Inference; r:gives { 2667 :numberToDigits (2 6 6 7). }; @@ -91554,32 +72002,9 @@ skolem:lemma3722 a r:Inference; 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:lemma4392. - -skolem:lemma3723 a r:Inference; - r:gives { - (2 6 6 7) :sort (2 6 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 7) list:firstRest (2 (6 6 7))}] - skolem:lemma5422 - skolem:lemma4395 - skolem:lemma5423 - [ a r:Fact; r:gives {(2 6 6 7) list:firstRest (2 (6 6 7))}] - [ a r:Fact; r:gives {(() (2 6 6 7)) list:append (2 6 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3724 a r:Inference; +skolem:lemma3068 a r:Inference; r:gives { (2 6 6 7) :digitsToNumber 2667 . }; @@ -91597,9 +72022,9 @@ skolem:lemma3724 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3725 a r:Inference; +skolem:lemma3069 a r:Inference; r:gives { (7 6 6 2) :digitsToNumber 7662 . }; @@ -91617,9 +72042,9 @@ skolem:lemma3725 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3726 a r:Inference; +skolem:lemma3070 a r:Inference; r:gives { 2668 :numberToDigits (2 6 6 8). }; @@ -91638,32 +72063,9 @@ skolem:lemma3726 a r:Inference; 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:lemma4392. - -skolem:lemma3727 a r:Inference; - r:gives { - (2 6 6 8) :sort (2 6 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 8) list:firstRest (2 (6 6 8))}] - skolem:lemma5424 - skolem:lemma4395 - skolem:lemma5425 - [ a r:Fact; r:gives {(2 6 6 8) list:firstRest (2 (6 6 8))}] - [ a r:Fact; r:gives {(() (2 6 6 8)) list:append (2 6 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3728 a r:Inference; +skolem:lemma3071 a r:Inference; r:gives { (2 6 6 8) :digitsToNumber 2668 . }; @@ -91681,9 +72083,9 @@ skolem:lemma3728 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3729 a r:Inference; +skolem:lemma3072 a r:Inference; r:gives { (8 6 6 2) :digitsToNumber 8662 . }; @@ -91701,9 +72103,9 @@ skolem:lemma3729 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3730 a r:Inference; +skolem:lemma3073 a r:Inference; r:gives { 2669 :numberToDigits (2 6 6 9). }; @@ -91722,32 +72124,9 @@ skolem:lemma3730 a r:Inference; 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:lemma4392. - -skolem:lemma3731 a r:Inference; - r:gives { - (2 6 6 9) :sort (2 6 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6 9) list:firstRest (2 (6 6 9))}] - skolem:lemma5426 - skolem:lemma4395 - skolem:lemma5427 - [ a r:Fact; r:gives {(2 6 6 9) list:firstRest (2 (6 6 9))}] - [ a r:Fact; r:gives {(() (2 6 6 9)) list:append (2 6 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 6 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_2"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3732 a r:Inference; +skolem:lemma3074 a r:Inference; r:gives { (2 6 6 9) :digitsToNumber 2669 . }; @@ -91765,9 +72144,9 @@ skolem:lemma3732 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3733 a r:Inference; +skolem:lemma3075 a r:Inference; r:gives { (9 6 6 2) :digitsToNumber 9662 . }; @@ -91785,9 +72164,9 @@ skolem:lemma3733 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3734 a r:Inference; +skolem:lemma3076 a r:Inference; r:gives { 2670 :numberToDigits (2 6 7 0). }; @@ -91806,32 +72185,9 @@ skolem:lemma3734 a r:Inference; 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:lemma4392. - -skolem:lemma3735 a r:Inference; - r:gives { - (2 6 7 0) :sort (0 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 0) list:firstRest (2 (6 7 0))}] - skolem:lemma5428 - skolem:lemma4506 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((0) (2 6 7)) list:append (0 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 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 (6 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 (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3736 a r:Inference; +skolem:lemma3077 a r:Inference; r:gives { 2671 :numberToDigits (2 6 7 1). }; @@ -91850,32 +72206,9 @@ skolem:lemma3736 a r:Inference; 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:lemma4392. - -skolem:lemma3737 a r:Inference; - r:gives { - (2 6 7 1) :sort (1 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 1) list:firstRest (2 (6 7 1))}] - skolem:lemma5429 - skolem:lemma4705 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((1) (2 6 7)) list:append (1 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 1)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3738 a r:Inference; +skolem:lemma3078 a r:Inference; r:gives { 2672 :numberToDigits (2 6 7 2). }; @@ -91894,32 +72227,9 @@ skolem:lemma3738 a r:Inference; 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:lemma4392. - -skolem:lemma3739 a r:Inference; - r:gives { - (2 6 7 2) :sort (2 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 2) list:firstRest (2 (6 7 2))}] - skolem:lemma5430 - skolem:lemma4833 - skolem:lemma4575 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((2) (2 6 7)) list:append (2 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 2)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3740 a r:Inference; +skolem:lemma3079 a r:Inference; r:gives { 2673 :numberToDigits (2 6 7 3). }; @@ -91938,32 +72248,9 @@ skolem:lemma3740 a r:Inference; 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:lemma4392. - -skolem:lemma3741 a r:Inference; - r:gives { - (2 6 7 3) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 3) list:firstRest (2 (6 7 3))}] - skolem:lemma5431 - skolem:lemma4395 - skolem:lemma5432 - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - [ a r:Fact; r:gives {(() (2 3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3742 a r:Inference; +skolem:lemma3080 a r:Inference; r:gives { 2674 :numberToDigits (2 6 7 4). }; @@ -91982,32 +72269,9 @@ skolem:lemma3742 a r:Inference; 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:lemma4392. - -skolem:lemma3743 a r:Inference; - r:gives { - (2 6 7 4) :sort (2 4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 4) list:firstRest (2 (6 7 4))}] - skolem:lemma5433 - skolem:lemma4395 - skolem:lemma5434 - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - [ a r:Fact; r:gives {(() (2 4 6 7)) list:append (2 4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3744 a r:Inference; +skolem:lemma3081 a r:Inference; r:gives { 2675 :numberToDigits (2 6 7 5). }; @@ -92026,32 +72290,9 @@ skolem:lemma3744 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3745 a r:Inference; - r:gives { - (2 6 7 5) :sort (2 5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 5) list:firstRest (2 (6 7 5))}] - skolem:lemma5435 - skolem:lemma4395 - skolem:lemma5436 - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - [ a r:Fact; r:gives {(() (2 5 6 7)) list:append (2 5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3746 a r:Inference; +skolem:lemma3082 a r:Inference; r:gives { 2676 :numberToDigits (2 6 7 6). }; @@ -92070,32 +72311,9 @@ skolem:lemma3746 a r:Inference; 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:lemma4392. - -skolem:lemma3747 a r:Inference; - r:gives { - (2 6 7 6) :sort (2 6 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 6) list:firstRest (2 (6 7 6))}] - skolem:lemma5437 - skolem:lemma4395 - skolem:lemma5438 - [ a r:Fact; r:gives {(2 6 6 7) list:firstRest (2 (6 6 7))}] - [ a r:Fact; r:gives {(() (2 6 6 7)) list:append (2 6 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3748 a r:Inference; +skolem:lemma3083 a r:Inference; r:gives { 2677 :numberToDigits (2 6 7 7). }; @@ -92114,32 +72332,9 @@ skolem:lemma3748 a r:Inference; 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:lemma4392. - -skolem:lemma3749 a r:Inference; - r:gives { - (2 6 7 7) :sort (2 6 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 7) list:firstRest (2 (6 7 7))}] - skolem:lemma5439 - skolem:lemma4395 - skolem:lemma5440 - [ a r:Fact; r:gives {(2 6 7 7) list:firstRest (2 (6 7 7))}] - [ a r:Fact; r:gives {(() (2 6 7 7)) list:append (2 6 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3750 a r:Inference; +skolem:lemma3084 a r:Inference; r:gives { (2 6 7 7) :digitsToNumber 2677 . }; @@ -92157,9 +72352,9 @@ skolem:lemma3750 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3751 a r:Inference; +skolem:lemma3085 a r:Inference; r:gives { (7 7 6 2) :digitsToNumber 7762 . }; @@ -92177,9 +72372,9 @@ skolem:lemma3751 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3752 a r:Inference; +skolem:lemma3086 a r:Inference; r:gives { 2678 :numberToDigits (2 6 7 8). }; @@ -92198,32 +72393,9 @@ skolem:lemma3752 a r:Inference; 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:lemma4392. - -skolem:lemma3753 a r:Inference; - r:gives { - (2 6 7 8) :sort (2 6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - skolem:lemma5441 - skolem:lemma4395 - skolem:lemma5442 - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - [ a r:Fact; r:gives {(() (2 6 7 8)) list:append (2 6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3754 a r:Inference; +skolem:lemma3087 a r:Inference; r:gives { (2 6 7 8) :digitsToNumber 2678 . }; @@ -92241,9 +72413,9 @@ skolem:lemma3754 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3755 a r:Inference; +skolem:lemma3088 a r:Inference; r:gives { (8 7 6 2) :digitsToNumber 8762 . }; @@ -92261,9 +72433,9 @@ skolem:lemma3755 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3756 a r:Inference; +skolem:lemma3089 a r:Inference; r:gives { 2679 :numberToDigits (2 6 7 9). }; @@ -92282,32 +72454,9 @@ skolem:lemma3756 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3757 a r:Inference; - r:gives { - (2 6 7 9) :sort (2 6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - skolem:lemma5443 - skolem:lemma4395 - skolem:lemma5444 - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - [ a r:Fact; r:gives {(() (2 6 7 9)) list:append (2 6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 7 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_2"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3758 a r:Inference; +skolem:lemma3090 a r:Inference; r:gives { (2 6 7 9) :digitsToNumber 2679 . }; @@ -92325,9 +72474,9 @@ skolem:lemma3758 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3759 a r:Inference; +skolem:lemma3091 a r:Inference; r:gives { (9 7 6 2) :digitsToNumber 9762 . }; @@ -92345,9 +72494,9 @@ skolem:lemma3759 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3760 a r:Inference; +skolem:lemma3092 a r:Inference; r:gives { 2680 :numberToDigits (2 6 8 0). }; @@ -92366,32 +72515,9 @@ skolem:lemma3760 a r:Inference; 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:lemma4392. - -skolem:lemma3761 a r:Inference; - r:gives { - (2 6 8 0) :sort (0 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8 0) list:firstRest (2 (6 8 0))}] - skolem:lemma5445 - skolem:lemma4506 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((0) (2 6 8)) list:append (0 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 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 (6 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 (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3762 a r:Inference; +skolem:lemma3093 a r:Inference; r:gives { 2681 :numberToDigits (2 6 8 1). }; @@ -92410,32 +72536,9 @@ skolem:lemma3762 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3763 a r:Inference; - r:gives { - (2 6 8 1) :sort (1 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8 1) list:firstRest (2 (6 8 1))}] - skolem:lemma5446 - skolem:lemma4705 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((1) (2 6 8)) list:append (1 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 1)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3764 a r:Inference; +skolem:lemma3094 a r:Inference; r:gives { 2682 :numberToDigits (2 6 8 2). }; @@ -92454,32 +72557,9 @@ skolem:lemma3764 a r:Inference; 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:lemma4392. - -skolem:lemma3765 a r:Inference; - r:gives { - (2 6 8 2) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8 2) list:firstRest (2 (6 8 2))}] - skolem:lemma5447 - skolem:lemma4833 - skolem:lemma4581 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((2) (2 6 8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 2)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3766 a r:Inference; +skolem:lemma3095 a r:Inference; r:gives { 2683 :numberToDigits (2 6 8 3). }; @@ -92498,32 +72578,30 @@ skolem:lemma3766 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3767 a r:Inference; +skolem:lemma3096 a r:Inference; r:gives { - (2 6 8 3) :sort (2 3 6 8). + 2684 :numberToDigits (2 6 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 6 8 3) list:firstRest (2 (6 8 3))}] - skolem:lemma5448 - skolem:lemma4395 - skolem:lemma5449 - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - [ a r:Fact; r:gives {(() (2 3 6 8)) list:append (2 3 6 8)}] + [ 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_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3768 a r:Inference; +skolem:lemma3097 a r:Inference; r:gives { 2685 :numberToDigits (2 6 8 5). }; @@ -92542,32 +72620,9 @@ skolem:lemma3768 a r:Inference; 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:lemma4392. - -skolem:lemma3769 a r:Inference; - r:gives { - (2 6 8 5) :sort (2 5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8 5) list:firstRest (2 (6 8 5))}] - skolem:lemma5450 - skolem:lemma4395 - skolem:lemma5451 - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - [ a r:Fact; r:gives {(() (2 5 6 8)) list:append (2 5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3770 a r:Inference; +skolem:lemma3098 a r:Inference; r:gives { 2686 :numberToDigits (2 6 8 6). }; @@ -92586,32 +72641,9 @@ skolem:lemma3770 a r:Inference; 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:lemma4392. - -skolem:lemma3771 a r:Inference; - r:gives { - (2 6 8 6) :sort (2 6 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8 6) list:firstRest (2 (6 8 6))}] - skolem:lemma5452 - skolem:lemma4395 - skolem:lemma5453 - [ a r:Fact; r:gives {(2 6 6 8) list:firstRest (2 (6 6 8))}] - [ a r:Fact; r:gives {(() (2 6 6 8)) list:append (2 6 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3772 a r:Inference; +skolem:lemma3099 a r:Inference; r:gives { 2687 :numberToDigits (2 6 8 7). }; @@ -92630,32 +72662,70 @@ skolem:lemma3772 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3773 a r:Inference; +skolem:lemma3100 a r:Inference; r:gives { - (2 6 8 7) :sort (2 6 7 8). + 2688 :numberToDigits (2 6 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 6 8 7) list:firstRest (2 (6 8 7))}] - skolem:lemma5454 - skolem:lemma4395 - skolem:lemma5455 - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - [ a r:Fact; r:gives {(() (2 6 7 8)) list:append (2 6 7 8)}] + [ 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_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. + +skolem:lemma3101 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:lemma3439. + +skolem:lemma3102 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:lemma3439. -skolem:lemma3774 a r:Inference; +skolem:lemma3103 a r:Inference; r:gives { 2689 :numberToDigits (2 6 8 9). }; @@ -92674,32 +72744,9 @@ skolem:lemma3774 a r:Inference; 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:lemma4392. - -skolem:lemma3775 a r:Inference; - r:gives { - (2 6 8 9) :sort (2 6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - skolem:lemma5456 - skolem:lemma4395 - skolem:lemma5457 - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - [ a r:Fact; r:gives {(() (2 6 8 9)) list:append (2 6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 8 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_2"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3776 a r:Inference; +skolem:lemma3104 a r:Inference; r:gives { (2 6 8 9) :digitsToNumber 2689 . }; @@ -92717,9 +72764,9 @@ skolem:lemma3776 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3777 a r:Inference; +skolem:lemma3105 a r:Inference; r:gives { (9 8 6 2) :digitsToNumber 9862 . }; @@ -92737,9 +72784,9 @@ skolem:lemma3777 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3778 a r:Inference; +skolem:lemma3106 a r:Inference; r:gives { 2690 :numberToDigits (2 6 9 0). }; @@ -92758,32 +72805,9 @@ skolem:lemma3778 a r:Inference; 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:lemma4392. - -skolem:lemma3779 a r:Inference; - r:gives { - (2 6 9 0) :sort (0 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 0) list:firstRest (2 (6 9 0))}] - skolem:lemma5458 - skolem:lemma4506 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((0) (2 6 9)) list:append (0 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 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 (6 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 (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3780 a r:Inference; +skolem:lemma3107 a r:Inference; r:gives { 2691 :numberToDigits (2 6 9 1). }; @@ -92802,32 +72826,9 @@ skolem:lemma3780 a r:Inference; 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:lemma4392. - -skolem:lemma3781 a r:Inference; - r:gives { - (2 6 9 1) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 1) list:firstRest (2 (6 9 1))}] - skolem:lemma5459 - skolem:lemma4705 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((1) (2 6 9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3782 a r:Inference; +skolem:lemma3108 a r:Inference; r:gives { 2692 :numberToDigits (2 6 9 2). }; @@ -92846,32 +72847,9 @@ skolem:lemma3782 a r:Inference; 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:lemma4392. - -skolem:lemma3783 a r:Inference; - r:gives { - (2 6 9 2) :sort (2 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 2) list:firstRest (2 (6 9 2))}] - skolem:lemma5460 - skolem:lemma4833 - skolem:lemma4583 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((2) (2 6 9)) list:append (2 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3784 a r:Inference; +skolem:lemma3109 a r:Inference; r:gives { 2693 :numberToDigits (2 6 9 3). }; @@ -92890,32 +72868,9 @@ skolem:lemma3784 a r:Inference; 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:lemma4392. - -skolem:lemma3785 a r:Inference; - r:gives { - (2 6 9 3) :sort (2 3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 3) list:firstRest (2 (6 9 3))}] - skolem:lemma5461 - skolem:lemma4395 - skolem:lemma5462 - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - [ a r:Fact; r:gives {(() (2 3 6 9)) list:append (2 3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3786 a r:Inference; +skolem:lemma3110 a r:Inference; r:gives { 2694 :numberToDigits (2 6 9 4). }; @@ -92934,32 +72889,9 @@ skolem:lemma3786 a r:Inference; 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:lemma4392. - -skolem:lemma3787 a r:Inference; - r:gives { - (2 6 9 4) :sort (2 4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 4) list:firstRest (2 (6 9 4))}] - skolem:lemma5463 - skolem:lemma4395 - skolem:lemma5464 - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - [ a r:Fact; r:gives {(() (2 4 6 9)) list:append (2 4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3788 a r:Inference; +skolem:lemma3111 a r:Inference; r:gives { 2695 :numberToDigits (2 6 9 5). }; @@ -92978,32 +72910,9 @@ skolem:lemma3788 a r:Inference; 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:lemma4392. - -skolem:lemma3789 a r:Inference; - r:gives { - (2 6 9 5) :sort (2 5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 5) list:firstRest (2 (6 9 5))}] - skolem:lemma5465 - skolem:lemma4395 - skolem:lemma5466 - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - [ a r:Fact; r:gives {(() (2 5 6 9)) list:append (2 5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3790 a r:Inference; +skolem:lemma3112 a r:Inference; r:gives { 2696 :numberToDigits (2 6 9 6). }; @@ -93022,32 +72931,9 @@ skolem:lemma3790 a r:Inference; 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:lemma4392. - -skolem:lemma3791 a r:Inference; - r:gives { - (2 6 9 6) :sort (2 6 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 6) list:firstRest (2 (6 9 6))}] - skolem:lemma5467 - skolem:lemma4395 - skolem:lemma5468 - [ a r:Fact; r:gives {(2 6 6 9) list:firstRest (2 (6 6 9))}] - [ a r:Fact; r:gives {(() (2 6 6 9)) list:append (2 6 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3792 a r:Inference; +skolem:lemma3113 a r:Inference; r:gives { 2697 :numberToDigits (2 6 9 7). }; @@ -93066,32 +72952,9 @@ skolem:lemma3792 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3793 a r:Inference; - r:gives { - (2 6 9 7) :sort (2 6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 7) list:firstRest (2 (6 9 7))}] - skolem:lemma5469 - skolem:lemma4395 - skolem:lemma5470 - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - [ a r:Fact; r:gives {(() (2 6 7 9)) list:append (2 6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3794 a r:Inference; +skolem:lemma3114 a r:Inference; r:gives { 2698 :numberToDigits (2 6 9 8). }; @@ -93110,32 +72973,9 @@ skolem:lemma3794 a r:Inference; 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:lemma4392. - -skolem:lemma3795 a r:Inference; - r:gives { - (2 6 9 8) :sort (2 6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 8) list:firstRest (2 (6 9 8))}] - skolem:lemma5471 - skolem:lemma4395 - skolem:lemma5472 - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - [ a r:Fact; r:gives {(() (2 6 8 9)) list:append (2 6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3796 a r:Inference; +skolem:lemma3115 a r:Inference; r:gives { 2699 :numberToDigits (2 6 9 9). }; @@ -93154,32 +72994,9 @@ skolem:lemma3796 a r:Inference; 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:lemma4392. - -skolem:lemma3797 a r:Inference; - r:gives { - (2 6 9 9) :sort (2 6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9 9) list:firstRest (2 (6 9 9))}] - skolem:lemma5473 - skolem:lemma4395 - skolem:lemma5474 - [ a r:Fact; r:gives {(2 6 9 9) list:firstRest (2 (6 9 9))}] - [ a r:Fact; r:gives {(() (2 6 9 9)) list:append (2 6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 9 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_2"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3798 a r:Inference; +skolem:lemma3116 a r:Inference; r:gives { (2 6 9 9) :digitsToNumber 2699 . }; @@ -93197,9 +73014,9 @@ skolem:lemma3798 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3799 a r:Inference; +skolem:lemma3117 a r:Inference; r:gives { (9 9 6 2) :digitsToNumber 9962 . }; @@ -93217,9 +73034,9 @@ skolem:lemma3799 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3800 a r:Inference; +skolem:lemma3118 a r:Inference; r:gives { 2700 :numberToDigits (2 7 0 0). }; @@ -93238,32 +73055,9 @@ skolem:lemma3800 a r:Inference; 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:lemma4392. - -skolem:lemma3801 a r:Inference; - r:gives { - (2 7 0 0) :sort (0 0 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 0) list:firstRest (2 (7 0 0))}] - skolem:lemma5475 - skolem:lemma4407 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 0) (2 7)) list:append (0 0 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3802 a r:Inference; +skolem:lemma3119 a r:Inference; r:gives { 2701 :numberToDigits (2 7 0 1). }; @@ -93282,32 +73076,9 @@ skolem:lemma3802 a r:Inference; 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:lemma4392. - -skolem:lemma3803 a r:Inference; - r:gives { - (2 7 0 1) :sort (0 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 1) list:firstRest (2 (7 0 1))}] - skolem:lemma5476 - skolem:lemma4442 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 1) (2 7)) list:append (0 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3804 a r:Inference; +skolem:lemma3120 a r:Inference; r:gives { 2702 :numberToDigits (2 7 0 2). }; @@ -93326,32 +73097,9 @@ skolem:lemma3804 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma3805 a r:Inference; - r:gives { - (2 7 0 2) :sort (0 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 2) list:firstRest (2 (7 0 2))}] - skolem:lemma5477 - skolem:lemma4479 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 2) (2 7)) list:append (0 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3806 a r:Inference; +skolem:lemma3121 a r:Inference; r:gives { 2703 :numberToDigits (2 7 0 3). }; @@ -93370,32 +73118,9 @@ skolem:lemma3806 a r:Inference; 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:lemma4392. - -skolem:lemma3807 a r:Inference; - r:gives { - (2 7 0 3) :sort (0 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 3) list:firstRest (2 (7 0 3))}] - skolem:lemma5478 - skolem:lemma4506 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((0) (2 3 7)) list:append (0 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3808 a r:Inference; +skolem:lemma3122 a r:Inference; r:gives { 2704 :numberToDigits (2 7 0 4). }; @@ -93414,32 +73139,9 @@ skolem:lemma3808 a r:Inference; 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:lemma4392. - -skolem:lemma3809 a r:Inference; - r:gives { - (2 7 0 4) :sort (0 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 4) list:firstRest (2 (7 0 4))}] - skolem:lemma5479 - skolem:lemma4506 - skolem:lemma4594 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((0) (2 4 7)) list:append (0 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3810 a r:Inference; +skolem:lemma3123 a r:Inference; r:gives { 2705 :numberToDigits (2 7 0 5). }; @@ -93458,32 +73160,9 @@ skolem:lemma3810 a r:Inference; 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:lemma4392. - -skolem:lemma3811 a r:Inference; - r:gives { - (2 7 0 5) :sort (0 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 5) list:firstRest (2 (7 0 5))}] - skolem:lemma5480 - skolem:lemma4506 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((0) (2 5 7)) list:append (0 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3812 a r:Inference; +skolem:lemma3124 a r:Inference; r:gives { 2706 :numberToDigits (2 7 0 6). }; @@ -93502,32 +73181,9 @@ skolem:lemma3812 a r:Inference; 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:lemma4392. - -skolem:lemma3813 a r:Inference; - r:gives { - (2 7 0 6) :sort (0 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 6) list:firstRest (2 (7 0 6))}] - skolem:lemma5481 - skolem:lemma4506 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((0) (2 6 7)) list:append (0 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3814 a r:Inference; +skolem:lemma3125 a r:Inference; r:gives { 2707 :numberToDigits (2 7 0 7). }; @@ -93546,32 +73202,9 @@ skolem:lemma3814 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3815 a r:Inference; - r:gives { - (2 7 0 7) :sort (0 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 7) list:firstRest (2 (7 0 7))}] - skolem:lemma5482 - skolem:lemma4506 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((0) (2 7 7)) list:append (0 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3816 a r:Inference; +skolem:lemma3126 a r:Inference; r:gives { 2708 :numberToDigits (2 7 0 8). }; @@ -93590,32 +73223,9 @@ skolem:lemma3816 a r:Inference; 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:lemma4392. - -skolem:lemma3817 a r:Inference; - r:gives { - (2 7 0 8) :sort (0 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 8) list:firstRest (2 (7 0 8))}] - skolem:lemma5483 - skolem:lemma4506 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((0) (2 7 8)) list:append (0 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 (7 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 (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3818 a r:Inference; +skolem:lemma3127 a r:Inference; r:gives { 2709 :numberToDigits (2 7 0 9). }; @@ -93634,32 +73244,9 @@ skolem:lemma3818 a r:Inference; 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:lemma4392. - -skolem:lemma3819 a r:Inference; - r:gives { - (2 7 0 9) :sort (0 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0 9) list:firstRest (2 (7 0 9))}] - skolem:lemma5484 - skolem:lemma4506 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((0) (2 7 9)) list:append (0 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 0 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_2"]; r:boundTo (7 0 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 (7 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 (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3820 a r:Inference; +skolem:lemma3128 a r:Inference; r:gives { 2710 :numberToDigits (2 7 1 0). }; @@ -93678,32 +73265,9 @@ skolem:lemma3820 a r:Inference; 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:lemma4392. - -skolem:lemma3821 a r:Inference; - r:gives { - (2 7 1 0) :sort (0 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 0) list:firstRest (2 (7 1 0))}] - skolem:lemma5485 - skolem:lemma4660 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 1) (2 7)) list:append (0 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3822 a r:Inference; +skolem:lemma3129 a r:Inference; r:gives { 2711 :numberToDigits (2 7 1 1). }; @@ -93722,32 +73286,9 @@ skolem:lemma3822 a r:Inference; 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:lemma4392. - -skolem:lemma3823 a r:Inference; - r:gives { - (2 7 1 1) :sort (1 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 1) list:firstRest (2 (7 1 1))}] - skolem:lemma5486 - skolem:lemma4680 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 1) (2 7)) list:append (1 1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3824 a r:Inference; +skolem:lemma3130 a r:Inference; r:gives { 2712 :numberToDigits (2 7 1 2). }; @@ -93766,32 +73307,9 @@ skolem:lemma3824 a r:Inference; 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:lemma4392. - -skolem:lemma3825 a r:Inference; - r:gives { - (2 7 1 2) :sort (1 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 2) list:firstRest (2 (7 1 2))}] - skolem:lemma5487 - skolem:lemma4694 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 2) (2 7)) list:append (1 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3826 a r:Inference; +skolem:lemma3131 a r:Inference; r:gives { 2713 :numberToDigits (2 7 1 3). }; @@ -93810,32 +73328,30 @@ skolem:lemma3826 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3827 a r:Inference; +skolem:lemma3132 a r:Inference; r:gives { - (2 7 1 3) :sort (1 2 3 7). + 2714 :numberToDigits (2 7 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 7 1 3) list:firstRest (2 (7 1 3))}] - skolem:lemma5488 - skolem:lemma4705 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((1) (2 3 7)) list:append (1 2 3 7)}] + [ 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_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 3)]; - 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 3)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3828 a r:Inference; +skolem:lemma3133 a r:Inference; r:gives { 2715 :numberToDigits (2 7 1 5). }; @@ -93854,32 +73370,9 @@ skolem:lemma3828 a r:Inference; 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:lemma4392. - -skolem:lemma3829 a r:Inference; - r:gives { - (2 7 1 5) :sort (1 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 5) list:firstRest (2 (7 1 5))}] - skolem:lemma5489 - skolem:lemma4705 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((1) (2 5 7)) list:append (1 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 5)]; - 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 5)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3830 a r:Inference; +skolem:lemma3134 a r:Inference; r:gives { 2716 :numberToDigits (2 7 1 6). }; @@ -93898,32 +73391,9 @@ skolem:lemma3830 a r:Inference; 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:lemma4392. - -skolem:lemma3831 a r:Inference; - r:gives { - (2 7 1 6) :sort (1 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 6) list:firstRest (2 (7 1 6))}] - skolem:lemma5490 - skolem:lemma4705 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((1) (2 6 7)) list:append (1 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 6)]; - 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 6)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3832 a r:Inference; +skolem:lemma3135 a r:Inference; r:gives { 2717 :numberToDigits (2 7 1 7). }; @@ -93942,32 +73412,9 @@ skolem:lemma3832 a r:Inference; 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:lemma4392. - -skolem:lemma3833 a r:Inference; - r:gives { - (2 7 1 7) :sort (1 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 7) list:firstRest (2 (7 1 7))}] - skolem:lemma5491 - skolem:lemma4705 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((1) (2 7 7)) list:append (1 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3834 a r:Inference; +skolem:lemma3136 a r:Inference; r:gives { 2718 :numberToDigits (2 7 1 8). }; @@ -93986,32 +73433,9 @@ skolem:lemma3834 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3835 a r:Inference; - r:gives { - (2 7 1 8) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 8) list:firstRest (2 (7 1 8))}] - skolem:lemma5492 - skolem:lemma4705 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((1) (2 7 8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3836 a r:Inference; +skolem:lemma3137 a r:Inference; r:gives { 2719 :numberToDigits (2 7 1 9). }; @@ -94030,32 +73454,9 @@ skolem:lemma3836 a r:Inference; 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:lemma4392. - -skolem:lemma3837 a r:Inference; - r:gives { - (2 7 1 9) :sort (1 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1 9) list:firstRest (2 (7 1 9))}] - skolem:lemma5493 - skolem:lemma4705 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((1) (2 7 9)) list:append (1 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 1 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_2"]; r:boundTo (7 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3838 a r:Inference; +skolem:lemma3138 a r:Inference; r:gives { 2720 :numberToDigits (2 7 2 0). }; @@ -94074,32 +73475,9 @@ skolem:lemma3838 a r:Inference; 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:lemma4392. - -skolem:lemma3839 a r:Inference; - r:gives { - (2 7 2 0) :sort (0 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 0) list:firstRest (2 (7 2 0))}] - skolem:lemma5494 - skolem:lemma4793 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((0 2) (2 7)) list:append (0 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3840 a r:Inference; +skolem:lemma3139 a r:Inference; r:gives { 2721 :numberToDigits (2 7 2 1). }; @@ -94118,32 +73496,9 @@ skolem:lemma3840 a r:Inference; 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:lemma4392. - -skolem:lemma3841 a r:Inference; - r:gives { - (2 7 2 1) :sort (1 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 1) list:firstRest (2 (7 2 1))}] - skolem:lemma5495 - skolem:lemma4807 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((1 2) (2 7)) list:append (1 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3842 a r:Inference; +skolem:lemma3140 a r:Inference; r:gives { 2722 :numberToDigits (2 7 2 2). }; @@ -94162,32 +73517,9 @@ skolem:lemma3842 a r:Inference; 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:lemma4392. - -skolem:lemma3843 a r:Inference; - r:gives { - (2 7 2 2) :sort (2 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 2) list:firstRest (2 (7 2 2))}] - skolem:lemma5496 - skolem:lemma4822 - skolem:lemma4422 - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {((2 2) (2 7)) list:append (2 2 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3844 a r:Inference; +skolem:lemma3141 a r:Inference; r:gives { 2723 :numberToDigits (2 7 2 3). }; @@ -94206,34 +73538,11 @@ skolem:lemma3844 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3845 a r:Inference; +skolem:lemma3142 a r:Inference; r:gives { - (2 7 2 3) :sort (2 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 3) list:firstRest (2 (7 2 3))}] - skolem:lemma5497 - skolem:lemma4833 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((2) (2 3 7)) list:append (2 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 3)]; - 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 3)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3846 a r:Inference; - r:gives { - 2724 :numberToDigits (2 7 2 4). + 2724 :numberToDigits (2 7 2 4). }; r:evidence ( [ a r:Fact; r:gives {(2724 1000) math:integerQuotient 2}] @@ -94250,32 +73559,9 @@ skolem:lemma3846 a r:Inference; 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:lemma4392. - -skolem:lemma3847 a r:Inference; - r:gives { - (2 7 2 4) :sort (2 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 4) list:firstRest (2 (7 2 4))}] - skolem:lemma5498 - skolem:lemma4833 - skolem:lemma4594 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((2) (2 4 7)) list:append (2 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 4)]; - 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 4)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3848 a r:Inference; +skolem:lemma3143 a r:Inference; r:gives { 2725 :numberToDigits (2 7 2 5). }; @@ -94294,32 +73580,9 @@ skolem:lemma3848 a r:Inference; 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:lemma4392. - -skolem:lemma3849 a r:Inference; - r:gives { - (2 7 2 5) :sort (2 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 5) list:firstRest (2 (7 2 5))}] - skolem:lemma5499 - skolem:lemma4833 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((2) (2 5 7)) list:append (2 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 5)]; - 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 5)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3850 a r:Inference; +skolem:lemma3144 a r:Inference; r:gives { 2726 :numberToDigits (2 7 2 6). }; @@ -94338,32 +73601,9 @@ skolem:lemma3850 a r:Inference; 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:lemma4392. - -skolem:lemma3851 a r:Inference; - r:gives { - (2 7 2 6) :sort (2 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 6) list:firstRest (2 (7 2 6))}] - skolem:lemma5500 - skolem:lemma4833 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((2) (2 6 7)) list:append (2 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 6)]; - 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 6)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3852 a r:Inference; +skolem:lemma3145 a r:Inference; r:gives { 2727 :numberToDigits (2 7 2 7). }; @@ -94382,32 +73622,9 @@ skolem:lemma3852 a r:Inference; 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:lemma4392. - -skolem:lemma3853 a r:Inference; - r:gives { - (2 7 2 7) :sort (2 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 7) list:firstRest (2 (7 2 7))}] - skolem:lemma5501 - skolem:lemma4833 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((2) (2 7 7)) list:append (2 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3854 a r:Inference; +skolem:lemma3146 a r:Inference; r:gives { 2728 :numberToDigits (2 7 2 8). }; @@ -94426,32 +73643,9 @@ skolem:lemma3854 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3855 a r:Inference; - r:gives { - (2 7 2 8) :sort (2 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 8) list:firstRest (2 (7 2 8))}] - skolem:lemma5502 - skolem:lemma4833 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((2) (2 7 8)) list:append (2 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3856 a r:Inference; +skolem:lemma3147 a r:Inference; r:gives { 2729 :numberToDigits (2 7 2 9). }; @@ -94470,32 +73664,9 @@ skolem:lemma3856 a r:Inference; 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:lemma4392. - -skolem:lemma3857 a r:Inference; - r:gives { - (2 7 2 9) :sort (2 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2 9) list:firstRest (2 (7 2 9))}] - skolem:lemma5503 - skolem:lemma4833 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((2) (2 7 9)) list:append (2 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 2 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_2"]; r:boundTo (7 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3858 a r:Inference; +skolem:lemma3148 a r:Inference; r:gives { 2730 :numberToDigits (2 7 3 0). }; @@ -94514,32 +73685,9 @@ skolem:lemma3858 a r:Inference; 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:lemma4392. - -skolem:lemma3859 a r:Inference; - r:gives { - (2 7 3 0) :sort (0 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 0) list:firstRest (2 (7 3 0))}] - skolem:lemma5504 - skolem:lemma4506 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((0) (2 3 7)) list:append (0 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3860 a r:Inference; +skolem:lemma3149 a r:Inference; r:gives { 2731 :numberToDigits (2 7 3 1). }; @@ -94558,32 +73706,9 @@ skolem:lemma3860 a r:Inference; 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:lemma4392. - -skolem:lemma3861 a r:Inference; - r:gives { - (2 7 3 1) :sort (1 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 1) list:firstRest (2 (7 3 1))}] - skolem:lemma5505 - skolem:lemma4705 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((1) (2 3 7)) list:append (1 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 1)]; - 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 3)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3862 a r:Inference; +skolem:lemma3150 a r:Inference; r:gives { 2732 :numberToDigits (2 7 3 2). }; @@ -94602,32 +73727,9 @@ skolem:lemma3862 a r:Inference; 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:lemma4392. - -skolem:lemma3863 a r:Inference; - r:gives { - (2 7 3 2) :sort (2 2 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 2) list:firstRest (2 (7 3 2))}] - skolem:lemma5506 - skolem:lemma4833 - skolem:lemma4592 - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {((2) (2 3 7)) list:append (2 2 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 2)]; - 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 3)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3864 a r:Inference; +skolem:lemma3151 a r:Inference; r:gives { 2733 :numberToDigits (2 7 3 3). }; @@ -94646,32 +73748,9 @@ skolem:lemma3864 a r:Inference; 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:lemma4392. - -skolem:lemma3865 a r:Inference; - r:gives { - (2 7 3 3) :sort (2 3 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 3) list:firstRest (2 (7 3 3))}] - skolem:lemma5507 - skolem:lemma4395 - skolem:lemma5508 - [ a r:Fact; r:gives {(2 3 3 7) list:firstRest (2 (3 3 7))}] - [ a r:Fact; r:gives {(() (2 3 3 7)) list:append (2 3 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3866 a r:Inference; +skolem:lemma3152 a r:Inference; r:gives { 2734 :numberToDigits (2 7 3 4). }; @@ -94690,32 +73769,9 @@ skolem:lemma3866 a r:Inference; 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:lemma4392. - -skolem:lemma3867 a r:Inference; - r:gives { - (2 7 3 4) :sort (2 3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 4) list:firstRest (2 (7 3 4))}] - skolem:lemma5509 - skolem:lemma4395 - skolem:lemma5510 - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - [ a r:Fact; r:gives {(() (2 3 4 7)) list:append (2 3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3868 a r:Inference; +skolem:lemma3153 a r:Inference; r:gives { 2735 :numberToDigits (2 7 3 5). }; @@ -94734,32 +73790,9 @@ skolem:lemma3868 a r:Inference; 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:lemma4392. - -skolem:lemma3869 a r:Inference; - r:gives { - (2 7 3 5) :sort (2 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 5) list:firstRest (2 (7 3 5))}] - skolem:lemma5511 - skolem:lemma4395 - skolem:lemma5512 - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - [ a r:Fact; r:gives {(() (2 3 5 7)) list:append (2 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3870 a r:Inference; +skolem:lemma3154 a r:Inference; r:gives { 2736 :numberToDigits (2 7 3 6). }; @@ -94778,32 +73811,9 @@ skolem:lemma3870 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3871 a r:Inference; - r:gives { - (2 7 3 6) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 6) list:firstRest (2 (7 3 6))}] - skolem:lemma5513 - skolem:lemma4395 - skolem:lemma5514 - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - [ a r:Fact; r:gives {(() (2 3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3872 a r:Inference; +skolem:lemma3155 a r:Inference; r:gives { 2737 :numberToDigits (2 7 3 7). }; @@ -94822,32 +73832,9 @@ skolem:lemma3872 a r:Inference; 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:lemma4392. - -skolem:lemma3873 a r:Inference; - r:gives { - (2 7 3 7) :sort (2 3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 7) list:firstRest (2 (7 3 7))}] - skolem:lemma5515 - skolem:lemma4395 - skolem:lemma5516 - [ a r:Fact; r:gives {(2 3 7 7) list:firstRest (2 (3 7 7))}] - [ a r:Fact; r:gives {(() (2 3 7 7)) list:append (2 3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3874 a r:Inference; +skolem:lemma3156 a r:Inference; r:gives { 2738 :numberToDigits (2 7 3 8). }; @@ -94866,32 +73853,9 @@ skolem:lemma3874 a r:Inference; 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:lemma4392. - -skolem:lemma3875 a r:Inference; - r:gives { - (2 7 3 8) :sort (2 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 8) list:firstRest (2 (7 3 8))}] - skolem:lemma5517 - skolem:lemma4395 - skolem:lemma5518 - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - [ a r:Fact; r:gives {(() (2 3 7 8)) list:append (2 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3876 a r:Inference; +skolem:lemma3157 a r:Inference; r:gives { 2739 :numberToDigits (2 7 3 9). }; @@ -94910,32 +73874,9 @@ skolem:lemma3876 a r:Inference; 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:lemma4392. - -skolem:lemma3877 a r:Inference; - r:gives { - (2 7 3 9) :sort (2 3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3 9) list:firstRest (2 (7 3 9))}] - skolem:lemma5519 - skolem:lemma4395 - skolem:lemma5520 - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - [ a r:Fact; r:gives {(() (2 3 7 9)) list:append (2 3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 3 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_2"]; r:boundTo (7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3878 a r:Inference; +skolem:lemma3158 a r:Inference; r:gives { 2740 :numberToDigits (2 7 4 0). }; @@ -94954,32 +73895,30 @@ skolem:lemma3878 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3879 a r:Inference; +skolem:lemma3159 a r:Inference; r:gives { - (2 7 4 0) :sort (0 2 4 7). + 2741 :numberToDigits (2 7 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2 7 4 0) list:firstRest (2 (7 4 0))}] - skolem:lemma5521 - skolem:lemma4506 - skolem:lemma4594 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((0) (2 4 7)) list:append (0 2 4 7)}] + [ 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_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3880 a r:Inference; +skolem:lemma3160 a r:Inference; r:gives { 2742 :numberToDigits (2 7 4 2). }; @@ -94998,32 +73937,9 @@ skolem:lemma3880 a r:Inference; 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:lemma4392. - -skolem:lemma3881 a r:Inference; - r:gives { - (2 7 4 2) :sort (2 2 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 2) list:firstRest (2 (7 4 2))}] - skolem:lemma5522 - skolem:lemma4833 - skolem:lemma4594 - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {((2) (2 4 7)) list:append (2 2 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 2)]; - 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 4)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3882 a r:Inference; +skolem:lemma3161 a r:Inference; r:gives { 2743 :numberToDigits (2 7 4 3). }; @@ -95042,32 +73958,9 @@ skolem:lemma3882 a r:Inference; 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:lemma4392. - -skolem:lemma3883 a r:Inference; - r:gives { - (2 7 4 3) :sort (2 3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 3) list:firstRest (2 (7 4 3))}] - skolem:lemma5523 - skolem:lemma4395 - skolem:lemma5524 - [ a r:Fact; r:gives {(2 3 4 7) list:firstRest (2 (3 4 7))}] - [ a r:Fact; r:gives {(() (2 3 4 7)) list:append (2 3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3884 a r:Inference; +skolem:lemma3162 a r:Inference; r:gives { 2744 :numberToDigits (2 7 4 4). }; @@ -95086,32 +73979,9 @@ skolem:lemma3884 a r:Inference; 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:lemma4392. - -skolem:lemma3885 a r:Inference; - r:gives { - (2 7 4 4) :sort (2 4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 4) list:firstRest (2 (7 4 4))}] - skolem:lemma5525 - skolem:lemma4395 - skolem:lemma5526 - [ a r:Fact; r:gives {(2 4 4 7) list:firstRest (2 (4 4 7))}] - [ a r:Fact; r:gives {(() (2 4 4 7)) list:append (2 4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3886 a r:Inference; +skolem:lemma3163 a r:Inference; r:gives { 2745 :numberToDigits (2 7 4 5). }; @@ -95130,32 +74000,9 @@ skolem:lemma3886 a r:Inference; 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:lemma4392. - -skolem:lemma3887 a r:Inference; - r:gives { - (2 7 4 5) :sort (2 4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 5) list:firstRest (2 (7 4 5))}] - skolem:lemma5527 - skolem:lemma4395 - skolem:lemma5528 - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - [ a r:Fact; r:gives {(() (2 4 5 7)) list:append (2 4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3888 a r:Inference; +skolem:lemma3164 a r:Inference; r:gives { 2746 :numberToDigits (2 7 4 6). }; @@ -95174,32 +74021,9 @@ skolem:lemma3888 a r:Inference; 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:lemma4392. - -skolem:lemma3889 a r:Inference; - r:gives { - (2 7 4 6) :sort (2 4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 6) list:firstRest (2 (7 4 6))}] - skolem:lemma5529 - skolem:lemma4395 - skolem:lemma5530 - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - [ a r:Fact; r:gives {(() (2 4 6 7)) list:append (2 4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3890 a r:Inference; +skolem:lemma3165 a r:Inference; r:gives { 2747 :numberToDigits (2 7 4 7). }; @@ -95218,32 +74042,9 @@ skolem:lemma3890 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3891 a r:Inference; - r:gives { - (2 7 4 7) :sort (2 4 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 7) list:firstRest (2 (7 4 7))}] - skolem:lemma5531 - skolem:lemma4395 - skolem:lemma5532 - [ a r:Fact; r:gives {(2 4 7 7) list:firstRest (2 (4 7 7))}] - [ a r:Fact; r:gives {(() (2 4 7 7)) list:append (2 4 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3892 a r:Inference; +skolem:lemma3166 a r:Inference; r:gives { 2748 :numberToDigits (2 7 4 8). }; @@ -95262,32 +74063,9 @@ skolem:lemma3892 a r:Inference; 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:lemma4392. - -skolem:lemma3893 a r:Inference; - r:gives { - (2 7 4 8) :sort (2 4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 8) list:firstRest (2 (7 4 8))}] - skolem:lemma5533 - skolem:lemma4395 - skolem:lemma5534 - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - [ a r:Fact; r:gives {(() (2 4 7 8)) list:append (2 4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3894 a r:Inference; +skolem:lemma3167 a r:Inference; r:gives { 2749 :numberToDigits (2 7 4 9). }; @@ -95306,32 +74084,9 @@ skolem:lemma3894 a r:Inference; 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:lemma4392. - -skolem:lemma3895 a r:Inference; - r:gives { - (2 7 4 9) :sort (2 4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4 9) list:firstRest (2 (7 4 9))}] - skolem:lemma5535 - skolem:lemma4395 - skolem:lemma5536 - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - [ a r:Fact; r:gives {(() (2 4 7 9)) list:append (2 4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 4 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_2"]; r:boundTo (7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3896 a r:Inference; +skolem:lemma3168 a r:Inference; r:gives { 2750 :numberToDigits (2 7 5 0). }; @@ -95350,32 +74105,9 @@ skolem:lemma3896 a r:Inference; 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:lemma4392. - -skolem:lemma3897 a r:Inference; - r:gives { - (2 7 5 0) :sort (0 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 0) list:firstRest (2 (7 5 0))}] - skolem:lemma5537 - skolem:lemma4506 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((0) (2 5 7)) list:append (0 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3898 a r:Inference; +skolem:lemma3169 a r:Inference; r:gives { 2751 :numberToDigits (2 7 5 1). }; @@ -95394,32 +74126,9 @@ skolem:lemma3898 a r:Inference; 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:lemma4392. - -skolem:lemma3899 a r:Inference; - r:gives { - (2 7 5 1) :sort (1 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 1) list:firstRest (2 (7 5 1))}] - skolem:lemma5538 - skolem:lemma4705 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((1) (2 5 7)) list:append (1 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 1)]; - 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 5)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3900 a r:Inference; +skolem:lemma3170 a r:Inference; r:gives { 2752 :numberToDigits (2 7 5 2). }; @@ -95438,32 +74147,9 @@ skolem:lemma3900 a r:Inference; 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:lemma4392. - -skolem:lemma3901 a r:Inference; - r:gives { - (2 7 5 2) :sort (2 2 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 2) list:firstRest (2 (7 5 2))}] - skolem:lemma5539 - skolem:lemma4833 - skolem:lemma4596 - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {((2) (2 5 7)) list:append (2 2 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 2)]; - 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 5)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3902 a r:Inference; +skolem:lemma3171 a r:Inference; r:gives { 2753 :numberToDigits (2 7 5 3). }; @@ -95482,32 +74168,9 @@ skolem:lemma3902 a r:Inference; 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:lemma4392. - -skolem:lemma3903 a r:Inference; - r:gives { - (2 7 5 3) :sort (2 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 3) list:firstRest (2 (7 5 3))}] - skolem:lemma5540 - skolem:lemma4395 - skolem:lemma5541 - [ a r:Fact; r:gives {(2 3 5 7) list:firstRest (2 (3 5 7))}] - [ a r:Fact; r:gives {(() (2 3 5 7)) list:append (2 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3904 a r:Inference; +skolem:lemma3172 a r:Inference; r:gives { 2754 :numberToDigits (2 7 5 4). }; @@ -95526,32 +74189,9 @@ skolem:lemma3904 a r:Inference; 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:lemma4392. - -skolem:lemma3905 a r:Inference; - r:gives { - (2 7 5 4) :sort (2 4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 4) list:firstRest (2 (7 5 4))}] - skolem:lemma5542 - skolem:lemma4395 - skolem:lemma5543 - [ a r:Fact; r:gives {(2 4 5 7) list:firstRest (2 (4 5 7))}] - [ a r:Fact; r:gives {(() (2 4 5 7)) list:append (2 4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3906 a r:Inference; +skolem:lemma3173 a r:Inference; r:gives { 2755 :numberToDigits (2 7 5 5). }; @@ -95570,32 +74210,9 @@ skolem:lemma3906 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3907 a r:Inference; - r:gives { - (2 7 5 5) :sort (2 5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 5) list:firstRest (2 (7 5 5))}] - skolem:lemma5544 - skolem:lemma4395 - skolem:lemma5545 - [ a r:Fact; r:gives {(2 5 5 7) list:firstRest (2 (5 5 7))}] - [ a r:Fact; r:gives {(() (2 5 5 7)) list:append (2 5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3908 a r:Inference; +skolem:lemma3174 a r:Inference; r:gives { 2756 :numberToDigits (2 7 5 6). }; @@ -95614,32 +74231,9 @@ skolem:lemma3908 a r:Inference; 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:lemma4392. - -skolem:lemma3909 a r:Inference; - r:gives { - (2 7 5 6) :sort (2 5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 6) list:firstRest (2 (7 5 6))}] - skolem:lemma5546 - skolem:lemma4395 - skolem:lemma5547 - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - [ a r:Fact; r:gives {(() (2 5 6 7)) list:append (2 5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3910 a r:Inference; +skolem:lemma3175 a r:Inference; r:gives { 2757 :numberToDigits (2 7 5 7). }; @@ -95658,32 +74252,30 @@ skolem:lemma3910 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3911 a r:Inference; +skolem:lemma3176 a r:Inference; r:gives { - (2 7 5 7) :sort (2 5 7 7). + 2758 :numberToDigits (2 7 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 7 5 7) list:firstRest (2 (7 5 7))}] - skolem:lemma5548 - skolem:lemma4395 - skolem:lemma5549 - [ a r:Fact; r:gives {(2 5 7 7) list:firstRest (2 (5 7 7))}] - [ a r:Fact; r:gives {(() (2 5 7 7)) list:append (2 5 7 7)}] + [ 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_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 7)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3912 a r:Inference; +skolem:lemma3177 a r:Inference; r:gives { 2759 :numberToDigits (2 7 5 9). }; @@ -95702,32 +74294,9 @@ skolem:lemma3912 a r:Inference; 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:lemma4392. - -skolem:lemma3913 a r:Inference; - r:gives { - (2 7 5 9) :sort (2 5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5 9) list:firstRest (2 (7 5 9))}] - skolem:lemma5550 - skolem:lemma4395 - skolem:lemma5551 - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - [ a r:Fact; r:gives {(() (2 5 7 9)) list:append (2 5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 5 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_2"]; r:boundTo (7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3914 a r:Inference; +skolem:lemma3178 a r:Inference; r:gives { 2760 :numberToDigits (2 7 6 0). }; @@ -95746,32 +74315,9 @@ skolem:lemma3914 a r:Inference; 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:lemma4392. - -skolem:lemma3915 a r:Inference; - r:gives { - (2 7 6 0) :sort (0 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 0) list:firstRest (2 (7 6 0))}] - skolem:lemma5552 - skolem:lemma4506 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((0) (2 6 7)) list:append (0 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3916 a r:Inference; +skolem:lemma3179 a r:Inference; r:gives { 2761 :numberToDigits (2 7 6 1). }; @@ -95790,32 +74336,9 @@ skolem:lemma3916 a r:Inference; 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:lemma4392. - -skolem:lemma3917 a r:Inference; - r:gives { - (2 7 6 1) :sort (1 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 1) list:firstRest (2 (7 6 1))}] - skolem:lemma5553 - skolem:lemma4705 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((1) (2 6 7)) list:append (1 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 1)]; - 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 6)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3918 a r:Inference; +skolem:lemma3180 a r:Inference; r:gives { 2762 :numberToDigits (2 7 6 2). }; @@ -95834,32 +74357,9 @@ skolem:lemma3918 a r:Inference; 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:lemma4392. - -skolem:lemma3919 a r:Inference; - r:gives { - (2 7 6 2) :sort (2 2 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 2) list:firstRest (2 (7 6 2))}] - skolem:lemma5554 - skolem:lemma4833 - skolem:lemma4598 - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {((2) (2 6 7)) list:append (2 2 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 2)]; - 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 6)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3920 a r:Inference; +skolem:lemma3181 a r:Inference; r:gives { 2763 :numberToDigits (2 7 6 3). }; @@ -95878,32 +74378,9 @@ skolem:lemma3920 a r:Inference; 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:lemma4392. - -skolem:lemma3921 a r:Inference; - r:gives { - (2 7 6 3) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 3) list:firstRest (2 (7 6 3))}] - skolem:lemma5555 - skolem:lemma4395 - skolem:lemma5556 - [ a r:Fact; r:gives {(2 3 6 7) list:firstRest (2 (3 6 7))}] - [ a r:Fact; r:gives {(() (2 3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3922 a r:Inference; +skolem:lemma3182 a r:Inference; r:gives { 2764 :numberToDigits (2 7 6 4). }; @@ -95922,32 +74399,9 @@ skolem:lemma3922 a r:Inference; 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:lemma4392. - -skolem:lemma3923 a r:Inference; - r:gives { - (2 7 6 4) :sort (2 4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 4) list:firstRest (2 (7 6 4))}] - skolem:lemma5557 - skolem:lemma4395 - skolem:lemma5558 - [ a r:Fact; r:gives {(2 4 6 7) list:firstRest (2 (4 6 7))}] - [ a r:Fact; r:gives {(() (2 4 6 7)) list:append (2 4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3924 a r:Inference; +skolem:lemma3183 a r:Inference; r:gives { 2765 :numberToDigits (2 7 6 5). }; @@ -95966,32 +74420,9 @@ skolem:lemma3924 a r:Inference; 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:lemma4392. - -skolem:lemma3925 a r:Inference; - r:gives { - (2 7 6 5) :sort (2 5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 5) list:firstRest (2 (7 6 5))}] - skolem:lemma5559 - skolem:lemma4395 - skolem:lemma5560 - [ a r:Fact; r:gives {(2 5 6 7) list:firstRest (2 (5 6 7))}] - [ a r:Fact; r:gives {(() (2 5 6 7)) list:append (2 5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3926 a r:Inference; +skolem:lemma3184 a r:Inference; r:gives { 2766 :numberToDigits (2 7 6 6). }; @@ -96010,32 +74441,9 @@ skolem:lemma3926 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3927 a r:Inference; - r:gives { - (2 7 6 6) :sort (2 6 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 6) list:firstRest (2 (7 6 6))}] - skolem:lemma5561 - skolem:lemma4395 - skolem:lemma5562 - [ a r:Fact; r:gives {(2 6 6 7) list:firstRest (2 (6 6 7))}] - [ a r:Fact; r:gives {(() (2 6 6 7)) list:append (2 6 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3928 a r:Inference; +skolem:lemma3185 a r:Inference; r:gives { 2767 :numberToDigits (2 7 6 7). }; @@ -96054,32 +74462,9 @@ skolem:lemma3928 a r:Inference; 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:lemma4392. - -skolem:lemma3929 a r:Inference; - r:gives { - (2 7 6 7) :sort (2 6 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 7) list:firstRest (2 (7 6 7))}] - skolem:lemma5563 - skolem:lemma4395 - skolem:lemma5564 - [ a r:Fact; r:gives {(2 6 7 7) list:firstRest (2 (6 7 7))}] - [ a r:Fact; r:gives {(() (2 6 7 7)) list:append (2 6 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3930 a r:Inference; +skolem:lemma3186 a r:Inference; r:gives { 2768 :numberToDigits (2 7 6 8). }; @@ -96098,32 +74483,9 @@ skolem:lemma3930 a r:Inference; 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:lemma4392. - -skolem:lemma3931 a r:Inference; - r:gives { - (2 7 6 8) :sort (2 6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 8) list:firstRest (2 (7 6 8))}] - skolem:lemma5565 - skolem:lemma4395 - skolem:lemma5566 - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - [ a r:Fact; r:gives {(() (2 6 7 8)) list:append (2 6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3932 a r:Inference; +skolem:lemma3187 a r:Inference; r:gives { 2769 :numberToDigits (2 7 6 9). }; @@ -96142,32 +74504,9 @@ skolem:lemma3932 a r:Inference; 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:lemma4392. - -skolem:lemma3933 a r:Inference; - r:gives { - (2 7 6 9) :sort (2 6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6 9) list:firstRest (2 (7 6 9))}] - skolem:lemma5567 - skolem:lemma4395 - skolem:lemma5568 - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - [ a r:Fact; r:gives {(() (2 6 7 9)) list:append (2 6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 6 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_2"]; r:boundTo (7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3934 a r:Inference; +skolem:lemma3188 a r:Inference; r:gives { 2770 :numberToDigits (2 7 7 0). }; @@ -96186,32 +74525,9 @@ skolem:lemma3934 a r:Inference; 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:lemma4392. - -skolem:lemma3935 a r:Inference; - r:gives { - (2 7 7 0) :sort (0 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 0) list:firstRest (2 (7 7 0))}] - skolem:lemma5569 - skolem:lemma4506 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((0) (2 7 7)) list:append (0 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 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 (7 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3936 a r:Inference; +skolem:lemma3189 a r:Inference; r:gives { 2771 :numberToDigits (2 7 7 1). }; @@ -96230,32 +74546,9 @@ skolem:lemma3936 a r:Inference; 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:lemma4392. - -skolem:lemma3937 a r:Inference; - r:gives { - (2 7 7 1) :sort (1 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 1) list:firstRest (2 (7 7 1))}] - skolem:lemma5570 - skolem:lemma4705 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((1) (2 7 7)) list:append (1 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 1)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3938 a r:Inference; +skolem:lemma3190 a r:Inference; r:gives { 2772 :numberToDigits (2 7 7 2). }; @@ -96274,32 +74567,9 @@ skolem:lemma3938 a r:Inference; 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:lemma4392. - -skolem:lemma3939 a r:Inference; - r:gives { - (2 7 7 2) :sort (2 2 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 2) list:firstRest (2 (7 7 2))}] - skolem:lemma5571 - skolem:lemma4833 - skolem:lemma4600 - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {((2) (2 7 7)) list:append (2 2 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 2)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3940 a r:Inference; +skolem:lemma3191 a r:Inference; r:gives { 2773 :numberToDigits (2 7 7 3). }; @@ -96318,32 +74588,9 @@ skolem:lemma3940 a r:Inference; 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:lemma4392. - -skolem:lemma3941 a r:Inference; - r:gives { - (2 7 7 3) :sort (2 3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 3) list:firstRest (2 (7 7 3))}] - skolem:lemma5572 - skolem:lemma4395 - skolem:lemma5573 - [ a r:Fact; r:gives {(2 3 7 7) list:firstRest (2 (3 7 7))}] - [ a r:Fact; r:gives {(() (2 3 7 7)) list:append (2 3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3942 a r:Inference; +skolem:lemma3192 a r:Inference; r:gives { 2774 :numberToDigits (2 7 7 4). }; @@ -96362,32 +74609,9 @@ skolem:lemma3942 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3943 a r:Inference; - r:gives { - (2 7 7 4) :sort (2 4 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 4) list:firstRest (2 (7 7 4))}] - skolem:lemma5574 - skolem:lemma4395 - skolem:lemma5575 - [ a r:Fact; r:gives {(2 4 7 7) list:firstRest (2 (4 7 7))}] - [ a r:Fact; r:gives {(() (2 4 7 7)) list:append (2 4 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma3944 a r:Inference; +skolem:lemma3193 a r:Inference; r:gives { 2775 :numberToDigits (2 7 7 5). }; @@ -96406,32 +74630,9 @@ skolem:lemma3944 a r:Inference; 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:lemma4392. - -skolem:lemma3945 a r:Inference; - r:gives { - (2 7 7 5) :sort (2 5 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 5) list:firstRest (2 (7 7 5))}] - skolem:lemma5576 - skolem:lemma4395 - skolem:lemma5577 - [ a r:Fact; r:gives {(2 5 7 7) list:firstRest (2 (5 7 7))}] - [ a r:Fact; r:gives {(() (2 5 7 7)) list:append (2 5 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3946 a r:Inference; +skolem:lemma3194 a r:Inference; r:gives { 2776 :numberToDigits (2 7 7 6). }; @@ -96450,32 +74651,9 @@ skolem:lemma3946 a r:Inference; 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:lemma4392. - -skolem:lemma3947 a r:Inference; - r:gives { - (2 7 7 6) :sort (2 6 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 6) list:firstRest (2 (7 7 6))}] - skolem:lemma5578 - skolem:lemma4395 - skolem:lemma5579 - [ a r:Fact; r:gives {(2 6 7 7) list:firstRest (2 (6 7 7))}] - [ a r:Fact; r:gives {(() (2 6 7 7)) list:append (2 6 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3948 a r:Inference; +skolem:lemma3195 a r:Inference; r:gives { 2777 :numberToDigits (2 7 7 7). }; @@ -96494,32 +74672,9 @@ skolem:lemma3948 a r:Inference; 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:lemma4392. - -skolem:lemma3949 a r:Inference; - r:gives { - (2 7 7 7) :sort (2 7 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 7) list:firstRest (2 (7 7 7))}] - skolem:lemma5580 - skolem:lemma4395 - skolem:lemma5581 - [ a r:Fact; r:gives {(2 7 7 7) list:firstRest (2 (7 7 7))}] - [ a r:Fact; r:gives {(() (2 7 7 7)) list:append (2 7 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 7)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3950 a r:Inference; +skolem:lemma3196 a r:Inference; r:gives { (2 7 7 7) :digitsToNumber 2777 . }; @@ -96537,9 +74692,9 @@ skolem:lemma3950 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3951 a r:Inference; +skolem:lemma3197 a r:Inference; r:gives { (7 7 7 2) :digitsToNumber 7772 . }; @@ -96557,9 +74712,9 @@ skolem:lemma3951 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3952 a r:Inference; +skolem:lemma3198 a r:Inference; r:gives { 2778 :numberToDigits (2 7 7 8). }; @@ -96578,32 +74733,9 @@ skolem:lemma3952 a r:Inference; 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:lemma4392. - -skolem:lemma3953 a r:Inference; - r:gives { - (2 7 7 8) :sort (2 7 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 8) list:firstRest (2 (7 7 8))}] - skolem:lemma5582 - skolem:lemma4395 - skolem:lemma5583 - [ a r:Fact; r:gives {(2 7 7 8) list:firstRest (2 (7 7 8))}] - [ a r:Fact; r:gives {(() (2 7 7 8)) list:append (2 7 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3954 a r:Inference; +skolem:lemma3199 a r:Inference; r:gives { (2 7 7 8) :digitsToNumber 2778 . }; @@ -96621,9 +74753,9 @@ skolem:lemma3954 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3955 a r:Inference; +skolem:lemma3200 a r:Inference; r:gives { (8 7 7 2) :digitsToNumber 8772 . }; @@ -96641,9 +74773,9 @@ skolem:lemma3955 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3956 a r:Inference; +skolem:lemma3201 a r:Inference; r:gives { 2779 :numberToDigits (2 7 7 9). }; @@ -96662,32 +74794,9 @@ skolem:lemma3956 a r:Inference; 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:lemma4392. - -skolem:lemma3957 a r:Inference; - r:gives { - (2 7 7 9) :sort (2 7 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7 9) list:firstRest (2 (7 7 9))}] - skolem:lemma5584 - skolem:lemma4395 - skolem:lemma5585 - [ a r:Fact; r:gives {(2 7 7 9) list:firstRest (2 (7 7 9))}] - [ a r:Fact; r:gives {(() (2 7 7 9)) list:append (2 7 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 7 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_2"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3958 a r:Inference; +skolem:lemma3202 a r:Inference; r:gives { (2 7 7 9) :digitsToNumber 2779 . }; @@ -96705,9 +74814,9 @@ skolem:lemma3958 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3959 a r:Inference; +skolem:lemma3203 a r:Inference; r:gives { (9 7 7 2) :digitsToNumber 9772 . }; @@ -96725,9 +74834,9 @@ skolem:lemma3959 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3960 a r:Inference; +skolem:lemma3204 a r:Inference; r:gives { 2780 :numberToDigits (2 7 8 0). }; @@ -96746,32 +74855,9 @@ skolem:lemma3960 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3961 a r:Inference; - r:gives { - (2 7 8 0) :sort (0 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 0) list:firstRest (2 (7 8 0))}] - skolem:lemma5586 - skolem:lemma4506 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((0) (2 7 8)) list:append (0 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 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 (7 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 (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma3962 a r:Inference; +skolem:lemma3205 a r:Inference; r:gives { 2781 :numberToDigits (2 7 8 1). }; @@ -96790,32 +74876,9 @@ skolem:lemma3962 a r:Inference; 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:lemma4392. - -skolem:lemma3963 a r:Inference; - r:gives { - (2 7 8 1) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 1) list:firstRest (2 (7 8 1))}] - skolem:lemma5587 - skolem:lemma4705 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((1) (2 7 8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 1)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3964 a r:Inference; +skolem:lemma3206 a r:Inference; r:gives { 2782 :numberToDigits (2 7 8 2). }; @@ -96834,32 +74897,9 @@ skolem:lemma3964 a r:Inference; 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:lemma4392. - -skolem:lemma3965 a r:Inference; - r:gives { - (2 7 8 2) :sort (2 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 2) list:firstRest (2 (7 8 2))}] - skolem:lemma5588 - skolem:lemma4833 - skolem:lemma4606 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((2) (2 7 8)) list:append (2 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 2)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3966 a r:Inference; +skolem:lemma3207 a r:Inference; r:gives { 2783 :numberToDigits (2 7 8 3). }; @@ -96878,32 +74918,9 @@ skolem:lemma3966 a r:Inference; 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:lemma4392. - -skolem:lemma3967 a r:Inference; - r:gives { - (2 7 8 3) :sort (2 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 3) list:firstRest (2 (7 8 3))}] - skolem:lemma5589 - skolem:lemma4395 - skolem:lemma5590 - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - [ a r:Fact; r:gives {(() (2 3 7 8)) list:append (2 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3968 a r:Inference; +skolem:lemma3208 a r:Inference; r:gives { 2784 :numberToDigits (2 7 8 4). }; @@ -96922,32 +74939,30 @@ skolem:lemma3968 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3969 a r:Inference; +skolem:lemma3209 a r:Inference; r:gives { - (2 7 8 4) :sort (2 4 7 8). + 2785 :numberToDigits (2 7 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2 7 8 4) list:firstRest (2 (7 8 4))}] - skolem:lemma5591 - skolem:lemma4395 - skolem:lemma5592 - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - [ a r:Fact; r:gives {(() (2 4 7 8)) list:append (2 4 7 8)}] + [ 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_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma3970 a r:Inference; +skolem:lemma3210 a r:Inference; r:gives { 2786 :numberToDigits (2 7 8 6). }; @@ -96966,32 +74981,9 @@ skolem:lemma3970 a r:Inference; 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:lemma4392. - -skolem:lemma3971 a r:Inference; - r:gives { - (2 7 8 6) :sort (2 6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 6) list:firstRest (2 (7 8 6))}] - skolem:lemma5593 - skolem:lemma4395 - skolem:lemma5594 - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - [ a r:Fact; r:gives {(() (2 6 7 8)) list:append (2 6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3972 a r:Inference; +skolem:lemma3211 a r:Inference; r:gives { 2787 :numberToDigits (2 7 8 7). }; @@ -97010,32 +75002,9 @@ skolem:lemma3972 a r:Inference; 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:lemma4392. - -skolem:lemma3973 a r:Inference; - r:gives { - (2 7 8 7) :sort (2 7 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 7) list:firstRest (2 (7 8 7))}] - skolem:lemma5595 - skolem:lemma4395 - skolem:lemma5596 - [ a r:Fact; r:gives {(2 7 7 8) list:firstRest (2 (7 7 8))}] - [ a r:Fact; r:gives {(() (2 7 7 8)) list:append (2 7 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3974 a r:Inference; +skolem:lemma3212 a r:Inference; r:gives { 2788 :numberToDigits (2 7 8 8). }; @@ -97054,32 +75023,9 @@ skolem:lemma3974 a r:Inference; 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:lemma4392. - -skolem:lemma3975 a r:Inference; - r:gives { - (2 7 8 8) :sort (2 7 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 8) list:firstRest (2 (7 8 8))}] - skolem:lemma5597 - skolem:lemma4395 - skolem:lemma5598 - [ a r:Fact; r:gives {(2 7 8 8) list:firstRest (2 (7 8 8))}] - [ a r:Fact; r:gives {(() (2 7 8 8)) list:append (2 7 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3976 a r:Inference; +skolem:lemma3213 a r:Inference; r:gives { (2 7 8 8) :digitsToNumber 2788 . }; @@ -97097,9 +75043,9 @@ skolem:lemma3976 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3977 a r:Inference; +skolem:lemma3214 a r:Inference; r:gives { (8 8 7 2) :digitsToNumber 8872 . }; @@ -97117,9 +75063,9 @@ skolem:lemma3977 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3978 a r:Inference; +skolem:lemma3215 a r:Inference; r:gives { 2789 :numberToDigits (2 7 8 9). }; @@ -97138,32 +75084,9 @@ skolem:lemma3978 a r:Inference; 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:lemma4392. - -skolem:lemma3979 a r:Inference; - r:gives { - (2 7 8 9) :sort (2 7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - skolem:lemma5599 - skolem:lemma4395 - skolem:lemma5600 - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - [ a r:Fact; r:gives {(() (2 7 8 9)) list:append (2 7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 8 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_2"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3980 a r:Inference; +skolem:lemma3216 a r:Inference; r:gives { (2 7 8 9) :digitsToNumber 2789 . }; @@ -97181,9 +75104,9 @@ skolem:lemma3980 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3981 a r:Inference; +skolem:lemma3217 a r:Inference; r:gives { (9 8 7 2) :digitsToNumber 9872 . }; @@ -97201,9 +75124,9 @@ skolem:lemma3981 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma3982 a r:Inference; +skolem:lemma3218 a r:Inference; r:gives { 2790 :numberToDigits (2 7 9 0). }; @@ -97222,32 +75145,9 @@ skolem:lemma3982 a r:Inference; 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:lemma4392. - -skolem:lemma3983 a r:Inference; - r:gives { - (2 7 9 0) :sort (0 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 0) list:firstRest (2 (7 9 0))}] - skolem:lemma5601 - skolem:lemma4506 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((0) (2 7 9)) list:append (0 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 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 (7 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 (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3984 a r:Inference; +skolem:lemma3219 a r:Inference; r:gives { 2791 :numberToDigits (2 7 9 1). }; @@ -97266,32 +75166,9 @@ skolem:lemma3984 a r:Inference; 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:lemma4392. - -skolem:lemma3985 a r:Inference; - r:gives { - (2 7 9 1) :sort (1 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 1) list:firstRest (2 (7 9 1))}] - skolem:lemma5602 - skolem:lemma4705 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((1) (2 7 9)) list:append (1 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3986 a r:Inference; +skolem:lemma3220 a r:Inference; r:gives { 2792 :numberToDigits (2 7 9 2). }; @@ -97310,32 +75187,9 @@ skolem:lemma3986 a r:Inference; 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:lemma4392. - -skolem:lemma3987 a r:Inference; - r:gives { - (2 7 9 2) :sort (2 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 2) list:firstRest (2 (7 9 2))}] - skolem:lemma5603 - skolem:lemma4833 - skolem:lemma4610 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((2) (2 7 9)) list:append (2 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3988 a r:Inference; +skolem:lemma3221 a r:Inference; r:gives { 2793 :numberToDigits (2 7 9 3). }; @@ -97354,32 +75208,9 @@ skolem:lemma3988 a r:Inference; 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:lemma4392. - -skolem:lemma3989 a r:Inference; - r:gives { - (2 7 9 3) :sort (2 3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 3) list:firstRest (2 (7 9 3))}] - skolem:lemma5604 - skolem:lemma4395 - skolem:lemma5605 - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - [ a r:Fact; r:gives {(() (2 3 7 9)) list:append (2 3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3990 a r:Inference; +skolem:lemma3222 a r:Inference; r:gives { 2794 :numberToDigits (2 7 9 4). }; @@ -97398,32 +75229,9 @@ skolem:lemma3990 a r:Inference; 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:lemma4392. - -skolem:lemma3991 a r:Inference; - r:gives { - (2 7 9 4) :sort (2 4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 4) list:firstRest (2 (7 9 4))}] - skolem:lemma5606 - skolem:lemma4395 - skolem:lemma5607 - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - [ a r:Fact; r:gives {(() (2 4 7 9)) list:append (2 4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3992 a r:Inference; +skolem:lemma3223 a r:Inference; r:gives { 2795 :numberToDigits (2 7 9 5). }; @@ -97442,32 +75250,9 @@ skolem:lemma3992 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3993 a r:Inference; - r:gives { - (2 7 9 5) :sort (2 5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 5) list:firstRest (2 (7 9 5))}] - skolem:lemma5608 - skolem:lemma4395 - skolem:lemma5609 - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - [ a r:Fact; r:gives {(() (2 5 7 9)) list:append (2 5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3994 a r:Inference; +skolem:lemma3224 a r:Inference; r:gives { 2796 :numberToDigits (2 7 9 6). }; @@ -97486,32 +75271,9 @@ skolem:lemma3994 a r:Inference; 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:lemma4392. - -skolem:lemma3995 a r:Inference; - r:gives { - (2 7 9 6) :sort (2 6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 6) list:firstRest (2 (7 9 6))}] - skolem:lemma5610 - skolem:lemma4395 - skolem:lemma5611 - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - [ a r:Fact; r:gives {(() (2 6 7 9)) list:append (2 6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma3996 a r:Inference; +skolem:lemma3225 a r:Inference; r:gives { 2797 :numberToDigits (2 7 9 7). }; @@ -97530,34 +75292,11 @@ skolem:lemma3996 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma3997 a r:Inference; +skolem:lemma3226 a r:Inference; r:gives { - (2 7 9 7) :sort (2 7 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 7) list:firstRest (2 (7 9 7))}] - skolem:lemma5612 - skolem:lemma4395 - skolem:lemma5613 - [ a r:Fact; r:gives {(2 7 7 9) list:firstRest (2 (7 7 9))}] - [ a r:Fact; r:gives {(() (2 7 7 9)) list:append (2 7 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma3998 a r:Inference; - r:gives { - 2798 :numberToDigits (2 7 9 8). + 2798 :numberToDigits (2 7 9 8). }; r:evidence ( [ a r:Fact; r:gives {(2798 1000) math:integerQuotient 2}] @@ -97574,32 +75313,9 @@ skolem:lemma3998 a r:Inference; 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:lemma4392. - -skolem:lemma3999 a r:Inference; - r:gives { - (2 7 9 8) :sort (2 7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 8) list:firstRest (2 (7 9 8))}] - skolem:lemma5614 - skolem:lemma4395 - skolem:lemma5615 - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - [ a r:Fact; r:gives {(() (2 7 8 9)) list:append (2 7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4000 a r:Inference; +skolem:lemma3227 a r:Inference; r:gives { 2799 :numberToDigits (2 7 9 9). }; @@ -97618,32 +75334,9 @@ skolem:lemma4000 a r:Inference; 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:lemma4392. - -skolem:lemma4001 a r:Inference; - r:gives { - (2 7 9 9) :sort (2 7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9 9) list:firstRest (2 (7 9 9))}] - skolem:lemma5616 - skolem:lemma4395 - skolem:lemma5617 - [ a r:Fact; r:gives {(2 7 9 9) list:firstRest (2 (7 9 9))}] - [ a r:Fact; r:gives {(() (2 7 9 9)) list:append (2 7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 9 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_2"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4002 a r:Inference; +skolem:lemma3228 a r:Inference; r:gives { (2 7 9 9) :digitsToNumber 2799 . }; @@ -97661,9 +75354,9 @@ skolem:lemma4002 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4003 a r:Inference; +skolem:lemma3229 a r:Inference; r:gives { (9 9 7 2) :digitsToNumber 9972 . }; @@ -97681,9 +75374,9 @@ skolem:lemma4003 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4004 a r:Inference; +skolem:lemma3230 a r:Inference; r:gives { 2800 :numberToDigits (2 8 0 0). }; @@ -97702,32 +75395,9 @@ skolem:lemma4004 a r:Inference; 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:lemma4392. - -skolem:lemma4005 a r:Inference; - r:gives { - (2 8 0 0) :sort (0 0 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 0) list:firstRest (2 (8 0 0))}] - skolem:lemma5618 - skolem:lemma4407 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 0) (2 8)) list:append (0 0 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4006 a r:Inference; +skolem:lemma3231 a r:Inference; r:gives { 2801 :numberToDigits (2 8 0 1). }; @@ -97746,32 +75416,9 @@ skolem:lemma4006 a r:Inference; 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:lemma4392. - -skolem:lemma4007 a r:Inference; - r:gives { - (2 8 0 1) :sort (0 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 1) list:firstRest (2 (8 0 1))}] - skolem:lemma5619 - skolem:lemma4442 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 1) (2 8)) list:append (0 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4008 a r:Inference; +skolem:lemma3232 a r:Inference; r:gives { 2802 :numberToDigits (2 8 0 2). }; @@ -97790,32 +75437,9 @@ skolem:lemma4008 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma4009 a r:Inference; - r:gives { - (2 8 0 2) :sort (0 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 2) list:firstRest (2 (8 0 2))}] - skolem:lemma5620 - skolem:lemma4479 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 2) (2 8)) list:append (0 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4010 a r:Inference; +skolem:lemma3233 a r:Inference; r:gives { 2803 :numberToDigits (2 8 0 3). }; @@ -97834,32 +75458,9 @@ skolem:lemma4010 a r:Inference; 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:lemma4392. - -skolem:lemma4011 a r:Inference; - r:gives { - (2 8 0 3) :sort (0 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 3) list:firstRest (2 (8 0 3))}] - skolem:lemma5621 - skolem:lemma4506 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((0) (2 3 8)) list:append (0 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4012 a r:Inference; +skolem:lemma3234 a r:Inference; r:gives { 2804 :numberToDigits (2 8 0 4). }; @@ -97878,32 +75479,9 @@ skolem:lemma4012 a r:Inference; 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:lemma4392. - -skolem:lemma4013 a r:Inference; - r:gives { - (2 8 0 4) :sort (0 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 4) list:firstRest (2 (8 0 4))}] - skolem:lemma5622 - skolem:lemma4506 - skolem:lemma4621 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((0) (2 4 8)) list:append (0 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4014 a r:Inference; +skolem:lemma3235 a r:Inference; r:gives { 2805 :numberToDigits (2 8 0 5). }; @@ -97922,32 +75500,9 @@ skolem:lemma4014 a r:Inference; 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:lemma4392. - -skolem:lemma4015 a r:Inference; - r:gives { - (2 8 0 5) :sort (0 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 5) list:firstRest (2 (8 0 5))}] - skolem:lemma5623 - skolem:lemma4506 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((0) (2 5 8)) list:append (0 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4016 a r:Inference; +skolem:lemma3236 a r:Inference; r:gives { 2806 :numberToDigits (2 8 0 6). }; @@ -97966,32 +75521,9 @@ skolem:lemma4016 a r:Inference; 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:lemma4392. - -skolem:lemma4017 a r:Inference; - r:gives { - (2 8 0 6) :sort (0 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 6) list:firstRest (2 (8 0 6))}] - skolem:lemma5624 - skolem:lemma4506 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((0) (2 6 8)) list:append (0 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4018 a r:Inference; +skolem:lemma3237 a r:Inference; r:gives { 2807 :numberToDigits (2 8 0 7). }; @@ -98010,32 +75542,9 @@ skolem:lemma4018 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4019 a r:Inference; - r:gives { - (2 8 0 7) :sort (0 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 7) list:firstRest (2 (8 0 7))}] - skolem:lemma5625 - skolem:lemma4506 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((0) (2 7 8)) list:append (0 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4020 a r:Inference; +skolem:lemma3238 a r:Inference; r:gives { 2808 :numberToDigits (2 8 0 8). }; @@ -98054,32 +75563,9 @@ skolem:lemma4020 a r:Inference; 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:lemma4392. - -skolem:lemma4021 a r:Inference; - r:gives { - (2 8 0 8) :sort (0 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 8) list:firstRest (2 (8 0 8))}] - skolem:lemma5626 - skolem:lemma4506 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((0) (2 8 8)) list:append (0 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4022 a r:Inference; +skolem:lemma3239 a r:Inference; r:gives { 2809 :numberToDigits (2 8 0 9). }; @@ -98098,32 +75584,9 @@ skolem:lemma4022 a r:Inference; 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:lemma4392. - -skolem:lemma4023 a r:Inference; - r:gives { - (2 8 0 9) :sort (0 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0 9) list:firstRest (2 (8 0 9))}] - skolem:lemma5627 - skolem:lemma4506 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((0) (2 8 9)) list:append (0 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 0 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_2"]; r:boundTo (8 0 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 (8 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 (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4024 a r:Inference; +skolem:lemma3240 a r:Inference; r:gives { 2810 :numberToDigits (2 8 1 0). }; @@ -98142,32 +75605,9 @@ skolem:lemma4024 a r:Inference; 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:lemma4392. - -skolem:lemma4025 a r:Inference; - r:gives { - (2 8 1 0) :sort (0 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 0) list:firstRest (2 (8 1 0))}] - skolem:lemma5628 - skolem:lemma4660 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 1) (2 8)) list:append (0 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4026 a r:Inference; +skolem:lemma3241 a r:Inference; r:gives { 2811 :numberToDigits (2 8 1 1). }; @@ -98186,32 +75626,9 @@ skolem:lemma4026 a r:Inference; 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:lemma4392. - -skolem:lemma4027 a r:Inference; - r:gives { - (2 8 1 1) :sort (1 1 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 1) list:firstRest (2 (8 1 1))}] - skolem:lemma5629 - skolem:lemma4680 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 1) (2 8)) list:append (1 1 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4028 a r:Inference; +skolem:lemma3242 a r:Inference; r:gives { 2812 :numberToDigits (2 8 1 2). }; @@ -98230,32 +75647,9 @@ skolem:lemma4028 a r:Inference; 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:lemma4392. - -skolem:lemma4029 a r:Inference; - r:gives { - (2 8 1 2) :sort (1 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 2) list:firstRest (2 (8 1 2))}] - skolem:lemma5630 - skolem:lemma4694 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 2) (2 8)) list:append (1 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4030 a r:Inference; +skolem:lemma3243 a r:Inference; r:gives { 2813 :numberToDigits (2 8 1 3). }; @@ -98274,32 +75668,9 @@ skolem:lemma4030 a r:Inference; 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:lemma4392. - -skolem:lemma4031 a r:Inference; - r:gives { - (2 8 1 3) :sort (1 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 3) list:firstRest (2 (8 1 3))}] - skolem:lemma5631 - skolem:lemma4705 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((1) (2 3 8)) list:append (1 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 3)]; - 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 3)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4032 a r:Inference; +skolem:lemma3244 a r:Inference; r:gives { 2814 :numberToDigits (2 8 1 4). }; @@ -98318,32 +75689,9 @@ skolem:lemma4032 a r:Inference; 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:lemma4392. - -skolem:lemma4033 a r:Inference; - r:gives { - (2 8 1 4) :sort (1 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 4) list:firstRest (2 (8 1 4))}] - skolem:lemma5632 - skolem:lemma4705 - skolem:lemma4621 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((1) (2 4 8)) list:append (1 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 4)]; - 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 4)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4034 a r:Inference; +skolem:lemma3245 a r:Inference; r:gives { 2815 :numberToDigits (2 8 1 5). }; @@ -98362,32 +75710,9 @@ skolem:lemma4034 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4035 a r:Inference; - r:gives { - (2 8 1 5) :sort (1 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 5) list:firstRest (2 (8 1 5))}] - skolem:lemma5633 - skolem:lemma4705 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((1) (2 5 8)) list:append (1 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 5)]; - 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 5)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4036 a r:Inference; +skolem:lemma3246 a r:Inference; r:gives { 2816 :numberToDigits (2 8 1 6). }; @@ -98406,32 +75731,9 @@ skolem:lemma4036 a r:Inference; 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:lemma4392. - -skolem:lemma4037 a r:Inference; - r:gives { - (2 8 1 6) :sort (1 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 6) list:firstRest (2 (8 1 6))}] - skolem:lemma5634 - skolem:lemma4705 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((1) (2 6 8)) list:append (1 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 6)]; - 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 6)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4038 a r:Inference; +skolem:lemma3247 a r:Inference; r:gives { 2817 :numberToDigits (2 8 1 7). }; @@ -98450,32 +75752,9 @@ skolem:lemma4038 a r:Inference; 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:lemma4392. - -skolem:lemma4039 a r:Inference; - r:gives { - (2 8 1 7) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 7) list:firstRest (2 (8 1 7))}] - skolem:lemma5635 - skolem:lemma4705 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((1) (2 7 8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 7)]; - 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 7)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4040 a r:Inference; +skolem:lemma3248 a r:Inference; r:gives { 2818 :numberToDigits (2 8 1 8). }; @@ -98494,32 +75773,9 @@ skolem:lemma4040 a r:Inference; 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:lemma4392. - -skolem:lemma4041 a r:Inference; - r:gives { - (2 8 1 8) :sort (1 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 8) list:firstRest (2 (8 1 8))}] - skolem:lemma5636 - skolem:lemma4705 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((1) (2 8 8)) list:append (1 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4042 a r:Inference; +skolem:lemma3249 a r:Inference; r:gives { 2819 :numberToDigits (2 8 1 9). }; @@ -98538,32 +75794,9 @@ skolem:lemma4042 a r:Inference; 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:lemma4392. - -skolem:lemma4043 a r:Inference; - r:gives { - (2 8 1 9) :sort (1 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1 9) list:firstRest (2 (8 1 9))}] - skolem:lemma5637 - skolem:lemma4705 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((1) (2 8 9)) list:append (1 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 1 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_2"]; r:boundTo (8 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4044 a r:Inference; +skolem:lemma3250 a r:Inference; r:gives { 2820 :numberToDigits (2 8 2 0). }; @@ -98582,32 +75815,9 @@ skolem:lemma4044 a r:Inference; 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:lemma4392. - -skolem:lemma4045 a r:Inference; - r:gives { - (2 8 2 0) :sort (0 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 0) list:firstRest (2 (8 2 0))}] - skolem:lemma5638 - skolem:lemma4793 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((0 2) (2 8)) list:append (0 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4046 a r:Inference; +skolem:lemma3251 a r:Inference; r:gives { 2821 :numberToDigits (2 8 2 1). }; @@ -98626,32 +75836,9 @@ skolem:lemma4046 a r:Inference; 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:lemma4392. - -skolem:lemma4047 a r:Inference; - r:gives { - (2 8 2 1) :sort (1 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 1) list:firstRest (2 (8 2 1))}] - skolem:lemma5639 - skolem:lemma4807 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((1 2) (2 8)) list:append (1 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4048 a r:Inference; +skolem:lemma3252 a r:Inference; r:gives { 2822 :numberToDigits (2 8 2 2). }; @@ -98670,32 +75857,9 @@ skolem:lemma4048 a r:Inference; 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:lemma4392. - -skolem:lemma4049 a r:Inference; - r:gives { - (2 8 2 2) :sort (2 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 2) list:firstRest (2 (8 2 2))}] - skolem:lemma5640 - skolem:lemma4822 - skolem:lemma4426 - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {((2 2) (2 8)) list:append (2 2 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4050 a r:Inference; +skolem:lemma3253 a r:Inference; r:gives { 2823 :numberToDigits (2 8 2 3). }; @@ -98714,32 +75878,30 @@ skolem:lemma4050 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4051 a r:Inference; +skolem:lemma3254 a r:Inference; r:gives { - (2 8 2 3) :sort (2 2 3 8). + 2824 :numberToDigits (2 8 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 2 3) list:firstRest (2 (8 2 3))}] - skolem:lemma5641 - skolem:lemma4833 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((2) (2 3 8)) list:append (2 2 3 8)}] + [ 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_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 3)]; - 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 3)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4052 a r:Inference; +skolem:lemma3255 a r:Inference; r:gives { 2825 :numberToDigits (2 8 2 5). }; @@ -98758,32 +75920,9 @@ skolem:lemma4052 a r:Inference; 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:lemma4392. - -skolem:lemma4053 a r:Inference; - r:gives { - (2 8 2 5) :sort (2 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 5) list:firstRest (2 (8 2 5))}] - skolem:lemma5642 - skolem:lemma4833 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((2) (2 5 8)) list:append (2 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 5)]; - 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 5)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4054 a r:Inference; +skolem:lemma3256 a r:Inference; r:gives { 2826 :numberToDigits (2 8 2 6). }; @@ -98802,32 +75941,9 @@ skolem:lemma4054 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4055 a r:Inference; - r:gives { - (2 8 2 6) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 6) list:firstRest (2 (8 2 6))}] - skolem:lemma5643 - skolem:lemma4833 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((2) (2 6 8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 6)]; - 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 6)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4056 a r:Inference; +skolem:lemma3257 a r:Inference; r:gives { 2827 :numberToDigits (2 8 2 7). }; @@ -98846,32 +75962,9 @@ skolem:lemma4056 a r:Inference; 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:lemma4392. - -skolem:lemma4057 a r:Inference; - r:gives { - (2 8 2 7) :sort (2 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 7) list:firstRest (2 (8 2 7))}] - skolem:lemma5644 - skolem:lemma4833 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((2) (2 7 8)) list:append (2 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 7)]; - 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 7)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4058 a r:Inference; +skolem:lemma3258 a r:Inference; r:gives { 2828 :numberToDigits (2 8 2 8). }; @@ -98890,32 +75983,9 @@ skolem:lemma4058 a r:Inference; 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:lemma4392. - -skolem:lemma4059 a r:Inference; - r:gives { - (2 8 2 8) :sort (2 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 8) list:firstRest (2 (8 2 8))}] - skolem:lemma5645 - skolem:lemma4833 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((2) (2 8 8)) list:append (2 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 8)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4060 a r:Inference; +skolem:lemma3259 a r:Inference; r:gives { 2829 :numberToDigits (2 8 2 9). }; @@ -98934,32 +76004,9 @@ skolem:lemma4060 a r:Inference; 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:lemma4392. - -skolem:lemma4061 a r:Inference; - r:gives { - (2 8 2 9) :sort (2 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2 9) list:firstRest (2 (8 2 9))}] - skolem:lemma5646 - skolem:lemma4833 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((2) (2 8 9)) list:append (2 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 2 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_2"]; r:boundTo (8 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4062 a r:Inference; +skolem:lemma3260 a r:Inference; r:gives { 2830 :numberToDigits (2 8 3 0). }; @@ -98978,32 +76025,9 @@ skolem:lemma4062 a r:Inference; 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:lemma4392. - -skolem:lemma4063 a r:Inference; - r:gives { - (2 8 3 0) :sort (0 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 0) list:firstRest (2 (8 3 0))}] - skolem:lemma5647 - skolem:lemma4506 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((0) (2 3 8)) list:append (0 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4064 a r:Inference; +skolem:lemma3261 a r:Inference; r:gives { 2831 :numberToDigits (2 8 3 1). }; @@ -99022,32 +76046,9 @@ skolem:lemma4064 a r:Inference; 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:lemma4392. - -skolem:lemma4065 a r:Inference; - r:gives { - (2 8 3 1) :sort (1 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 1) list:firstRest (2 (8 3 1))}] - skolem:lemma5648 - skolem:lemma4705 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((1) (2 3 8)) list:append (1 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 1)]; - 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 3)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4066 a r:Inference; +skolem:lemma3262 a r:Inference; r:gives { 2832 :numberToDigits (2 8 3 2). }; @@ -99066,32 +76067,9 @@ skolem:lemma4066 a r:Inference; 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:lemma4392. - -skolem:lemma4067 a r:Inference; - r:gives { - (2 8 3 2) :sort (2 2 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 2) list:firstRest (2 (8 3 2))}] - skolem:lemma5649 - skolem:lemma4833 - skolem:lemma4619 - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {((2) (2 3 8)) list:append (2 2 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 2)]; - 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 3)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4068 a r:Inference; +skolem:lemma3263 a r:Inference; r:gives { 2833 :numberToDigits (2 8 3 3). }; @@ -99110,32 +76088,9 @@ skolem:lemma4068 a r:Inference; 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:lemma4392. - -skolem:lemma4069 a r:Inference; - r:gives { - (2 8 3 3) :sort (2 3 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 3) list:firstRest (2 (8 3 3))}] - skolem:lemma5650 - skolem:lemma4395 - skolem:lemma5651 - [ a r:Fact; r:gives {(2 3 3 8) list:firstRest (2 (3 3 8))}] - [ a r:Fact; r:gives {(() (2 3 3 8)) list:append (2 3 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4070 a r:Inference; +skolem:lemma3264 a r:Inference; r:gives { 2834 :numberToDigits (2 8 3 4). }; @@ -99154,32 +76109,30 @@ skolem:lemma4070 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4071 a r:Inference; +skolem:lemma3265 a r:Inference; r:gives { - (2 8 3 4) :sort (2 3 4 8). + 2835 :numberToDigits (2 8 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 3 4) list:firstRest (2 (8 3 4))}] - skolem:lemma5652 - skolem:lemma4395 - skolem:lemma5653 - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - [ a r:Fact; r:gives {(() (2 3 4 8)) list:append (2 3 4 8)}] + [ 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_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4072 a r:Inference; +skolem:lemma3266 a r:Inference; r:gives { 2836 :numberToDigits (2 8 3 6). }; @@ -99198,32 +76151,9 @@ skolem:lemma4072 a r:Inference; 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:lemma4392. - -skolem:lemma4073 a r:Inference; - r:gives { - (2 8 3 6) :sort (2 3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 6) list:firstRest (2 (8 3 6))}] - skolem:lemma5654 - skolem:lemma4395 - skolem:lemma5655 - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - [ a r:Fact; r:gives {(() (2 3 6 8)) list:append (2 3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4074 a r:Inference; +skolem:lemma3267 a r:Inference; r:gives { 2837 :numberToDigits (2 8 3 7). }; @@ -99242,32 +76172,9 @@ skolem:lemma4074 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4075 a r:Inference; - r:gives { - (2 8 3 7) :sort (2 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 7) list:firstRest (2 (8 3 7))}] - skolem:lemma5656 - skolem:lemma4395 - skolem:lemma5657 - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - [ a r:Fact; r:gives {(() (2 3 7 8)) list:append (2 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4076 a r:Inference; +skolem:lemma3268 a r:Inference; r:gives { 2838 :numberToDigits (2 8 3 8). }; @@ -99286,32 +76193,9 @@ skolem:lemma4076 a r:Inference; 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:lemma4392. - -skolem:lemma4077 a r:Inference; - r:gives { - (2 8 3 8) :sort (2 3 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 8) list:firstRest (2 (8 3 8))}] - skolem:lemma5658 - skolem:lemma4395 - skolem:lemma5659 - [ a r:Fact; r:gives {(2 3 8 8) list:firstRest (2 (3 8 8))}] - [ a r:Fact; r:gives {(() (2 3 8 8)) list:append (2 3 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4078 a r:Inference; +skolem:lemma3269 a r:Inference; r:gives { 2839 :numberToDigits (2 8 3 9). }; @@ -99330,32 +76214,9 @@ skolem:lemma4078 a r:Inference; 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:lemma4392. - -skolem:lemma4079 a r:Inference; - r:gives { - (2 8 3 9) :sort (2 3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3 9) list:firstRest (2 (8 3 9))}] - skolem:lemma5660 - skolem:lemma4395 - skolem:lemma5661 - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - [ a r:Fact; r:gives {(() (2 3 8 9)) list:append (2 3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 3 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_2"]; r:boundTo (8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4080 a r:Inference; +skolem:lemma3270 a r:Inference; r:gives { 2840 :numberToDigits (2 8 4 0). }; @@ -99374,32 +76235,9 @@ skolem:lemma4080 a r:Inference; 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:lemma4392. - -skolem:lemma4081 a r:Inference; - r:gives { - (2 8 4 0) :sort (0 2 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 4 0) list:firstRest (2 (8 4 0))}] - skolem:lemma5662 - skolem:lemma4506 - skolem:lemma4621 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((0) (2 4 8)) list:append (0 2 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4082 a r:Inference; +skolem:lemma3271 a r:Inference; r:gives { 2841 :numberToDigits (2 8 4 1). }; @@ -99418,32 +76256,30 @@ skolem:lemma4082 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4083 a r:Inference; +skolem:lemma3272 a r:Inference; r:gives { - (2 8 4 1) :sort (1 2 4 8). + 2842 :numberToDigits (2 8 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 4 1) list:firstRest (2 (8 4 1))}] - skolem:lemma5663 - skolem:lemma4705 - skolem:lemma4621 - [ a r:Fact; r:gives {(2 4 8) list:firstRest (2 (4 8))}] - [ a r:Fact; r:gives {((1) (2 4 8)) list:append (1 2 4 8)}] + [ 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_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 1)]; - 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 4)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4084 a r:Inference; +skolem:lemma3273 a r:Inference; r:gives { 2843 :numberToDigits (2 8 4 3). }; @@ -99462,32 +76298,9 @@ skolem:lemma4084 a r:Inference; 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:lemma4392. - -skolem:lemma4085 a r:Inference; - r:gives { - (2 8 4 3) :sort (2 3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 4 3) list:firstRest (2 (8 4 3))}] - skolem:lemma5664 - skolem:lemma4395 - skolem:lemma5665 - [ a r:Fact; r:gives {(2 3 4 8) list:firstRest (2 (3 4 8))}] - [ a r:Fact; r:gives {(() (2 3 4 8)) list:append (2 3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4086 a r:Inference; +skolem:lemma3274 a r:Inference; r:gives { 2844 :numberToDigits (2 8 4 4). }; @@ -99506,32 +76319,9 @@ skolem:lemma4086 a r:Inference; 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:lemma4392. - -skolem:lemma4087 a r:Inference; - r:gives { - (2 8 4 4) :sort (2 4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 4 4) list:firstRest (2 (8 4 4))}] - skolem:lemma5666 - skolem:lemma4395 - skolem:lemma5667 - [ a r:Fact; r:gives {(2 4 4 8) list:firstRest (2 (4 4 8))}] - [ a r:Fact; r:gives {(() (2 4 4 8)) list:append (2 4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4088 a r:Inference; +skolem:lemma3275 a r:Inference; r:gives { 2845 :numberToDigits (2 8 4 5). }; @@ -99550,32 +76340,30 @@ skolem:lemma4088 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4089 a r:Inference; +skolem:lemma3276 a r:Inference; r:gives { - (2 8 4 5) :sort (2 4 5 8). + 2846 :numberToDigits (2 8 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 4 5) list:firstRest (2 (8 4 5))}] - skolem:lemma5668 - skolem:lemma4395 - skolem:lemma5669 - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - [ a r:Fact; r:gives {(() (2 4 5 8)) list:append (2 4 5 8)}] + [ 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_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4090 a r:Inference; +skolem:lemma3277 a r:Inference; r:gives { 2847 :numberToDigits (2 8 4 7). }; @@ -99594,32 +76382,9 @@ skolem:lemma4090 a r:Inference; 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:lemma4392. - -skolem:lemma4091 a r:Inference; - r:gives { - (2 8 4 7) :sort (2 4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 4 7) list:firstRest (2 (8 4 7))}] - skolem:lemma5670 - skolem:lemma4395 - skolem:lemma5671 - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - [ a r:Fact; r:gives {(() (2 4 7 8)) list:append (2 4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4092 a r:Inference; +skolem:lemma3278 a r:Inference; r:gives { 2848 :numberToDigits (2 8 4 8). }; @@ -99638,32 +76403,9 @@ skolem:lemma4092 a r:Inference; 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:lemma4392. - -skolem:lemma4093 a r:Inference; - r:gives { - (2 8 4 8) :sort (2 4 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 4 8) list:firstRest (2 (8 4 8))}] - skolem:lemma5672 - skolem:lemma4395 - skolem:lemma5673 - [ a r:Fact; r:gives {(2 4 8 8) list:firstRest (2 (4 8 8))}] - [ a r:Fact; r:gives {(() (2 4 8 8)) list:append (2 4 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4094 a r:Inference; +skolem:lemma3279 a r:Inference; r:gives { 2849 :numberToDigits (2 8 4 9). }; @@ -99682,32 +76424,9 @@ skolem:lemma4094 a r:Inference; 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:lemma4392. - -skolem:lemma4095 a r:Inference; - r:gives { - (2 8 4 9) :sort (2 4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 4 9) list:firstRest (2 (8 4 9))}] - skolem:lemma5674 - skolem:lemma4395 - skolem:lemma5675 - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - [ a r:Fact; r:gives {(() (2 4 8 9)) list:append (2 4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 4 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_2"]; r:boundTo (8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4096 a r:Inference; +skolem:lemma3280 a r:Inference; r:gives { 2850 :numberToDigits (2 8 5 0). }; @@ -99726,32 +76445,9 @@ skolem:lemma4096 a r:Inference; 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:lemma4392. - -skolem:lemma4097 a r:Inference; - r:gives { - (2 8 5 0) :sort (0 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5 0) list:firstRest (2 (8 5 0))}] - skolem:lemma5676 - skolem:lemma4506 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((0) (2 5 8)) list:append (0 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4098 a r:Inference; +skolem:lemma3281 a r:Inference; r:gives { 2851 :numberToDigits (2 8 5 1). }; @@ -99770,32 +76466,9 @@ skolem:lemma4098 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4099 a r:Inference; - r:gives { - (2 8 5 1) :sort (1 2 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5 1) list:firstRest (2 (8 5 1))}] - skolem:lemma5677 - skolem:lemma4705 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((1) (2 5 8)) list:append (1 2 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 1)]; - 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 5)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4100 a r:Inference; +skolem:lemma3282 a r:Inference; r:gives { 2852 :numberToDigits (2 8 5 2). }; @@ -99814,32 +76487,30 @@ skolem:lemma4100 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4101 a r:Inference; +skolem:lemma3283 a r:Inference; r:gives { - (2 8 5 2) :sort (2 2 5 8). + 2853 :numberToDigits (2 8 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 5 2) list:firstRest (2 (8 5 2))}] - skolem:lemma5678 - skolem:lemma4833 - skolem:lemma4623 - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {((2) (2 5 8)) list:append (2 2 5 8)}] + [ 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_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 2)]; - 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 5)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4102 a r:Inference; +skolem:lemma3284 a r:Inference; r:gives { 2854 :numberToDigits (2 8 5 4). }; @@ -99858,32 +76529,9 @@ skolem:lemma4102 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4103 a r:Inference; - r:gives { - (2 8 5 4) :sort (2 4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5 4) list:firstRest (2 (8 5 4))}] - skolem:lemma5679 - skolem:lemma4395 - skolem:lemma5680 - [ a r:Fact; r:gives {(2 4 5 8) list:firstRest (2 (4 5 8))}] - [ a r:Fact; r:gives {(() (2 4 5 8)) list:append (2 4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4104 a r:Inference; +skolem:lemma3285 a r:Inference; r:gives { 2855 :numberToDigits (2 8 5 5). }; @@ -99902,32 +76550,9 @@ skolem:lemma4104 a r:Inference; 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:lemma4392. - -skolem:lemma4105 a r:Inference; - r:gives { - (2 8 5 5) :sort (2 5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5 5) list:firstRest (2 (8 5 5))}] - skolem:lemma5681 - skolem:lemma4395 - skolem:lemma5682 - [ a r:Fact; r:gives {(2 5 5 8) list:firstRest (2 (5 5 8))}] - [ a r:Fact; r:gives {(() (2 5 5 8)) list:append (2 5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4106 a r:Inference; +skolem:lemma3286 a r:Inference; r:gives { 2856 :numberToDigits (2 8 5 6). }; @@ -99946,32 +76571,30 @@ skolem:lemma4106 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4107 a r:Inference; +skolem:lemma3287 a r:Inference; r:gives { - (2 8 5 6) :sort (2 5 6 8). + 2857 :numberToDigits (2 8 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 5 6) list:firstRest (2 (8 5 6))}] - skolem:lemma5683 - skolem:lemma4395 - skolem:lemma5684 - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - [ a r:Fact; r:gives {(() (2 5 6 8)) list:append (2 5 6 8)}] + [ 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_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4108 a r:Inference; +skolem:lemma3288 a r:Inference; r:gives { 2858 :numberToDigits (2 8 5 8). }; @@ -99990,32 +76613,9 @@ skolem:lemma4108 a r:Inference; 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:lemma4392. - -skolem:lemma4109 a r:Inference; - r:gives { - (2 8 5 8) :sort (2 5 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5 8) list:firstRest (2 (8 5 8))}] - skolem:lemma5685 - skolem:lemma4395 - skolem:lemma5686 - [ a r:Fact; r:gives {(2 5 8 8) list:firstRest (2 (5 8 8))}] - [ a r:Fact; r:gives {(() (2 5 8 8)) list:append (2 5 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4110 a r:Inference; +skolem:lemma3289 a r:Inference; r:gives { 2859 :numberToDigits (2 8 5 9). }; @@ -100034,32 +76634,9 @@ skolem:lemma4110 a r:Inference; 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:lemma4392. - -skolem:lemma4111 a r:Inference; - r:gives { - (2 8 5 9) :sort (2 5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5 9) list:firstRest (2 (8 5 9))}] - skolem:lemma5687 - skolem:lemma4395 - skolem:lemma5688 - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - [ a r:Fact; r:gives {(() (2 5 8 9)) list:append (2 5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 5 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_2"]; r:boundTo (8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4112 a r:Inference; +skolem:lemma3290 a r:Inference; r:gives { 2860 :numberToDigits (2 8 6 0). }; @@ -100078,32 +76655,9 @@ skolem:lemma4112 a r:Inference; 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:lemma4392. - -skolem:lemma4113 a r:Inference; - r:gives { - (2 8 6 0) :sort (0 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6 0) list:firstRest (2 (8 6 0))}] - skolem:lemma5689 - skolem:lemma4506 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((0) (2 6 8)) list:append (0 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4114 a r:Inference; +skolem:lemma3291 a r:Inference; r:gives { 2861 :numberToDigits (2 8 6 1). }; @@ -100122,32 +76676,9 @@ skolem:lemma4114 a r:Inference; 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:lemma4392. - -skolem:lemma4115 a r:Inference; - r:gives { - (2 8 6 1) :sort (1 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6 1) list:firstRest (2 (8 6 1))}] - skolem:lemma5690 - skolem:lemma4705 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((1) (2 6 8)) list:append (1 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 1)]; - 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 6)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4116 a r:Inference; +skolem:lemma3292 a r:Inference; r:gives { 2862 :numberToDigits (2 8 6 2). }; @@ -100166,32 +76697,9 @@ skolem:lemma4116 a r:Inference; 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:lemma4392. - -skolem:lemma4117 a r:Inference; - r:gives { - (2 8 6 2) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6 2) list:firstRest (2 (8 6 2))}] - skolem:lemma5691 - skolem:lemma4833 - skolem:lemma4625 - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {((2) (2 6 8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 2)]; - 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 6)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4118 a r:Inference; +skolem:lemma3293 a r:Inference; r:gives { 2863 :numberToDigits (2 8 6 3). }; @@ -100210,32 +76718,30 @@ skolem:lemma4118 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4119 a r:Inference; +skolem:lemma3294 a r:Inference; r:gives { - (2 8 6 3) :sort (2 3 6 8). + 2864 :numberToDigits (2 8 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 6 3) list:firstRest (2 (8 6 3))}] - skolem:lemma5692 - skolem:lemma4395 - skolem:lemma5693 - [ a r:Fact; r:gives {(2 3 6 8) list:firstRest (2 (3 6 8))}] - [ a r:Fact; r:gives {(() (2 3 6 8)) list:append (2 3 6 8)}] + [ 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_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4120 a r:Inference; +skolem:lemma3295 a r:Inference; r:gives { 2865 :numberToDigits (2 8 6 5). }; @@ -100254,32 +76760,9 @@ skolem:lemma4120 a r:Inference; 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:lemma4392. - -skolem:lemma4121 a r:Inference; - r:gives { - (2 8 6 5) :sort (2 5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6 5) list:firstRest (2 (8 6 5))}] - skolem:lemma5694 - skolem:lemma4395 - skolem:lemma5695 - [ a r:Fact; r:gives {(2 5 6 8) list:firstRest (2 (5 6 8))}] - [ a r:Fact; r:gives {(() (2 5 6 8)) list:append (2 5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4122 a r:Inference; +skolem:lemma3296 a r:Inference; r:gives { 2866 :numberToDigits (2 8 6 6). }; @@ -100298,32 +76781,9 @@ skolem:lemma4122 a r:Inference; 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:lemma4392. - -skolem:lemma4123 a r:Inference; - r:gives { - (2 8 6 6) :sort (2 6 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6 6) list:firstRest (2 (8 6 6))}] - skolem:lemma5696 - skolem:lemma4395 - skolem:lemma5697 - [ a r:Fact; r:gives {(2 6 6 8) list:firstRest (2 (6 6 8))}] - [ a r:Fact; r:gives {(() (2 6 6 8)) list:append (2 6 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4124 a r:Inference; +skolem:lemma3297 a r:Inference; r:gives { 2867 :numberToDigits (2 8 6 7). }; @@ -100342,32 +76802,30 @@ skolem:lemma4124 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4125 a r:Inference; +skolem:lemma3298 a r:Inference; r:gives { - (2 8 6 7) :sort (2 6 7 8). + 2868 :numberToDigits (2 8 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 6 7) list:firstRest (2 (8 6 7))}] - skolem:lemma5698 - skolem:lemma4395 - skolem:lemma5699 - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - [ a r:Fact; r:gives {(() (2 6 7 8)) list:append (2 6 7 8)}] + [ 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_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4126 a r:Inference; +skolem:lemma3299 a r:Inference; r:gives { 2869 :numberToDigits (2 8 6 9). }; @@ -100386,32 +76844,9 @@ skolem:lemma4126 a r:Inference; 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:lemma4392. - -skolem:lemma4127 a r:Inference; - r:gives { - (2 8 6 9) :sort (2 6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6 9) list:firstRest (2 (8 6 9))}] - skolem:lemma5700 - skolem:lemma4395 - skolem:lemma5701 - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - [ a r:Fact; r:gives {(() (2 6 8 9)) list:append (2 6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 6 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_2"]; r:boundTo (8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4128 a r:Inference; +skolem:lemma3300 a r:Inference; r:gives { 2870 :numberToDigits (2 8 7 0). }; @@ -100430,32 +76865,9 @@ skolem:lemma4128 a r:Inference; 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:lemma4392. - -skolem:lemma4129 a r:Inference; - r:gives { - (2 8 7 0) :sort (0 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 0) list:firstRest (2 (8 7 0))}] - skolem:lemma5702 - skolem:lemma4506 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((0) (2 7 8)) list:append (0 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4130 a r:Inference; +skolem:lemma3301 a r:Inference; r:gives { 2871 :numberToDigits (2 8 7 1). }; @@ -100474,32 +76886,9 @@ skolem:lemma4130 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4131 a r:Inference; - r:gives { - (2 8 7 1) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 1) list:firstRest (2 (8 7 1))}] - skolem:lemma5703 - skolem:lemma4705 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((1) (2 7 8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 1)]; - 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 7)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4132 a r:Inference; +skolem:lemma3302 a r:Inference; r:gives { 2872 :numberToDigits (2 8 7 2). }; @@ -100518,32 +76907,9 @@ skolem:lemma4132 a r:Inference; 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:lemma4392. - -skolem:lemma4133 a r:Inference; - r:gives { - (2 8 7 2) :sort (2 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 2) list:firstRest (2 (8 7 2))}] - skolem:lemma5704 - skolem:lemma4833 - skolem:lemma4627 - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {((2) (2 7 8)) list:append (2 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 2)]; - 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 7)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4134 a r:Inference; +skolem:lemma3303 a r:Inference; r:gives { 2873 :numberToDigits (2 8 7 3). }; @@ -100562,32 +76928,9 @@ skolem:lemma4134 a r:Inference; 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:lemma4392. - -skolem:lemma4135 a r:Inference; - r:gives { - (2 8 7 3) :sort (2 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 3) list:firstRest (2 (8 7 3))}] - skolem:lemma5705 - skolem:lemma4395 - skolem:lemma5706 - [ a r:Fact; r:gives {(2 3 7 8) list:firstRest (2 (3 7 8))}] - [ a r:Fact; r:gives {(() (2 3 7 8)) list:append (2 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4136 a r:Inference; +skolem:lemma3304 a r:Inference; r:gives { 2874 :numberToDigits (2 8 7 4). }; @@ -100606,32 +76949,30 @@ skolem:lemma4136 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4137 a r:Inference; +skolem:lemma3305 a r:Inference; r:gives { - (2 8 7 4) :sort (2 4 7 8). + 2875 :numberToDigits (2 8 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 7 4) list:firstRest (2 (8 7 4))}] - skolem:lemma5707 - skolem:lemma4395 - skolem:lemma5708 - [ a r:Fact; r:gives {(2 4 7 8) list:firstRest (2 (4 7 8))}] - [ a r:Fact; r:gives {(() (2 4 7 8)) list:append (2 4 7 8)}] + [ 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_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4138 a r:Inference; +skolem:lemma3306 a r:Inference; r:gives { 2876 :numberToDigits (2 8 7 6). }; @@ -100650,34 +76991,11 @@ skolem:lemma4138 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4139 a r:Inference; +skolem:lemma3307 a r:Inference; r:gives { - (2 8 7 6) :sort (2 6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 6) list:firstRest (2 (8 7 6))}] - skolem:lemma5709 - skolem:lemma4395 - skolem:lemma5710 - [ a r:Fact; r:gives {(2 6 7 8) list:firstRest (2 (6 7 8))}] - [ a r:Fact; r:gives {(() (2 6 7 8)) list:append (2 6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4140 a r:Inference; - r:gives { - 2877 :numberToDigits (2 8 7 7). + 2877 :numberToDigits (2 8 7 7). }; r:evidence ( [ a r:Fact; r:gives {(2877 1000) math:integerQuotient 2}] @@ -100694,32 +77012,9 @@ skolem:lemma4140 a r:Inference; 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:lemma4392. - -skolem:lemma4141 a r:Inference; - r:gives { - (2 8 7 7) :sort (2 7 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 7) list:firstRest (2 (8 7 7))}] - skolem:lemma5711 - skolem:lemma4395 - skolem:lemma5712 - [ a r:Fact; r:gives {(2 7 7 8) list:firstRest (2 (7 7 8))}] - [ a r:Fact; r:gives {(() (2 7 7 8)) list:append (2 7 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4142 a r:Inference; +skolem:lemma3308 a r:Inference; r:gives { 2878 :numberToDigits (2 8 7 8). }; @@ -100738,32 +77033,9 @@ skolem:lemma4142 a r:Inference; 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:lemma4392. - -skolem:lemma4143 a r:Inference; - r:gives { - (2 8 7 8) :sort (2 7 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 8) list:firstRest (2 (8 7 8))}] - skolem:lemma5713 - skolem:lemma4395 - skolem:lemma5714 - [ a r:Fact; r:gives {(2 7 8 8) list:firstRest (2 (7 8 8))}] - [ a r:Fact; r:gives {(() (2 7 8 8)) list:append (2 7 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4144 a r:Inference; +skolem:lemma3309 a r:Inference; r:gives { 2879 :numberToDigits (2 8 7 9). }; @@ -100782,32 +77054,9 @@ skolem:lemma4144 a r:Inference; 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:lemma4392. - -skolem:lemma4145 a r:Inference; - r:gives { - (2 8 7 9) :sort (2 7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7 9) list:firstRest (2 (8 7 9))}] - skolem:lemma5715 - skolem:lemma4395 - skolem:lemma5716 - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - [ a r:Fact; r:gives {(() (2 7 8 9)) list:append (2 7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 7 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_2"]; r:boundTo (8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4146 a r:Inference; +skolem:lemma3310 a r:Inference; r:gives { 2880 :numberToDigits (2 8 8 0). }; @@ -100826,32 +77075,9 @@ skolem:lemma4146 a r:Inference; 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:lemma4392. - -skolem:lemma4147 a r:Inference; - r:gives { - (2 8 8 0) :sort (0 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 0) list:firstRest (2 (8 8 0))}] - skolem:lemma5717 - skolem:lemma4506 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((0) (2 8 8)) list:append (0 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4148 a r:Inference; +skolem:lemma3311 a r:Inference; r:gives { 2881 :numberToDigits (2 8 8 1). }; @@ -100870,32 +77096,9 @@ skolem:lemma4148 a r:Inference; 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:lemma4392. - -skolem:lemma4149 a r:Inference; - r:gives { - (2 8 8 1) :sort (1 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 1) list:firstRest (2 (8 8 1))}] - skolem:lemma5718 - skolem:lemma4705 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((1) (2 8 8)) list:append (1 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 1)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4150 a r:Inference; +skolem:lemma3312 a r:Inference; r:gives { 2882 :numberToDigits (2 8 8 2). }; @@ -100914,32 +77117,9 @@ skolem:lemma4150 a r:Inference; 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:lemma4392. - -skolem:lemma4151 a r:Inference; - r:gives { - (2 8 8 2) :sort (2 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 2) list:firstRest (2 (8 8 2))}] - skolem:lemma5719 - skolem:lemma4833 - skolem:lemma4629 - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {((2) (2 8 8)) list:append (2 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 2)]; - 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 8)]; - 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4152 a r:Inference; +skolem:lemma3313 a r:Inference; r:gives { 2883 :numberToDigits (2 8 8 3). }; @@ -100958,32 +77138,9 @@ skolem:lemma4152 a r:Inference; 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:lemma4392. - -skolem:lemma4153 a r:Inference; - r:gives { - (2 8 8 3) :sort (2 3 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 3) list:firstRest (2 (8 8 3))}] - skolem:lemma5720 - skolem:lemma4395 - skolem:lemma5721 - [ a r:Fact; r:gives {(2 3 8 8) list:firstRest (2 (3 8 8))}] - [ a r:Fact; r:gives {(() (2 3 8 8)) list:append (2 3 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4154 a r:Inference; +skolem:lemma3314 a r:Inference; r:gives { 2884 :numberToDigits (2 8 8 4). }; @@ -101002,32 +77159,9 @@ skolem:lemma4154 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4155 a r:Inference; - r:gives { - (2 8 8 4) :sort (2 4 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 4) list:firstRest (2 (8 8 4))}] - skolem:lemma5722 - skolem:lemma4395 - skolem:lemma5723 - [ a r:Fact; r:gives {(2 4 8 8) list:firstRest (2 (4 8 8))}] - [ a r:Fact; r:gives {(() (2 4 8 8)) list:append (2 4 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4156 a r:Inference; +skolem:lemma3315 a r:Inference; r:gives { 2885 :numberToDigits (2 8 8 5). }; @@ -101046,32 +77180,30 @@ skolem:lemma4156 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4157 a r:Inference; +skolem:lemma3316 a r:Inference; r:gives { - (2 8 8 5) :sort (2 5 8 8). + 2886 :numberToDigits (2 8 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2 8 8 5) list:firstRest (2 (8 8 5))}] - skolem:lemma5724 - skolem:lemma4395 - skolem:lemma5725 - [ a r:Fact; r:gives {(2 5 8 8) list:firstRest (2 (5 8 8))}] - [ a r:Fact; r:gives {(() (2 5 8 8)) list:append (2 5 8 8)}] + [ 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_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 8)]; - r:rule skolem:lemma4396. + 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:lemma3438. -skolem:lemma4158 a r:Inference; +skolem:lemma3317 a r:Inference; r:gives { 2887 :numberToDigits (2 8 8 7). }; @@ -101090,32 +77222,9 @@ skolem:lemma4158 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4159 a r:Inference; - r:gives { - (2 8 8 7) :sort (2 7 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 7) list:firstRest (2 (8 8 7))}] - skolem:lemma5726 - skolem:lemma4395 - skolem:lemma5727 - [ a r:Fact; r:gives {(2 7 8 8) list:firstRest (2 (7 8 8))}] - [ a r:Fact; r:gives {(() (2 7 8 8)) list:append (2 7 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4160 a r:Inference; +skolem:lemma3318 a r:Inference; r:gives { 2888 :numberToDigits (2 8 8 8). }; @@ -101134,32 +77243,9 @@ skolem:lemma4160 a r:Inference; 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:lemma4392. - -skolem:lemma4161 a r:Inference; - r:gives { - (2 8 8 8) :sort (2 8 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 8) list:firstRest (2 (8 8 8))}] - skolem:lemma5728 - skolem:lemma4395 - skolem:lemma5729 - [ a r:Fact; r:gives {(2 8 8 8) list:firstRest (2 (8 8 8))}] - [ a r:Fact; r:gives {(() (2 8 8 8)) list:append (2 8 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 8 8)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4162 a r:Inference; +skolem:lemma3319 a r:Inference; r:gives { (2 8 8 8) :digitsToNumber 2888 . }; @@ -101177,9 +77263,9 @@ skolem:lemma4162 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4163 a r:Inference; +skolem:lemma3320 a r:Inference; r:gives { (8 8 8 2) :digitsToNumber 8882 . }; @@ -101197,9 +77283,9 @@ skolem:lemma4163 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4164 a r:Inference; +skolem:lemma3321 a r:Inference; r:gives { 2889 :numberToDigits (2 8 8 9). }; @@ -101218,32 +77304,9 @@ skolem:lemma4164 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4165 a r:Inference; - r:gives { - (2 8 8 9) :sort (2 8 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8 9) list:firstRest (2 (8 8 9))}] - skolem:lemma5730 - skolem:lemma4395 - skolem:lemma5731 - [ a r:Fact; r:gives {(2 8 8 9) list:firstRest (2 (8 8 9))}] - [ a r:Fact; r:gives {(() (2 8 8 9)) list:append (2 8 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 8 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_2"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4166 a r:Inference; +skolem:lemma3322 a r:Inference; r:gives { (2 8 8 9) :digitsToNumber 2889 . }; @@ -101261,9 +77324,9 @@ skolem:lemma4166 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4167 a r:Inference; +skolem:lemma3323 a r:Inference; r:gives { (9 8 8 2) :digitsToNumber 9882 . }; @@ -101281,9 +77344,9 @@ skolem:lemma4167 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4168 a r:Inference; +skolem:lemma3324 a r:Inference; r:gives { 2890 :numberToDigits (2 8 9 0). }; @@ -101302,32 +77365,9 @@ skolem:lemma4168 a r:Inference; 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:lemma4392. - -skolem:lemma4169 a r:Inference; - r:gives { - (2 8 9 0) :sort (0 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 0) list:firstRest (2 (8 9 0))}] - skolem:lemma5732 - skolem:lemma4506 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((0) (2 8 9)) list:append (0 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 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 (8 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 (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4170 a r:Inference; +skolem:lemma3325 a r:Inference; r:gives { 2891 :numberToDigits (2 8 9 1). }; @@ -101346,32 +77386,9 @@ skolem:lemma4170 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4171 a r:Inference; - r:gives { - (2 8 9 1) :sort (1 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 1) list:firstRest (2 (8 9 1))}] - skolem:lemma5733 - skolem:lemma4705 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((1) (2 8 9)) list:append (1 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4172 a r:Inference; +skolem:lemma3326 a r:Inference; r:gives { 2892 :numberToDigits (2 8 9 2). }; @@ -101390,32 +77407,9 @@ skolem:lemma4172 a r:Inference; 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:lemma4392. - -skolem:lemma4173 a r:Inference; - r:gives { - (2 8 9 2) :sort (2 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 2) list:firstRest (2 (8 9 2))}] - skolem:lemma5734 - skolem:lemma4833 - skolem:lemma4631 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((2) (2 8 9)) list:append (2 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4174 a r:Inference; +skolem:lemma3327 a r:Inference; r:gives { 2893 :numberToDigits (2 8 9 3). }; @@ -101434,32 +77428,9 @@ skolem:lemma4174 a r:Inference; 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:lemma4392. - -skolem:lemma4175 a r:Inference; - r:gives { - (2 8 9 3) :sort (2 3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 3) list:firstRest (2 (8 9 3))}] - skolem:lemma5735 - skolem:lemma4395 - skolem:lemma5736 - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - [ a r:Fact; r:gives {(() (2 3 8 9)) list:append (2 3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4176 a r:Inference; +skolem:lemma3328 a r:Inference; r:gives { 2894 :numberToDigits (2 8 9 4). }; @@ -101478,32 +77449,9 @@ skolem:lemma4176 a r:Inference; 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:lemma4392. - -skolem:lemma4177 a r:Inference; - r:gives { - (2 8 9 4) :sort (2 4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 4) list:firstRest (2 (8 9 4))}] - skolem:lemma5737 - skolem:lemma4395 - skolem:lemma5738 - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - [ a r:Fact; r:gives {(() (2 4 8 9)) list:append (2 4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4178 a r:Inference; +skolem:lemma3329 a r:Inference; r:gives { 2895 :numberToDigits (2 8 9 5). }; @@ -101522,32 +77470,9 @@ skolem:lemma4178 a r:Inference; 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:lemma4392. - -skolem:lemma4179 a r:Inference; - r:gives { - (2 8 9 5) :sort (2 5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 5) list:firstRest (2 (8 9 5))}] - skolem:lemma5739 - skolem:lemma4395 - skolem:lemma5740 - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - [ a r:Fact; r:gives {(() (2 5 8 9)) list:append (2 5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4180 a r:Inference; +skolem:lemma3330 a r:Inference; r:gives { 2896 :numberToDigits (2 8 9 6). }; @@ -101566,32 +77491,9 @@ skolem:lemma4180 a r:Inference; 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:lemma4392. - -skolem:lemma4181 a r:Inference; - r:gives { - (2 8 9 6) :sort (2 6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 6) list:firstRest (2 (8 9 6))}] - skolem:lemma5741 - skolem:lemma4395 - skolem:lemma5742 - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - [ a r:Fact; r:gives {(() (2 6 8 9)) list:append (2 6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4182 a r:Inference; +skolem:lemma3331 a r:Inference; r:gives { 2897 :numberToDigits (2 8 9 7). }; @@ -101610,32 +77512,9 @@ skolem:lemma4182 a r:Inference; 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:lemma4392. - -skolem:lemma4183 a r:Inference; - r:gives { - (2 8 9 7) :sort (2 7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 7) list:firstRest (2 (8 9 7))}] - skolem:lemma5743 - skolem:lemma4395 - skolem:lemma5744 - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - [ a r:Fact; r:gives {(() (2 7 8 9)) list:append (2 7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4184 a r:Inference; +skolem:lemma3332 a r:Inference; r:gives { 2898 :numberToDigits (2 8 9 8). }; @@ -101654,32 +77533,9 @@ skolem:lemma4184 a r:Inference; 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:lemma4392. - -skolem:lemma4185 a r:Inference; - r:gives { - (2 8 9 8) :sort (2 8 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 8) list:firstRest (2 (8 9 8))}] - skolem:lemma5745 - skolem:lemma4395 - skolem:lemma5746 - [ a r:Fact; r:gives {(2 8 8 9) list:firstRest (2 (8 8 9))}] - [ a r:Fact; r:gives {(() (2 8 8 9)) list:append (2 8 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4186 a r:Inference; +skolem:lemma3333 a r:Inference; r:gives { 2899 :numberToDigits (2 8 9 9). }; @@ -101698,32 +77554,9 @@ skolem:lemma4186 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4187 a r:Inference; - r:gives { - (2 8 9 9) :sort (2 8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9 9) list:firstRest (2 (8 9 9))}] - skolem:lemma5747 - skolem:lemma4395 - skolem:lemma5748 - [ a r:Fact; r:gives {(2 8 9 9) list:firstRest (2 (8 9 9))}] - [ a r:Fact; r:gives {(() (2 8 9 9)) list:append (2 8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 9 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_2"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4188 a r:Inference; +skolem:lemma3334 a r:Inference; r:gives { (2 8 9 9) :digitsToNumber 2899 . }; @@ -101741,9 +77574,9 @@ skolem:lemma4188 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4189 a r:Inference; +skolem:lemma3335 a r:Inference; r:gives { (9 9 8 2) :digitsToNumber 9982 . }; @@ -101761,9 +77594,9 @@ skolem:lemma4189 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4190 a r:Inference; +skolem:lemma3336 a r:Inference; r:gives { 2900 :numberToDigits (2 9 0 0). }; @@ -101782,32 +77615,9 @@ skolem:lemma4190 a r:Inference; 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:lemma4392. - -skolem:lemma4191 a r:Inference; - r:gives { - (2 9 0 0) :sort (0 0 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 0) list:firstRest (2 (9 0 0))}] - skolem:lemma5749 - skolem:lemma4407 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 0) (2 9)) list:append (0 0 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4192 a r:Inference; +skolem:lemma3337 a r:Inference; r:gives { 2901 :numberToDigits (2 9 0 1). }; @@ -101826,32 +77636,9 @@ skolem:lemma4192 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4193 a r:Inference; - r:gives { - (2 9 0 1) :sort (0 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 1) list:firstRest (2 (9 0 1))}] - skolem:lemma5750 - skolem:lemma4442 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 1) (2 9)) list:append (0 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4194 a r:Inference; +skolem:lemma3338 a r:Inference; r:gives { 2902 :numberToDigits (2 9 0 2). }; @@ -101870,32 +77657,9 @@ skolem:lemma4194 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/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:lemma4392. - -skolem:lemma4195 a r:Inference; - r:gives { - (2 9 0 2) :sort (0 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 2) list:firstRest (2 (9 0 2))}] - skolem:lemma5751 - skolem:lemma4479 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 2) (2 9)) list:append (0 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4196 a r:Inference; +skolem:lemma3339 a r:Inference; r:gives { 2903 :numberToDigits (2 9 0 3). }; @@ -101914,32 +77678,9 @@ skolem:lemma4196 a r:Inference; 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:lemma4392. - -skolem:lemma4197 a r:Inference; - r:gives { - (2 9 0 3) :sort (0 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 3) list:firstRest (2 (9 0 3))}] - skolem:lemma5752 - skolem:lemma4506 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((0) (2 3 9)) list:append (0 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4198 a r:Inference; +skolem:lemma3340 a r:Inference; r:gives { 2904 :numberToDigits (2 9 0 4). }; @@ -101958,32 +77699,9 @@ skolem:lemma4198 a r:Inference; 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:lemma4392. - -skolem:lemma4199 a r:Inference; - r:gives { - (2 9 0 4) :sort (0 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 4) list:firstRest (2 (9 0 4))}] - skolem:lemma5753 - skolem:lemma4506 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((0) (2 4 9)) list:append (0 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4200 a r:Inference; +skolem:lemma3341 a r:Inference; r:gives { 2905 :numberToDigits (2 9 0 5). }; @@ -102002,32 +77720,9 @@ skolem:lemma4200 a r:Inference; 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:lemma4392. - -skolem:lemma4201 a r:Inference; - r:gives { - (2 9 0 5) :sort (0 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 5) list:firstRest (2 (9 0 5))}] - skolem:lemma5754 - skolem:lemma4506 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((0) (2 5 9)) list:append (0 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4202 a r:Inference; +skolem:lemma3342 a r:Inference; r:gives { 2906 :numberToDigits (2 9 0 6). }; @@ -102046,32 +77741,9 @@ skolem:lemma4202 a r:Inference; 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:lemma4392. - -skolem:lemma4203 a r:Inference; - r:gives { - (2 9 0 6) :sort (0 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 6) list:firstRest (2 (9 0 6))}] - skolem:lemma5755 - skolem:lemma4506 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((0) (2 6 9)) list:append (0 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4204 a r:Inference; +skolem:lemma3343 a r:Inference; r:gives { 2907 :numberToDigits (2 9 0 7). }; @@ -102090,32 +77762,9 @@ skolem:lemma4204 a r:Inference; 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:lemma4392. - -skolem:lemma4205 a r:Inference; - r:gives { - (2 9 0 7) :sort (0 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 7) list:firstRest (2 (9 0 7))}] - skolem:lemma5756 - skolem:lemma4506 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((0) (2 7 9)) list:append (0 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4206 a r:Inference; +skolem:lemma3344 a r:Inference; r:gives { 2908 :numberToDigits (2 9 0 8). }; @@ -102134,32 +77783,9 @@ skolem:lemma4206 a r:Inference; 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:lemma4392. - -skolem:lemma4207 a r:Inference; - r:gives { - (2 9 0 8) :sort (0 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 8) list:firstRest (2 (9 0 8))}] - skolem:lemma5757 - skolem:lemma4506 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((0) (2 8 9)) list:append (0 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4208 a r:Inference; +skolem:lemma3345 a r:Inference; r:gives { 2909 :numberToDigits (2 9 0 9). }; @@ -102178,32 +77804,9 @@ skolem:lemma4208 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4209 a r:Inference; - r:gives { - (2 9 0 9) :sort (0 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0 9) list:firstRest (2 (9 0 9))}] - skolem:lemma5758 - skolem:lemma4506 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((0) (2 9 9)) list:append (0 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 0 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_2"]; r:boundTo (9 0 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 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4210 a r:Inference; +skolem:lemma3346 a r:Inference; r:gives { 2910 :numberToDigits (2 9 1 0). }; @@ -102222,32 +77825,9 @@ skolem:lemma4210 a r:Inference; 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:lemma4392. - -skolem:lemma4211 a r:Inference; - r:gives { - (2 9 1 0) :sort (0 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 0) list:firstRest (2 (9 1 0))}] - skolem:lemma5759 - skolem:lemma4660 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 1) (2 9)) list:append (0 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4212 a r:Inference; +skolem:lemma3347 a r:Inference; r:gives { 2911 :numberToDigits (2 9 1 1). }; @@ -102266,32 +77846,9 @@ skolem:lemma4212 a r:Inference; 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:lemma4392. - -skolem:lemma4213 a r:Inference; - r:gives { - (2 9 1 1) :sort (1 1 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 1) list:firstRest (2 (9 1 1))}] - skolem:lemma5760 - skolem:lemma4680 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 1) (2 9)) list:append (1 1 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4214 a r:Inference; +skolem:lemma3348 a r:Inference; r:gives { 2912 :numberToDigits (2 9 1 2). }; @@ -102310,32 +77867,9 @@ skolem:lemma4214 a r:Inference; 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:lemma4392. - -skolem:lemma4215 a r:Inference; - r:gives { - (2 9 1 2) :sort (1 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 2) list:firstRest (2 (9 1 2))}] - skolem:lemma5761 - skolem:lemma4694 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 2) (2 9)) list:append (1 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4216 a r:Inference; +skolem:lemma3349 a r:Inference; r:gives { 2913 :numberToDigits (2 9 1 3). }; @@ -102354,32 +77888,9 @@ skolem:lemma4216 a r:Inference; 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:lemma4392. - -skolem:lemma4217 a r:Inference; - r:gives { - (2 9 1 3) :sort (1 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 3) list:firstRest (2 (9 1 3))}] - skolem:lemma5762 - skolem:lemma4705 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((1) (2 3 9)) list:append (1 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 3)]; - 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 3)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4218 a r:Inference; +skolem:lemma3350 a r:Inference; r:gives { 2914 :numberToDigits (2 9 1 4). }; @@ -102398,32 +77909,9 @@ skolem:lemma4218 a r:Inference; 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:lemma4392. - -skolem:lemma4219 a r:Inference; - r:gives { - (2 9 1 4) :sort (1 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 4) list:firstRest (2 (9 1 4))}] - skolem:lemma5763 - skolem:lemma4705 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((1) (2 4 9)) list:append (1 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 4)]; - 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 4)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4220 a r:Inference; +skolem:lemma3351 a r:Inference; r:gives { 2915 :numberToDigits (2 9 1 5). }; @@ -102442,32 +77930,9 @@ skolem:lemma4220 a r:Inference; 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:lemma4392. - -skolem:lemma4221 a r:Inference; - r:gives { - (2 9 1 5) :sort (1 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 5) list:firstRest (2 (9 1 5))}] - skolem:lemma5764 - skolem:lemma4705 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((1) (2 5 9)) list:append (1 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 5)]; - 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 5)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4222 a r:Inference; +skolem:lemma3352 a r:Inference; r:gives { 2916 :numberToDigits (2 9 1 6). }; @@ -102486,32 +77951,9 @@ skolem:lemma4222 a r:Inference; 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:lemma4392. - -skolem:lemma4223 a r:Inference; - r:gives { - (2 9 1 6) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 6) list:firstRest (2 (9 1 6))}] - skolem:lemma5765 - skolem:lemma4705 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((1) (2 6 9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 6)]; - 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 6)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4224 a r:Inference; +skolem:lemma3353 a r:Inference; r:gives { 2917 :numberToDigits (2 9 1 7). }; @@ -102530,32 +77972,9 @@ skolem:lemma4224 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4225 a r:Inference; - r:gives { - (2 9 1 7) :sort (1 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 7) list:firstRest (2 (9 1 7))}] - skolem:lemma5766 - skolem:lemma4705 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((1) (2 7 9)) list:append (1 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 7)]; - 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 7)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4226 a r:Inference; +skolem:lemma3354 a r:Inference; r:gives { 2918 :numberToDigits (2 9 1 8). }; @@ -102574,32 +77993,9 @@ skolem:lemma4226 a r:Inference; 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:lemma4392. - -skolem:lemma4227 a r:Inference; - r:gives { - (2 9 1 8) :sort (1 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 8) list:firstRest (2 (9 1 8))}] - skolem:lemma5767 - skolem:lemma4705 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((1) (2 8 9)) list:append (1 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 8)]; - 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 8)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4228 a r:Inference; +skolem:lemma3355 a r:Inference; r:gives { 2919 :numberToDigits (2 9 1 9). }; @@ -102618,32 +78014,9 @@ skolem:lemma4228 a r:Inference; 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:lemma4392. - -skolem:lemma4229 a r:Inference; - r:gives { - (2 9 1 9) :sort (1 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1 9) list:firstRest (2 (9 1 9))}] - skolem:lemma5768 - skolem:lemma4705 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((1) (2 9 9)) list:append (1 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 1 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_2"]; r:boundTo (9 1 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4230 a r:Inference; +skolem:lemma3356 a r:Inference; r:gives { 2920 :numberToDigits (2 9 2 0). }; @@ -102662,32 +78035,9 @@ skolem:lemma4230 a r:Inference; 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:lemma4392. - -skolem:lemma4231 a r:Inference; - r:gives { - (2 9 2 0) :sort (0 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 0) list:firstRest (2 (9 2 0))}] - skolem:lemma5769 - skolem:lemma4793 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((0 2) (2 9)) list:append (0 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4232 a r:Inference; +skolem:lemma3357 a r:Inference; r:gives { 2921 :numberToDigits (2 9 2 1). }; @@ -102706,32 +78056,9 @@ skolem:lemma4232 a r:Inference; 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:lemma4392. - -skolem:lemma4233 a r:Inference; - r:gives { - (2 9 2 1) :sort (1 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 1) list:firstRest (2 (9 2 1))}] - skolem:lemma5770 - skolem:lemma4807 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((1 2) (2 9)) list:append (1 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4234 a r:Inference; +skolem:lemma3358 a r:Inference; r:gives { 2922 :numberToDigits (2 9 2 2). }; @@ -102750,32 +78077,9 @@ skolem:lemma4234 a r:Inference; 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:lemma4392. - -skolem:lemma4235 a r:Inference; - r:gives { - (2 9 2 2) :sort (2 2 2 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 2) list:firstRest (2 (9 2 2))}] - skolem:lemma5771 - skolem:lemma4822 - skolem:lemma4430 - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {((2 2) (2 9)) list:append (2 2 2 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 2 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4236 a r:Inference; +skolem:lemma3359 a r:Inference; r:gives { 2923 :numberToDigits (2 9 2 3). }; @@ -102794,32 +78098,9 @@ skolem:lemma4236 a r:Inference; 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:lemma4392. - -skolem:lemma4237 a r:Inference; - r:gives { - (2 9 2 3) :sort (2 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 3) list:firstRest (2 (9 2 3))}] - skolem:lemma5772 - skolem:lemma4833 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((2) (2 3 9)) list:append (2 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 3)]; - 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 3)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4238 a r:Inference; +skolem:lemma3360 a r:Inference; r:gives { 2924 :numberToDigits (2 9 2 4). }; @@ -102838,32 +78119,9 @@ skolem:lemma4238 a r:Inference; 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:lemma4392. - -skolem:lemma4239 a r:Inference; - r:gives { - (2 9 2 4) :sort (2 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 4) list:firstRest (2 (9 2 4))}] - skolem:lemma5773 - skolem:lemma4833 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((2) (2 4 9)) list:append (2 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 4)]; - 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 4)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4240 a r:Inference; +skolem:lemma3361 a r:Inference; r:gives { 2925 :numberToDigits (2 9 2 5). }; @@ -102882,32 +78140,9 @@ skolem:lemma4240 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4241 a r:Inference; - r:gives { - (2 9 2 5) :sort (2 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 5) list:firstRest (2 (9 2 5))}] - skolem:lemma5774 - skolem:lemma4833 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((2) (2 5 9)) list:append (2 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 5)]; - 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 5)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4242 a r:Inference; +skolem:lemma3362 a r:Inference; r:gives { 2926 :numberToDigits (2 9 2 6). }; @@ -102926,32 +78161,9 @@ skolem:lemma4242 a r:Inference; 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:lemma4392. - -skolem:lemma4243 a r:Inference; - r:gives { - (2 9 2 6) :sort (2 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 6) list:firstRest (2 (9 2 6))}] - skolem:lemma5775 - skolem:lemma4833 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((2) (2 6 9)) list:append (2 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 6)]; - 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 6)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4244 a r:Inference; +skolem:lemma3363 a r:Inference; r:gives { 2927 :numberToDigits (2 9 2 7). }; @@ -102970,32 +78182,9 @@ skolem:lemma4244 a r:Inference; 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:lemma4392. - -skolem:lemma4245 a r:Inference; - r:gives { - (2 9 2 7) :sort (2 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 7) list:firstRest (2 (9 2 7))}] - skolem:lemma5776 - skolem:lemma4833 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((2) (2 7 9)) list:append (2 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 7)]; - 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 7)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4246 a r:Inference; +skolem:lemma3364 a r:Inference; r:gives { 2928 :numberToDigits (2 9 2 8). }; @@ -103014,32 +78203,9 @@ skolem:lemma4246 a r:Inference; 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:lemma4392. - -skolem:lemma4247 a r:Inference; - r:gives { - (2 9 2 8) :sort (2 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 8) list:firstRest (2 (9 2 8))}] - skolem:lemma5777 - skolem:lemma4833 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((2) (2 8 9)) list:append (2 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 8)]; - 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 8)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4248 a r:Inference; +skolem:lemma3365 a r:Inference; r:gives { 2929 :numberToDigits (2 9 2 9). }; @@ -103058,32 +78224,9 @@ skolem:lemma4248 a r:Inference; 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:lemma4392. - -skolem:lemma4249 a r:Inference; - r:gives { - (2 9 2 9) :sort (2 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2 9) list:firstRest (2 (9 2 9))}] - skolem:lemma5778 - skolem:lemma4833 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((2) (2 9 9)) list:append (2 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 2 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_2"]; r:boundTo (9 2 9)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4250 a r:Inference; +skolem:lemma3366 a r:Inference; r:gives { 2930 :numberToDigits (2 9 3 0). }; @@ -103102,32 +78245,9 @@ skolem:lemma4250 a r:Inference; 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:lemma4392. - -skolem:lemma4251 a r:Inference; - r:gives { - (2 9 3 0) :sort (0 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 0) list:firstRest (2 (9 3 0))}] - skolem:lemma5779 - skolem:lemma4506 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((0) (2 3 9)) list:append (0 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4252 a r:Inference; +skolem:lemma3367 a r:Inference; r:gives { 2931 :numberToDigits (2 9 3 1). }; @@ -103146,32 +78266,9 @@ skolem:lemma4252 a r:Inference; 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:lemma4392. - -skolem:lemma4253 a r:Inference; - r:gives { - (2 9 3 1) :sort (1 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 1) list:firstRest (2 (9 3 1))}] - skolem:lemma5780 - skolem:lemma4705 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((1) (2 3 9)) list:append (1 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 1)]; - 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 3)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4254 a r:Inference; +skolem:lemma3368 a r:Inference; r:gives { 2932 :numberToDigits (2 9 3 2). }; @@ -103190,32 +78287,9 @@ skolem:lemma4254 a r:Inference; 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:lemma4392. - -skolem:lemma4255 a r:Inference; - r:gives { - (2 9 3 2) :sort (2 2 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 2) list:firstRest (2 (9 3 2))}] - skolem:lemma5781 - skolem:lemma4833 - skolem:lemma4638 - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {((2) (2 3 9)) list:append (2 2 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 2)]; - 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 3)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 3 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4256 a r:Inference; +skolem:lemma3369 a r:Inference; r:gives { 2933 :numberToDigits (2 9 3 3). }; @@ -103234,32 +78308,9 @@ skolem:lemma4256 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4257 a r:Inference; - r:gives { - (2 9 3 3) :sort (2 3 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 3) list:firstRest (2 (9 3 3))}] - skolem:lemma5782 - skolem:lemma4395 - skolem:lemma5783 - [ a r:Fact; r:gives {(2 3 3 9) list:firstRest (2 (3 3 9))}] - [ a r:Fact; r:gives {(() (2 3 3 9)) list:append (2 3 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4258 a r:Inference; +skolem:lemma3370 a r:Inference; r:gives { 2934 :numberToDigits (2 9 3 4). }; @@ -103278,32 +78329,9 @@ skolem:lemma4258 a r:Inference; 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:lemma4392. - -skolem:lemma4259 a r:Inference; - r:gives { - (2 9 3 4) :sort (2 3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 4) list:firstRest (2 (9 3 4))}] - skolem:lemma5784 - skolem:lemma4395 - skolem:lemma5785 - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - [ a r:Fact; r:gives {(() (2 3 4 9)) list:append (2 3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4260 a r:Inference; +skolem:lemma3371 a r:Inference; r:gives { 2935 :numberToDigits (2 9 3 5). }; @@ -103322,32 +78350,9 @@ skolem:lemma4260 a r:Inference; 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:lemma4392. - -skolem:lemma4261 a r:Inference; - r:gives { - (2 9 3 5) :sort (2 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 5) list:firstRest (2 (9 3 5))}] - skolem:lemma5786 - skolem:lemma4395 - skolem:lemma5787 - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - [ a r:Fact; r:gives {(() (2 3 5 9)) list:append (2 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4262 a r:Inference; +skolem:lemma3372 a r:Inference; r:gives { 2936 :numberToDigits (2 9 3 6). }; @@ -103366,32 +78371,9 @@ skolem:lemma4262 a r:Inference; 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:lemma4392. - -skolem:lemma4263 a r:Inference; - r:gives { - (2 9 3 6) :sort (2 3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 6) list:firstRest (2 (9 3 6))}] - skolem:lemma5788 - skolem:lemma4395 - skolem:lemma5789 - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - [ a r:Fact; r:gives {(() (2 3 6 9)) list:append (2 3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4264 a r:Inference; +skolem:lemma3373 a r:Inference; r:gives { 2937 :numberToDigits (2 9 3 7). }; @@ -103410,32 +78392,9 @@ skolem:lemma4264 a r:Inference; 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:lemma4392. - -skolem:lemma4265 a r:Inference; - r:gives { - (2 9 3 7) :sort (2 3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 7) list:firstRest (2 (9 3 7))}] - skolem:lemma5790 - skolem:lemma4395 - skolem:lemma5791 - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - [ a r:Fact; r:gives {(() (2 3 7 9)) list:append (2 3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4266 a r:Inference; +skolem:lemma3374 a r:Inference; r:gives { 2938 :numberToDigits (2 9 3 8). }; @@ -103454,32 +78413,9 @@ skolem:lemma4266 a r:Inference; 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:lemma4392. - -skolem:lemma4267 a r:Inference; - r:gives { - (2 9 3 8) :sort (2 3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 8) list:firstRest (2 (9 3 8))}] - skolem:lemma5792 - skolem:lemma4395 - skolem:lemma5793 - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - [ a r:Fact; r:gives {(() (2 3 8 9)) list:append (2 3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4268 a r:Inference; +skolem:lemma3375 a r:Inference; r:gives { 2939 :numberToDigits (2 9 3 9). }; @@ -103498,32 +78434,9 @@ skolem:lemma4268 a r:Inference; 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:lemma4392. - -skolem:lemma4269 a r:Inference; - r:gives { - (2 9 3 9) :sort (2 3 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3 9) list:firstRest (2 (9 3 9))}] - skolem:lemma5794 - skolem:lemma4395 - skolem:lemma5795 - [ a r:Fact; r:gives {(2 3 9 9) list:firstRest (2 (3 9 9))}] - [ a r:Fact; r:gives {(() (2 3 9 9)) list:append (2 3 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 3 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_2"]; r:boundTo (9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4270 a r:Inference; +skolem:lemma3376 a r:Inference; r:gives { 2940 :numberToDigits (2 9 4 0). }; @@ -103542,32 +78455,9 @@ skolem:lemma4270 a r:Inference; 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:lemma4392. - -skolem:lemma4271 a r:Inference; - r:gives { - (2 9 4 0) :sort (0 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 0) list:firstRest (2 (9 4 0))}] - skolem:lemma5796 - skolem:lemma4506 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((0) (2 4 9)) list:append (0 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4272 a r:Inference; +skolem:lemma3377 a r:Inference; r:gives { 2941 :numberToDigits (2 9 4 1). }; @@ -103586,32 +78476,9 @@ skolem:lemma4272 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4273 a r:Inference; - r:gives { - (2 9 4 1) :sort (1 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 1) list:firstRest (2 (9 4 1))}] - skolem:lemma5797 - skolem:lemma4705 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((1) (2 4 9)) list:append (1 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 1)]; - 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 4)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4274 a r:Inference; +skolem:lemma3378 a r:Inference; r:gives { 2942 :numberToDigits (2 9 4 2). }; @@ -103630,32 +78497,9 @@ skolem:lemma4274 a r:Inference; 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:lemma4392. - -skolem:lemma4275 a r:Inference; - r:gives { - (2 9 4 2) :sort (2 2 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 2) list:firstRest (2 (9 4 2))}] - skolem:lemma5798 - skolem:lemma4833 - skolem:lemma4640 - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {((2) (2 4 9)) list:append (2 2 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 2)]; - 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 4)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4276 a r:Inference; +skolem:lemma3379 a r:Inference; r:gives { 2943 :numberToDigits (2 9 4 3). }; @@ -103674,32 +78518,9 @@ skolem:lemma4276 a r:Inference; 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:lemma4392. - -skolem:lemma4277 a r:Inference; - r:gives { - (2 9 4 3) :sort (2 3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 3) list:firstRest (2 (9 4 3))}] - skolem:lemma5799 - skolem:lemma4395 - skolem:lemma5800 - [ a r:Fact; r:gives {(2 3 4 9) list:firstRest (2 (3 4 9))}] - [ a r:Fact; r:gives {(() (2 3 4 9)) list:append (2 3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4278 a r:Inference; +skolem:lemma3380 a r:Inference; r:gives { 2944 :numberToDigits (2 9 4 4). }; @@ -103718,32 +78539,9 @@ skolem:lemma4278 a r:Inference; 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:lemma4392. - -skolem:lemma4279 a r:Inference; - r:gives { - (2 9 4 4) :sort (2 4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 4) list:firstRest (2 (9 4 4))}] - skolem:lemma5801 - skolem:lemma4395 - skolem:lemma5802 - [ a r:Fact; r:gives {(2 4 4 9) list:firstRest (2 (4 4 9))}] - [ a r:Fact; r:gives {(() (2 4 4 9)) list:append (2 4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4280 a r:Inference; +skolem:lemma3381 a r:Inference; r:gives { 2945 :numberToDigits (2 9 4 5). }; @@ -103762,32 +78560,9 @@ skolem:lemma4280 a r:Inference; 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:lemma4392. - -skolem:lemma4281 a r:Inference; - r:gives { - (2 9 4 5) :sort (2 4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 5) list:firstRest (2 (9 4 5))}] - skolem:lemma5803 - skolem:lemma4395 - skolem:lemma5804 - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - [ a r:Fact; r:gives {(() (2 4 5 9)) list:append (2 4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4282 a r:Inference; +skolem:lemma3382 a r:Inference; r:gives { 2946 :numberToDigits (2 9 4 6). }; @@ -103806,32 +78581,9 @@ skolem:lemma4282 a r:Inference; 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:lemma4392. - -skolem:lemma4283 a r:Inference; - r:gives { - (2 9 4 6) :sort (2 4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 6) list:firstRest (2 (9 4 6))}] - skolem:lemma5805 - skolem:lemma4395 - skolem:lemma5806 - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - [ a r:Fact; r:gives {(() (2 4 6 9)) list:append (2 4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4284 a r:Inference; +skolem:lemma3383 a r:Inference; r:gives { 2947 :numberToDigits (2 9 4 7). }; @@ -103850,32 +78602,9 @@ skolem:lemma4284 a r:Inference; 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:lemma4392. - -skolem:lemma4285 a r:Inference; - r:gives { - (2 9 4 7) :sort (2 4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 7) list:firstRest (2 (9 4 7))}] - skolem:lemma5807 - skolem:lemma4395 - skolem:lemma5808 - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - [ a r:Fact; r:gives {(() (2 4 7 9)) list:append (2 4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4286 a r:Inference; +skolem:lemma3384 a r:Inference; r:gives { 2948 :numberToDigits (2 9 4 8). }; @@ -103894,32 +78623,9 @@ skolem:lemma4286 a r:Inference; 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:lemma4392. - -skolem:lemma4287 a r:Inference; - r:gives { - (2 9 4 8) :sort (2 4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 8) list:firstRest (2 (9 4 8))}] - skolem:lemma5809 - skolem:lemma4395 - skolem:lemma5810 - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - [ a r:Fact; r:gives {(() (2 4 8 9)) list:append (2 4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4288 a r:Inference; +skolem:lemma3385 a r:Inference; r:gives { 2949 :numberToDigits (2 9 4 9). }; @@ -103938,32 +78644,9 @@ skolem:lemma4288 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4289 a r:Inference; - r:gives { - (2 9 4 9) :sort (2 4 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4 9) list:firstRest (2 (9 4 9))}] - skolem:lemma5811 - skolem:lemma4395 - skolem:lemma5812 - [ a r:Fact; r:gives {(2 4 9 9) list:firstRest (2 (4 9 9))}] - [ a r:Fact; r:gives {(() (2 4 9 9)) list:append (2 4 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 4 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_2"]; r:boundTo (9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4290 a r:Inference; +skolem:lemma3386 a r:Inference; r:gives { 2950 :numberToDigits (2 9 5 0). }; @@ -103982,32 +78665,9 @@ skolem:lemma4290 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4291 a r:Inference; - r:gives { - (2 9 5 0) :sort (0 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 0) list:firstRest (2 (9 5 0))}] - skolem:lemma5813 - skolem:lemma4506 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((0) (2 5 9)) list:append (0 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4292 a r:Inference; +skolem:lemma3387 a r:Inference; r:gives { 2951 :numberToDigits (2 9 5 1). }; @@ -104026,32 +78686,9 @@ skolem:lemma4292 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4293 a r:Inference; - r:gives { - (2 9 5 1) :sort (1 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 1) list:firstRest (2 (9 5 1))}] - skolem:lemma5814 - skolem:lemma4705 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((1) (2 5 9)) list:append (1 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 1)]; - 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 5)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4294 a r:Inference; +skolem:lemma3388 a r:Inference; r:gives { 2952 :numberToDigits (2 9 5 2). }; @@ -104070,32 +78707,9 @@ skolem:lemma4294 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4295 a r:Inference; - r:gives { - (2 9 5 2) :sort (2 2 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 2) list:firstRest (2 (9 5 2))}] - skolem:lemma5815 - skolem:lemma4833 - skolem:lemma4642 - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {((2) (2 5 9)) list:append (2 2 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 2)]; - 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 5)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4296 a r:Inference; +skolem:lemma3389 a r:Inference; r:gives { 2953 :numberToDigits (2 9 5 3). }; @@ -104114,32 +78728,9 @@ skolem:lemma4296 a r:Inference; 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:lemma4392. - -skolem:lemma4297 a r:Inference; - r:gives { - (2 9 5 3) :sort (2 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 3) list:firstRest (2 (9 5 3))}] - skolem:lemma5816 - skolem:lemma4395 - skolem:lemma5817 - [ a r:Fact; r:gives {(2 3 5 9) list:firstRest (2 (3 5 9))}] - [ a r:Fact; r:gives {(() (2 3 5 9)) list:append (2 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4298 a r:Inference; +skolem:lemma3390 a r:Inference; r:gives { 2954 :numberToDigits (2 9 5 4). }; @@ -104158,32 +78749,9 @@ skolem:lemma4298 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4299 a r:Inference; - r:gives { - (2 9 5 4) :sort (2 4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 4) list:firstRest (2 (9 5 4))}] - skolem:lemma5818 - skolem:lemma4395 - skolem:lemma5819 - [ a r:Fact; r:gives {(2 4 5 9) list:firstRest (2 (4 5 9))}] - [ a r:Fact; r:gives {(() (2 4 5 9)) list:append (2 4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4300 a r:Inference; +skolem:lemma3391 a r:Inference; r:gives { 2955 :numberToDigits (2 9 5 5). }; @@ -104202,32 +78770,9 @@ skolem:lemma4300 a r:Inference; 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:lemma4392. - -skolem:lemma4301 a r:Inference; - r:gives { - (2 9 5 5) :sort (2 5 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 5) list:firstRest (2 (9 5 5))}] - skolem:lemma5820 - skolem:lemma4395 - skolem:lemma5821 - [ a r:Fact; r:gives {(2 5 5 9) list:firstRest (2 (5 5 9))}] - [ a r:Fact; r:gives {(() (2 5 5 9)) list:append (2 5 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4302 a r:Inference; +skolem:lemma3392 a r:Inference; r:gives { 2956 :numberToDigits (2 9 5 6). }; @@ -104246,32 +78791,9 @@ skolem:lemma4302 a r:Inference; 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:lemma4392. - -skolem:lemma4303 a r:Inference; - r:gives { - (2 9 5 6) :sort (2 5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 6) list:firstRest (2 (9 5 6))}] - skolem:lemma5822 - skolem:lemma4395 - skolem:lemma5823 - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - [ a r:Fact; r:gives {(() (2 5 6 9)) list:append (2 5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4304 a r:Inference; +skolem:lemma3393 a r:Inference; r:gives { 2957 :numberToDigits (2 9 5 7). }; @@ -104290,32 +78812,9 @@ skolem:lemma4304 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4305 a r:Inference; - r:gives { - (2 9 5 7) :sort (2 5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 7) list:firstRest (2 (9 5 7))}] - skolem:lemma5824 - skolem:lemma4395 - skolem:lemma5825 - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - [ a r:Fact; r:gives {(() (2 5 7 9)) list:append (2 5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4306 a r:Inference; +skolem:lemma3394 a r:Inference; r:gives { 2958 :numberToDigits (2 9 5 8). }; @@ -104334,32 +78833,9 @@ skolem:lemma4306 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4307 a r:Inference; - r:gives { - (2 9 5 8) :sort (2 5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 8) list:firstRest (2 (9 5 8))}] - skolem:lemma5826 - skolem:lemma4395 - skolem:lemma5827 - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - [ a r:Fact; r:gives {(() (2 5 8 9)) list:append (2 5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4308 a r:Inference; +skolem:lemma3395 a r:Inference; r:gives { 2959 :numberToDigits (2 9 5 9). }; @@ -104378,32 +78854,9 @@ skolem:lemma4308 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4309 a r:Inference; - r:gives { - (2 9 5 9) :sort (2 5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5 9) list:firstRest (2 (9 5 9))}] - skolem:lemma5828 - skolem:lemma4395 - skolem:lemma5829 - [ a r:Fact; r:gives {(2 5 9 9) list:firstRest (2 (5 9 9))}] - [ a r:Fact; r:gives {(() (2 5 9 9)) list:append (2 5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 5 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_2"]; r:boundTo (9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4310 a r:Inference; +skolem:lemma3396 a r:Inference; r:gives { 2960 :numberToDigits (2 9 6 0). }; @@ -104422,32 +78875,9 @@ skolem:lemma4310 a r:Inference; 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:lemma4392. - -skolem:lemma4311 a r:Inference; - r:gives { - (2 9 6 0) :sort (0 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 0) list:firstRest (2 (9 6 0))}] - skolem:lemma5830 - skolem:lemma4506 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((0) (2 6 9)) list:append (0 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4312 a r:Inference; +skolem:lemma3397 a r:Inference; r:gives { 2961 :numberToDigits (2 9 6 1). }; @@ -104466,32 +78896,9 @@ skolem:lemma4312 a r:Inference; 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:lemma4392. - -skolem:lemma4313 a r:Inference; - r:gives { - (2 9 6 1) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 1) list:firstRest (2 (9 6 1))}] - skolem:lemma5831 - skolem:lemma4705 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((1) (2 6 9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 1)]; - 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 6)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4314 a r:Inference; +skolem:lemma3398 a r:Inference; r:gives { 2962 :numberToDigits (2 9 6 2). }; @@ -104510,32 +78917,9 @@ skolem:lemma4314 a r:Inference; 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:lemma4392. - -skolem:lemma4315 a r:Inference; - r:gives { - (2 9 6 2) :sort (2 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 2) list:firstRest (2 (9 6 2))}] - skolem:lemma5832 - skolem:lemma4833 - skolem:lemma4644 - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {((2) (2 6 9)) list:append (2 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 2)]; - 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 6)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4316 a r:Inference; +skolem:lemma3399 a r:Inference; r:gives { 2963 :numberToDigits (2 9 6 3). }; @@ -104554,32 +78938,9 @@ skolem:lemma4316 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4317 a r:Inference; - r:gives { - (2 9 6 3) :sort (2 3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 3) list:firstRest (2 (9 6 3))}] - skolem:lemma5833 - skolem:lemma4395 - skolem:lemma5834 - [ a r:Fact; r:gives {(2 3 6 9) list:firstRest (2 (3 6 9))}] - [ a r:Fact; r:gives {(() (2 3 6 9)) list:append (2 3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4318 a r:Inference; +skolem:lemma3400 a r:Inference; r:gives { 2964 :numberToDigits (2 9 6 4). }; @@ -104598,32 +78959,9 @@ skolem:lemma4318 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4319 a r:Inference; - r:gives { - (2 9 6 4) :sort (2 4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 4) list:firstRest (2 (9 6 4))}] - skolem:lemma5835 - skolem:lemma4395 - skolem:lemma5836 - [ a r:Fact; r:gives {(2 4 6 9) list:firstRest (2 (4 6 9))}] - [ a r:Fact; r:gives {(() (2 4 6 9)) list:append (2 4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4320 a r:Inference; +skolem:lemma3401 a r:Inference; r:gives { 2965 :numberToDigits (2 9 6 5). }; @@ -104642,32 +78980,9 @@ skolem:lemma4320 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4321 a r:Inference; - r:gives { - (2 9 6 5) :sort (2 5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 5) list:firstRest (2 (9 6 5))}] - skolem:lemma5837 - skolem:lemma4395 - skolem:lemma5838 - [ a r:Fact; r:gives {(2 5 6 9) list:firstRest (2 (5 6 9))}] - [ a r:Fact; r:gives {(() (2 5 6 9)) list:append (2 5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4322 a r:Inference; +skolem:lemma3402 a r:Inference; r:gives { 2966 :numberToDigits (2 9 6 6). }; @@ -104686,32 +79001,9 @@ skolem:lemma4322 a r:Inference; 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:lemma4392. - -skolem:lemma4323 a r:Inference; - r:gives { - (2 9 6 6) :sort (2 6 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 6) list:firstRest (2 (9 6 6))}] - skolem:lemma5839 - skolem:lemma4395 - skolem:lemma5840 - [ a r:Fact; r:gives {(2 6 6 9) list:firstRest (2 (6 6 9))}] - [ a r:Fact; r:gives {(() (2 6 6 9)) list:append (2 6 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 6 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4324 a r:Inference; +skolem:lemma3403 a r:Inference; r:gives { 2967 :numberToDigits (2 9 6 7). }; @@ -104730,32 +79022,9 @@ skolem:lemma4324 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4325 a r:Inference; - r:gives { - (2 9 6 7) :sort (2 6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 7) list:firstRest (2 (9 6 7))}] - skolem:lemma5841 - skolem:lemma4395 - skolem:lemma5842 - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - [ a r:Fact; r:gives {(() (2 6 7 9)) list:append (2 6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4326 a r:Inference; +skolem:lemma3404 a r:Inference; r:gives { 2968 :numberToDigits (2 9 6 8). }; @@ -104774,32 +79043,9 @@ skolem:lemma4326 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4327 a r:Inference; - r:gives { - (2 9 6 8) :sort (2 6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 8) list:firstRest (2 (9 6 8))}] - skolem:lemma5843 - skolem:lemma4395 - skolem:lemma5844 - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - [ a r:Fact; r:gives {(() (2 6 8 9)) list:append (2 6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4328 a r:Inference; +skolem:lemma3405 a r:Inference; r:gives { 2969 :numberToDigits (2 9 6 9). }; @@ -104818,32 +79064,9 @@ skolem:lemma4328 a r:Inference; 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:lemma4392. - -skolem:lemma4329 a r:Inference; - r:gives { - (2 9 6 9) :sort (2 6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6 9) list:firstRest (2 (9 6 9))}] - skolem:lemma5845 - skolem:lemma4395 - skolem:lemma5846 - [ a r:Fact; r:gives {(2 6 9 9) list:firstRest (2 (6 9 9))}] - [ a r:Fact; r:gives {(() (2 6 9 9)) list:append (2 6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 6 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_2"]; r:boundTo (9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4330 a r:Inference; +skolem:lemma3406 a r:Inference; r:gives { 2970 :numberToDigits (2 9 7 0). }; @@ -104862,32 +79085,9 @@ skolem:lemma4330 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4331 a r:Inference; - r:gives { - (2 9 7 0) :sort (0 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 0) list:firstRest (2 (9 7 0))}] - skolem:lemma5847 - skolem:lemma4506 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((0) (2 7 9)) list:append (0 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4332 a r:Inference; +skolem:lemma3407 a r:Inference; r:gives { 2971 :numberToDigits (2 9 7 1). }; @@ -104906,32 +79106,9 @@ skolem:lemma4332 a r:Inference; 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:lemma4392. - -skolem:lemma4333 a r:Inference; - r:gives { - (2 9 7 1) :sort (1 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 1) list:firstRest (2 (9 7 1))}] - skolem:lemma5848 - skolem:lemma4705 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((1) (2 7 9)) list:append (1 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 1)]; - 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 7)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4334 a r:Inference; +skolem:lemma3408 a r:Inference; r:gives { 2972 :numberToDigits (2 9 7 2). }; @@ -104950,32 +79127,9 @@ skolem:lemma4334 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4335 a r:Inference; - r:gives { - (2 9 7 2) :sort (2 2 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 2) list:firstRest (2 (9 7 2))}] - skolem:lemma5849 - skolem:lemma4833 - skolem:lemma4646 - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {((2) (2 7 9)) list:append (2 2 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 2)]; - 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 7)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4336 a r:Inference; +skolem:lemma3409 a r:Inference; r:gives { 2973 :numberToDigits (2 9 7 3). }; @@ -104994,32 +79148,9 @@ skolem:lemma4336 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4337 a r:Inference; - r:gives { - (2 9 7 3) :sort (2 3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 3) list:firstRest (2 (9 7 3))}] - skolem:lemma5850 - skolem:lemma4395 - skolem:lemma5851 - [ a r:Fact; r:gives {(2 3 7 9) list:firstRest (2 (3 7 9))}] - [ a r:Fact; r:gives {(() (2 3 7 9)) list:append (2 3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4338 a r:Inference; +skolem:lemma3410 a r:Inference; r:gives { 2974 :numberToDigits (2 9 7 4). }; @@ -105038,32 +79169,9 @@ skolem:lemma4338 a r:Inference; 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:lemma4392. - -skolem:lemma4339 a r:Inference; - r:gives { - (2 9 7 4) :sort (2 4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 4) list:firstRest (2 (9 7 4))}] - skolem:lemma5852 - skolem:lemma4395 - skolem:lemma5853 - [ a r:Fact; r:gives {(2 4 7 9) list:firstRest (2 (4 7 9))}] - [ a r:Fact; r:gives {(() (2 4 7 9)) list:append (2 4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4340 a r:Inference; +skolem:lemma3411 a r:Inference; r:gives { 2975 :numberToDigits (2 9 7 5). }; @@ -105082,32 +79190,9 @@ skolem:lemma4340 a r:Inference; 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:lemma4392. - -skolem:lemma4341 a r:Inference; - r:gives { - (2 9 7 5) :sort (2 5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 5) list:firstRest (2 (9 7 5))}] - skolem:lemma5854 - skolem:lemma4395 - skolem:lemma5855 - [ a r:Fact; r:gives {(2 5 7 9) list:firstRest (2 (5 7 9))}] - [ a r:Fact; r:gives {(() (2 5 7 9)) list:append (2 5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4342 a r:Inference; +skolem:lemma3412 a r:Inference; r:gives { 2976 :numberToDigits (2 9 7 6). }; @@ -105126,32 +79211,9 @@ skolem:lemma4342 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4343 a r:Inference; - r:gives { - (2 9 7 6) :sort (2 6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 6) list:firstRest (2 (9 7 6))}] - skolem:lemma5856 - skolem:lemma4395 - skolem:lemma5857 - [ a r:Fact; r:gives {(2 6 7 9) list:firstRest (2 (6 7 9))}] - [ a r:Fact; r:gives {(() (2 6 7 9)) list:append (2 6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4344 a r:Inference; +skolem:lemma3413 a r:Inference; r:gives { 2977 :numberToDigits (2 9 7 7). }; @@ -105170,32 +79232,9 @@ skolem:lemma4344 a r:Inference; 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:lemma4392. - -skolem:lemma4345 a r:Inference; - r:gives { - (2 9 7 7) :sort (2 7 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 7) list:firstRest (2 (9 7 7))}] - skolem:lemma5858 - skolem:lemma4395 - skolem:lemma5859 - [ a r:Fact; r:gives {(2 7 7 9) list:firstRest (2 (7 7 9))}] - [ a r:Fact; r:gives {(() (2 7 7 9)) list:append (2 7 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 7 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4346 a r:Inference; +skolem:lemma3414 a r:Inference; r:gives { 2978 :numberToDigits (2 9 7 8). }; @@ -105214,32 +79253,9 @@ skolem:lemma4346 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4347 a r:Inference; - r:gives { - (2 9 7 8) :sort (2 7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 8) list:firstRest (2 (9 7 8))}] - skolem:lemma5860 - skolem:lemma4395 - skolem:lemma5861 - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - [ a r:Fact; r:gives {(() (2 7 8 9)) list:append (2 7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4348 a r:Inference; +skolem:lemma3415 a r:Inference; r:gives { 2979 :numberToDigits (2 9 7 9). }; @@ -105258,32 +79274,9 @@ skolem:lemma4348 a r:Inference; 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:lemma4392. - -skolem:lemma4349 a r:Inference; - r:gives { - (2 9 7 9) :sort (2 7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7 9) list:firstRest (2 (9 7 9))}] - skolem:lemma5862 - skolem:lemma4395 - skolem:lemma5863 - [ a r:Fact; r:gives {(2 7 9 9) list:firstRest (2 (7 9 9))}] - [ a r:Fact; r:gives {(() (2 7 9 9)) list:append (2 7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 7 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_2"]; r:boundTo (9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4350 a r:Inference; +skolem:lemma3416 a r:Inference; r:gives { 2980 :numberToDigits (2 9 8 0). }; @@ -105302,32 +79295,9 @@ skolem:lemma4350 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4351 a r:Inference; - r:gives { - (2 9 8 0) :sort (0 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 0) list:firstRest (2 (9 8 0))}] - skolem:lemma5864 - skolem:lemma4506 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((0) (2 8 9)) list:append (0 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4352 a r:Inference; +skolem:lemma3417 a r:Inference; r:gives { 2981 :numberToDigits (2 9 8 1). }; @@ -105346,32 +79316,9 @@ skolem:lemma4352 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4353 a r:Inference; - r:gives { - (2 9 8 1) :sort (1 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 1) list:firstRest (2 (9 8 1))}] - skolem:lemma5865 - skolem:lemma4705 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((1) (2 8 9)) list:append (1 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 1)]; - 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 8)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4354 a r:Inference; +skolem:lemma3418 a r:Inference; r:gives { 2982 :numberToDigits (2 9 8 2). }; @@ -105390,32 +79337,9 @@ skolem:lemma4354 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4355 a r:Inference; - r:gives { - (2 9 8 2) :sort (2 2 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 2) list:firstRest (2 (9 8 2))}] - skolem:lemma5866 - skolem:lemma4833 - skolem:lemma4648 - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {((2) (2 8 9)) list:append (2 2 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 2)]; - 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 8)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4356 a r:Inference; +skolem:lemma3419 a r:Inference; r:gives { 2983 :numberToDigits (2 9 8 3). }; @@ -105434,32 +79358,9 @@ skolem:lemma4356 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4357 a r:Inference; - r:gives { - (2 9 8 3) :sort (2 3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 3) list:firstRest (2 (9 8 3))}] - skolem:lemma5867 - skolem:lemma4395 - skolem:lemma5868 - [ a r:Fact; r:gives {(2 3 8 9) list:firstRest (2 (3 8 9))}] - [ a r:Fact; r:gives {(() (2 3 8 9)) list:append (2 3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4358 a r:Inference; +skolem:lemma3420 a r:Inference; r:gives { 2984 :numberToDigits (2 9 8 4). }; @@ -105478,32 +79379,9 @@ skolem:lemma4358 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4359 a r:Inference; - r:gives { - (2 9 8 4) :sort (2 4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 4) list:firstRest (2 (9 8 4))}] - skolem:lemma5869 - skolem:lemma4395 - skolem:lemma5870 - [ a r:Fact; r:gives {(2 4 8 9) list:firstRest (2 (4 8 9))}] - [ a r:Fact; r:gives {(() (2 4 8 9)) list:append (2 4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4360 a r:Inference; +skolem:lemma3421 a r:Inference; r:gives { 2985 :numberToDigits (2 9 8 5). }; @@ -105522,32 +79400,9 @@ skolem:lemma4360 a r:Inference; 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:lemma4392. - -skolem:lemma4361 a r:Inference; - r:gives { - (2 9 8 5) :sort (2 5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 5) list:firstRest (2 (9 8 5))}] - skolem:lemma5871 - skolem:lemma4395 - skolem:lemma5872 - [ a r:Fact; r:gives {(2 5 8 9) list:firstRest (2 (5 8 9))}] - [ a r:Fact; r:gives {(() (2 5 8 9)) list:append (2 5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4362 a r:Inference; +skolem:lemma3422 a r:Inference; r:gives { 2986 :numberToDigits (2 9 8 6). }; @@ -105566,32 +79421,9 @@ skolem:lemma4362 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4363 a r:Inference; - r:gives { - (2 9 8 6) :sort (2 6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 6) list:firstRest (2 (9 8 6))}] - skolem:lemma5873 - skolem:lemma4395 - skolem:lemma5874 - [ a r:Fact; r:gives {(2 6 8 9) list:firstRest (2 (6 8 9))}] - [ a r:Fact; r:gives {(() (2 6 8 9)) list:append (2 6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4364 a r:Inference; +skolem:lemma3423 a r:Inference; r:gives { 2987 :numberToDigits (2 9 8 7). }; @@ -105610,32 +79442,9 @@ skolem:lemma4364 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4365 a r:Inference; - r:gives { - (2 9 8 7) :sort (2 7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 7) list:firstRest (2 (9 8 7))}] - skolem:lemma5875 - skolem:lemma4395 - skolem:lemma5876 - [ a r:Fact; r:gives {(2 7 8 9) list:firstRest (2 (7 8 9))}] - [ a r:Fact; r:gives {(() (2 7 8 9)) list:append (2 7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4366 a r:Inference; +skolem:lemma3424 a r:Inference; r:gives { 2988 :numberToDigits (2 9 8 8). }; @@ -105654,32 +79463,9 @@ skolem:lemma4366 a r:Inference; 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:lemma4392. - -skolem:lemma4367 a r:Inference; - r:gives { - (2 9 8 8) :sort (2 8 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 8) list:firstRest (2 (9 8 8))}] - skolem:lemma5877 - skolem:lemma4395 - skolem:lemma5878 - [ a r:Fact; r:gives {(2 8 8 9) list:firstRest (2 (8 8 9))}] - [ a r:Fact; r:gives {(() (2 8 8 9)) list:append (2 8 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 8 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4368 a r:Inference; +skolem:lemma3425 a r:Inference; r:gives { 2989 :numberToDigits (2 9 8 9). }; @@ -105698,32 +79484,9 @@ skolem:lemma4368 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4369 a r:Inference; - r:gives { - (2 9 8 9) :sort (2 8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8 9) list:firstRest (2 (9 8 9))}] - skolem:lemma5879 - skolem:lemma4395 - skolem:lemma5880 - [ a r:Fact; r:gives {(2 8 9 9) list:firstRest (2 (8 9 9))}] - [ a r:Fact; r:gives {(() (2 8 9 9)) list:append (2 8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 8 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_2"]; r:boundTo (9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4370 a r:Inference; +skolem:lemma3426 a r:Inference; r:gives { 2990 :numberToDigits (2 9 9 0). }; @@ -105742,32 +79505,9 @@ skolem:lemma4370 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4371 a r:Inference; - r:gives { - (2 9 9 0) :sort (0 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 0) list:firstRest (2 (9 9 0))}] - skolem:lemma5881 - skolem:lemma4506 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((0) (2 9 9)) list:append (0 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 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 (9 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4372 a r:Inference; +skolem:lemma3427 a r:Inference; r:gives { 2991 :numberToDigits (2 9 9 1). }; @@ -105786,32 +79526,9 @@ skolem:lemma4372 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4373 a r:Inference; - r:gives { - (2 9 9 1) :sort (1 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 1) list:firstRest (2 (9 9 1))}] - skolem:lemma5882 - skolem:lemma4705 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((1) (2 9 9)) list:append (1 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4374 a r:Inference; +skolem:lemma3428 a r:Inference; r:gives { 2992 :numberToDigits (2 9 9 2). }; @@ -105830,32 +79547,9 @@ skolem:lemma4374 a r:Inference; 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:lemma4392. - -skolem:lemma4375 a r:Inference; - r:gives { - (2 9 9 2) :sort (2 2 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 2) list:firstRest (2 (9 9 2))}] - skolem:lemma5883 - skolem:lemma4833 - skolem:lemma4650 - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {((2) (2 9 9)) list:append (2 2 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4376 a r:Inference; +skolem:lemma3429 a r:Inference; r:gives { 2993 :numberToDigits (2 9 9 3). }; @@ -105874,32 +79568,9 @@ skolem:lemma4376 a r:Inference; 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:lemma4392. - -skolem:lemma4377 a r:Inference; - r:gives { - (2 9 9 3) :sort (2 3 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 3) list:firstRest (2 (9 9 3))}] - skolem:lemma5884 - skolem:lemma4395 - skolem:lemma5885 - [ a r:Fact; r:gives {(2 3 9 9) list:firstRest (2 (3 9 9))}] - [ a r:Fact; r:gives {(() (2 3 9 9)) list:append (2 3 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4378 a r:Inference; +skolem:lemma3430 a r:Inference; r:gives { 2994 :numberToDigits (2 9 9 4). }; @@ -105918,32 +79589,9 @@ skolem:lemma4378 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4379 a r:Inference; - r:gives { - (2 9 9 4) :sort (2 4 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 4) list:firstRest (2 (9 9 4))}] - skolem:lemma5886 - skolem:lemma4395 - skolem:lemma5887 - [ a r:Fact; r:gives {(2 4 9 9) list:firstRest (2 (4 9 9))}] - [ a r:Fact; r:gives {(() (2 4 9 9)) list:append (2 4 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4380 a r:Inference; +skolem:lemma3431 a r:Inference; r:gives { 2995 :numberToDigits (2 9 9 5). }; @@ -105962,32 +79610,9 @@ skolem:lemma4380 a r:Inference; 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:lemma4392. - -skolem:lemma4381 a r:Inference; - r:gives { - (2 9 9 5) :sort (2 5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 5) list:firstRest (2 (9 9 5))}] - skolem:lemma5888 - skolem:lemma4395 - skolem:lemma5889 - [ a r:Fact; r:gives {(2 5 9 9) list:firstRest (2 (5 9 9))}] - [ a r:Fact; r:gives {(() (2 5 9 9)) list:append (2 5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4382 a r:Inference; +skolem:lemma3432 a r:Inference; r:gives { 2996 :numberToDigits (2 9 9 6). }; @@ -106006,32 +79631,9 @@ skolem:lemma4382 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4383 a r:Inference; - r:gives { - (2 9 9 6) :sort (2 6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 6) list:firstRest (2 (9 9 6))}] - skolem:lemma5890 - skolem:lemma4395 - skolem:lemma5891 - [ a r:Fact; r:gives {(2 6 9 9) list:firstRest (2 (6 9 9))}] - [ a r:Fact; r:gives {(() (2 6 9 9)) list:append (2 6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 6 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4384 a r:Inference; +skolem:lemma3433 a r:Inference; r:gives { 2997 :numberToDigits (2 9 9 7). }; @@ -106050,32 +79652,9 @@ skolem:lemma4384 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4385 a r:Inference; - r:gives { - (2 9 9 7) :sort (2 7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 7) list:firstRest (2 (9 9 7))}] - skolem:lemma5892 - skolem:lemma4395 - skolem:lemma5893 - [ a r:Fact; r:gives {(2 7 9 9) list:firstRest (2 (7 9 9))}] - [ a r:Fact; r:gives {(() (2 7 9 9)) list:append (2 7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4386 a r:Inference; +skolem:lemma3434 a r:Inference; r:gives { 2998 :numberToDigits (2 9 9 8). }; @@ -106094,32 +79673,9 @@ skolem:lemma4386 a r:Inference; 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:lemma4392. - -skolem:lemma4387 a r:Inference; - r:gives { - (2 9 9 8) :sort (2 8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 8) list:firstRest (2 (9 9 8))}] - skolem:lemma5894 - skolem:lemma4395 - skolem:lemma5895 - [ a r:Fact; r:gives {(2 8 9 9) list:firstRest (2 (8 9 9))}] - [ a r:Fact; r:gives {(() (2 8 9 9)) list:append (2 8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8 9 9)]; - r:rule skolem:lemma4396. + r:rule skolem:lemma3438. -skolem:lemma4388 a r:Inference; +skolem:lemma3435 a r:Inference; r:gives { 2999 :numberToDigits (2 9 9 9). }; @@ -106138,32 +79694,9 @@ skolem:lemma4388 a r:Inference; 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:lemma4392. + r:rule skolem:lemma3438. -skolem:lemma4389 a r:Inference; - r:gives { - (2 9 9 9) :sort (2 9 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9 9) list:firstRest (2 (9 9 9))}] - skolem:lemma5896 - skolem:lemma4395 - skolem:lemma5897 - [ a r:Fact; r:gives {(2 9 9 9) list:firstRest (2 (9 9 9))}] - [ a r:Fact; r:gives {(() (2 9 9 9)) list:append (2 9 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 9 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_2"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 9 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4390 a r:Inference; +skolem:lemma3436 a r:Inference; r:gives { (2 9 9 9) :digitsToNumber 2999 . }; @@ -106181,9 +79714,9 @@ skolem:lemma4390 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4391 a r:Inference; +skolem:lemma3437 a r:Inference; r:gives { (9 9 9 2) :digitsToNumber 9992 . }; @@ -106201,9 +79734,9 @@ skolem:lemma4391 a r:Inference; 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:lemma4397. + r:rule skolem:lemma3439. -skolem:lemma4392 a r:Extraction; +skolem:lemma3438 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). @@ -106218,70 +79751,7 @@ skolem:lemma4392 a r:Extraction; }; r:because [ a r:Parsing; r:source ]. -skolem:lemma4393 a r:Inference; - r:gives { - (2 (0 0 0)) :split ((0 0 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 0) list:firstRest (0 (0 0))}] - [ a r:Fact; r:gives {(0 0 0) list:firstRest (0 (0 0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 0)]; - 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_2"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4394 a r:Inference; - r:gives { - (0 0 0) :sort (0 0 0). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 0) list:firstRest (0 (0 0))}] - skolem:lemma5900 - skolem:lemma4407 - skolem:lemma4395 - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {((0 0) (0)) list:append (0 0 0)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 0)]; - 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_2"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 0)]; - r:rule skolem:lemma4396. - -skolem:lemma4395 a r:Extraction; - r:gives { - () :sort (). - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma4396 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_0 :sort var:x_8. - } <= { - var:x_0 list:firstRest (var:x_1 var:x_2). - (var:x_1 var:x_2) :split (var:x_3 var:x_4). - var:x_3 :sort var:x_5. - var:x_4 :sort var:x_6. - var:x_7 list:firstRest (var:x_1 var:x_6). - (var:x_5 var:x_7) list:append var:x_8. - }. - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma4397 a r:Extraction; +skolem:lemma3439 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. @@ -106294,42619 +79764,3 @@ skolem:lemma4397 a r:Extraction; }; r:because [ a r:Parsing; r:source ]. -skolem:lemma4398 a r:Inference; - r:gives { - 1998 :numberToDigits (1 9 9 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(1998 1000) math:integerQuotient 1}] - [ a r:Fact; r:gives {(1998 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 1]; - 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_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:lemma4392. - -skolem:lemma4399 a r:Inference; - r:gives { - (1 9 9 8) :sort (1 8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 9 8) list:firstRest (1 (9 9 8))}] - skolem:lemma5901 - skolem:lemma4395 - skolem:lemma5895 - [ a r:Fact; r:gives {(1 8 9 9) list:firstRest (1 (8 9 9))}] - [ a r:Fact; r:gives {(() (1 8 9 9)) list:append (1 8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4400 a r:Inference; - r:gives { - (1 8 9 9) :digitsToNumber 1899 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ 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 {(1000 800 90 9) math:sum 1899}] - ); - 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 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 1899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4401 a r:Inference; - r:gives { - (9 9 8 1) :digitsToNumber 9981 . - }; - 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 1) math:sum 9981}] - ); - 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 9981]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma4397. - -skolem:lemma4402 a r:Inference; - r:gives { - (2 (0 0 1)) :split ((0 0 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 1) list:firstRest (0 (0 1))}] - [ a r:Fact; r:gives {(0 0 1) list:firstRest (0 (0 1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 1)]; - 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_2"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4403 a r:Inference; - r:gives { - (0 0 1) :sort (0 0 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 1) list:firstRest (0 (0 1))}] - skolem:lemma5903 - skolem:lemma4506 - skolem:lemma4705 - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {((0) (0 1)) list:append (0 0 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 1)]; - 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_2"]; r:boundTo (0 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:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4404 a r:Inference; - r:gives { - (2 (0 0 2)) :split ((0 0 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 2) list:firstRest (0 (0 2))}] - [ a r:Fact; r:gives {(0 0 2) list:firstRest (0 (0 2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 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_2"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4405 a r:Inference; - r:gives { - (0 0 2) :sort (0 0 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 2) list:firstRest (0 (0 2))}] - skolem:lemma5905 - skolem:lemma4506 - skolem:lemma4833 - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {((0) (0 2)) list:append (0 0 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 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_2"]; r:boundTo (0 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:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4406 a r:Inference; - r:gives { - (2 (0 0 3)) :split ((0 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 3) list:firstRest (0 (0 3))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 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_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4407 a r:Inference; - r:gives { - (0 0) :sort (0 0). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - skolem:lemma5907 - skolem:lemma4506 - skolem:lemma4395 - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {((0) (0)) list:append (0 0)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0)]; - 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_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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0)]; - r:rule skolem:lemma4396. - -skolem:lemma4408 a r:Inference; - r:gives { - (3) :sort (3). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - skolem:lemma5908 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(() (3)) list:append (3)}] - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (3)]; - r:rule skolem:lemma4396. - -skolem:lemma4409 a r:Inference; - r:gives { - 3177 :numberToDigits (3 1 7 7). - }; - r:evidence ( - [ 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 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:lemma4392. - -skolem:lemma4410 a r:Inference; - r:gives { - (3 1 7 7) :sort (1 3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 7 7) list:firstRest (3 (1 7 7))}] - skolem:lemma5909 - skolem:lemma4705 - skolem:lemma4600 - [ a r:Fact; r:gives {(3 7 7) list:firstRest (3 (7 7))}] - [ a r:Fact; r:gives {((1) (3 7 7)) list:append (1 3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4411 a r:Inference; - r:gives { - (1 3 7 7) :digitsToNumber 1377 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ 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 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 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 1377]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma4397. - -skolem:lemma4412 a r:Inference; - r:gives { - (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 {(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 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:lemma4397. - -skolem:lemma4413 a r:Inference; - r:gives { - (2 (0 0 4)) :split ((0 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 4) list:firstRest (0 (0 4))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 4)]; - 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_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4414 a r:Inference; - r:gives { - (4) :sort (4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - skolem:lemma5911 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(() (4)) list:append (4)}] - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4)]; - r:rule skolem:lemma4396. - -skolem:lemma4415 a r:Inference; - r:gives { - (2 (0 0 5)) :split ((0 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 5) list:firstRest (0 (0 5))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 5)]; - 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_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4416 a r:Inference; - r:gives { - (5) :sort (5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - skolem:lemma5913 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(() (5)) list:append (5)}] - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5)]; - r:rule skolem:lemma4396. - -skolem:lemma4417 a r:Inference; - r:gives { - 5175 :numberToDigits (5 1 7 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5175 1000) math:integerQuotient 5}] - [ a r:Fact; r:gives {(5175 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5175]; - 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:lemma4392. - -skolem:lemma4418 a r:Inference; - r:gives { - (5 1 7 5) :sort (1 5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 7 5) list:firstRest (5 (1 7 5))}] - skolem:lemma5914 - skolem:lemma5915 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((1 5) (5 7)) list:append (1 5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 5 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4419 a r:Inference; - r:gives { - (1 5 5 7) :digitsToNumber 1557 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ 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 {(1000 500 50 7) math:sum 1557}] - ); - 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 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 1557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma4397. - -skolem:lemma4420 a r:Inference; - r:gives { - (7 5 5 1) :digitsToNumber 7551 . - }; - 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 1) math:sum 7551}] - ); - 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 7551]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma4397. - -skolem:lemma4421 a r:Inference; - r:gives { - (2 (0 0 7)) :split ((0 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 7) list:firstRest (0 (0 7))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 7)]; - 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_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4422 a r:Inference; - r:gives { - (7) :sort (7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - skolem:lemma5917 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(() (7)) list:append (7)}] - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7)]; - r:rule skolem:lemma4396. - -skolem:lemma4423 a r:Inference; - r:gives { - 7173 :numberToDigits (7 1 7 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7173 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7173 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7173]; - 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:lemma4392. - -skolem:lemma4424 a r:Inference; - r:gives { - (7 1 7 3) :sort (1 3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 7 3) list:firstRest (7 (1 7 3))}] - skolem:lemma5918 - skolem:lemma5919 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((1 3 7) (7)) list:append (1 3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4425 a r:Inference; - r:gives { - (2 (0 0 8)) :split ((0 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 8) list:firstRest (0 (0 8))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 8)]; - 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_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4426 a r:Inference; - r:gives { - (8) :sort (8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - skolem:lemma5921 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(() (8)) list:append (8)}] - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8)]; - r:rule skolem:lemma4396. - -skolem:lemma4427 a r:Inference; - r:gives { - 8172 :numberToDigits (8 1 7 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(8172 1000) math:integerQuotient 8}] - [ a r:Fact; r:gives {(8172 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8172]; - 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:lemma4392. - -skolem:lemma4428 a r:Inference; - r:gives { - (8 1 7 2) :sort (1 2 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 7 2) list:firstRest (8 (1 7 2))}] - skolem:lemma5922 - skolem:lemma5923 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((1 2 7) (8)) list:append (1 2 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4429 a r:Inference; - r:gives { - (2 (0 0 9)) :split ((0 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0 9) list:firstRest (0 (0 9))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0 9)]; - 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_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4430 a r:Inference; - r:gives { - (9) :sort (9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - skolem:lemma5925 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(() (9)) list:append (9)}] - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (9)]; - r:rule skolem:lemma4396. - -skolem:lemma4431 a r:Inference; - r:gives { - 9171 :numberToDigits (9 1 7 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9171 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9171 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9171]; - 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:lemma4392. - -skolem:lemma4432 a r:Inference; - r:gives { - (9 1 7 1) :sort (1 1 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 7 1) list:firstRest (9 (1 7 1))}] - skolem:lemma5926 - skolem:lemma5927 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((1 1 7) (9)) list:append (1 1 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4433 a r:Inference; - r:gives { - (1 1 7 9) :digitsToNumber 1179 . - }; - 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 {(7 10) math:product 70}] - [ a r:Fact; r:gives {(1000 100 70 9) math:sum 1179}] - ); - 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 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 1179]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4434 a r:Inference; - r:gives { - (9 7 1 1) :digitsToNumber 9711 . - }; - 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 {(1 10) math:product 10}] - [ a r:Fact; r:gives {(9000 700 10 1) math:sum 9711}] - ); - 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 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 9711]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma4397. - -skolem:lemma4435 a r:Inference; - r:gives { - (2 (0 1 0)) :split ((0 1 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 0) list:firstRest (0 (1 0))}] - [ a r:Fact; r:gives {(0 1 0) list:firstRest (0 (1 0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 0)]; - 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_2"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4436 a r:Inference; - r:gives { - (0 1 0) :sort (0 0 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 0) list:firstRest (0 (1 0))}] - skolem:lemma5929 - skolem:lemma4506 - skolem:lemma4705 - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {((0) (0 1)) list:append (0 0 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 0)]; - 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_2"]; r:boundTo (1 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 (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:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4437 a r:Inference; - r:gives { - (2 (0 1 1)) :split ((0 1 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 1) list:firstRest (0 (1 1))}] - [ a r:Fact; r:gives {(0 1 1) list:firstRest (0 (1 1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 1)]; - 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_2"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4438 a r:Inference; - r:gives { - (0 1 1) :sort (0 1 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 1) list:firstRest (0 (1 1))}] - skolem:lemma5931 - skolem:lemma4395 - skolem:lemma4680 - [ a r:Fact; r:gives {(0 1 1) list:firstRest (0 (1 1))}] - [ a r:Fact; r:gives {(() (0 1 1)) list:append (0 1 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 1)]; - 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_2"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4439 a r:Inference; - r:gives { - (2 (0 1 2)) :split ((0 1 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 2) list:firstRest (0 (1 2))}] - [ a r:Fact; r:gives {(0 1 2) list:firstRest (0 (1 2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 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_2"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4440 a r:Inference; - r:gives { - (0 1 2) :sort (0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 2) list:firstRest (0 (1 2))}] - skolem:lemma5933 - skolem:lemma4395 - skolem:lemma4694 - [ a r:Fact; r:gives {(0 1 2) list:firstRest (0 (1 2))}] - [ a r:Fact; r:gives {(() (0 1 2)) list:append (0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 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_2"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4441 a r:Inference; - r:gives { - (2 (0 1 3)) :split ((0 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 3) list:firstRest (0 (1 3))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 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_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4442 a r:Inference; - r:gives { - (0 1) :sort (0 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - skolem:lemma5935 - skolem:lemma4395 - skolem:lemma4705 - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {(() (0 1)) list:append (0 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1)]; - 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4443 a r:Inference; - r:gives { - 3087 :numberToDigits (3 0 8 7). - }; - r:evidence ( - [ 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 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:lemma4392. - -skolem:lemma4444 a r:Inference; - r:gives { - (3 0 8 7) :sort (0 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 8 7) list:firstRest (3 (0 8 7))}] - skolem:lemma5936 - skolem:lemma4506 - skolem:lemma4627 - [ a r:Fact; r:gives {(3 7 8) list:firstRest (3 (7 8))}] - [ a r:Fact; r:gives {((0) (3 7 8)) list:append (0 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4445 a r:Inference; - r:gives { - (0 3 7 8) :digitsToNumber 378 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ 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 {(0 300 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 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 378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma4397. - -skolem:lemma4446 a r:Inference; - r:gives { - (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 {(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 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:lemma4397. - -skolem:lemma4447 a r:Inference; - r:gives { - (2 (0 1 4)) :split ((0 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 4) list:firstRest (0 (1 4))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 4)]; - 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_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4448 a r:Inference; - r:gives { - 4086 :numberToDigits (4 0 8 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4086 1000) math:integerQuotient 4}] - [ a r:Fact; r:gives {(4086 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4086]; - 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:lemma4392. - -skolem:lemma4449 a r:Inference; - r:gives { - (4 0 8 6) :sort (0 4 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 8 6) list:firstRest (4 (0 8 6))}] - skolem:lemma5938 - skolem:lemma4506 - skolem:lemma4625 - [ a r:Fact; r:gives {(4 6 8) list:firstRest (4 (6 8))}] - [ a r:Fact; r:gives {((0) (4 6 8)) list:append (0 4 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 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 (8 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 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 4 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4450 a r:Inference; - r:gives { - (0 4 6 8) :digitsToNumber 468 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ 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 {(0 400 60 8) math:sum 468}] - ); - 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 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 468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma4397. - -skolem:lemma4451 a r:Inference; - r:gives { - (8 6 4 0) :digitsToNumber 8640 . - }; - 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 0) math:sum 8640}] - ); - 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 8640]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma4397. - -skolem:lemma4452 a r:Inference; - r:gives { - (2 (0 1 5)) :split ((0 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 5) list:firstRest (0 (1 5))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 5)]; - 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_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4453 a r:Inference; - r:gives { - 5085 :numberToDigits (5 0 8 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5085 1000) math:integerQuotient 5}] - [ a r:Fact; r:gives {(5085 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5085]; - 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:lemma4392. - -skolem:lemma4454 a r:Inference; - r:gives { - (5 0 8 5) :sort (0 5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 8 5) list:firstRest (5 (0 8 5))}] - skolem:lemma5940 - skolem:lemma5941 - skolem:lemma4426 - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {((0 5) (5 8)) list:append (0 5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 5 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4455 a r:Inference; - r:gives { - (0 5 5 8) :digitsToNumber 558 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ 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 {(0 500 50 8) math:sum 558}] - ); - 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 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 558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma4397. - -skolem:lemma4456 a r:Inference; - r:gives { - (8 5 5 0) :digitsToNumber 8550 . - }; - 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 0) math:sum 8550}] - ); - 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 8550]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma4397. - -skolem:lemma4457 a r:Inference; - r:gives { - (2 (0 1 6)) :split ((0 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 6) list:firstRest (0 (1 6))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 6)]; - 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_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4458 a r:Inference; - r:gives { - (6) :sort (6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - skolem:lemma5943 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(() (6)) list:append (6)}] - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6)]; - r:rule skolem:lemma4396. - -skolem:lemma4459 a r:Inference; - r:gives { - 6084 :numberToDigits (6 0 8 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(6084 1000) math:integerQuotient 6}] - [ a r:Fact; r:gives {(6084 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6084]; - 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:lemma4392. - -skolem:lemma4460 a r:Inference; - r:gives { - (6 0 8 4) :sort (0 4 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 8 4) list:firstRest (6 (0 8 4))}] - skolem:lemma5944 - skolem:lemma5945 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((0 4) (6 8)) list:append (0 4 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 4 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4461 a r:Inference; - r:gives { - (2 (0 1 7)) :split ((0 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 7) list:firstRest (0 (1 7))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 7)]; - 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_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4462 a r:Inference; - r:gives { - 7083 :numberToDigits (7 0 8 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7083 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7083 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7083]; - 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:lemma4392. - -skolem:lemma4463 a r:Inference; - r:gives { - (7 0 8 3) :sort (0 3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 8 3) list:firstRest (7 (0 8 3))}] - skolem:lemma5947 - skolem:lemma5948 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((0 3) (7 8)) list:append (0 3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4464 a r:Inference; - r:gives { - (2 (0 1 8)) :split ((0 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 8) list:firstRest (0 (1 8))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 8)]; - 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_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4465 a r:Inference; - r:gives { - 8082 :numberToDigits (8 0 8 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(8082 1000) math:integerQuotient 8}] - [ a r:Fact; r:gives {(8082 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8082]; - 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:lemma4392. - -skolem:lemma4466 a r:Inference; - r:gives { - (8 0 8 2) :sort (0 2 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 8 2) list:firstRest (8 (0 8 2))}] - skolem:lemma5950 - skolem:lemma5951 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((0 2 8) (8)) list:append (0 2 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4467 a r:Inference; - r:gives { - (2 (0 1 9)) :split ((0 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1 9) list:firstRest (0 (1 9))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1 9)]; - 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_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4468 a r:Inference; - r:gives { - 9081 :numberToDigits (9 0 8 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9081 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9081 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9081]; - 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:lemma4392. - -skolem:lemma4469 a r:Inference; - r:gives { - (9 0 8 1) :sort (0 1 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 8 1) list:firstRest (9 (0 8 1))}] - skolem:lemma5953 - skolem:lemma5954 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((0 1 8) (9)) list:append (0 1 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4470 a r:Inference; - r:gives { - (0 1 8 9) :digitsToNumber 189 . - }; - 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 {(8 10) math:product 80}] - [ a r:Fact; r:gives {(0 100 80 9) math:sum 189}] - ); - 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 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 189]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4471 a r:Inference; - r:gives { - (9 8 1 0) :digitsToNumber 9810 . - }; - 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 {(1 10) math:product 10}] - [ a r:Fact; r:gives {(9000 800 10 0) math:sum 9810}] - ); - 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 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 9810]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma4397. - -skolem:lemma4472 a r:Inference; - r:gives { - (2 (0 2 0)) :split ((0 2 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 0) list:firstRest (0 (2 0))}] - [ a r:Fact; r:gives {(0 2 0) list:firstRest (0 (2 0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 0)]; - 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_2"]; r:boundTo (2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4473 a r:Inference; - r:gives { - (0 2 0) :sort (0 0 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 0) list:firstRest (0 (2 0))}] - skolem:lemma5956 - skolem:lemma4506 - skolem:lemma4833 - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {((0) (0 2)) list:append (0 0 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 0)]; - 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_2"]; r:boundTo (2 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 (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:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4474 a r:Inference; - r:gives { - (2 (0 2 1)) :split ((0 2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 1) list:firstRest (0 (2 1))}] - [ a r:Fact; r:gives {(0 2 1) list:firstRest (0 (2 1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 1)]; - 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_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4475 a r:Inference; - r:gives { - (0 2 1) :sort (0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 1) list:firstRest (0 (2 1))}] - skolem:lemma5958 - skolem:lemma4395 - skolem:lemma4807 - [ a r:Fact; r:gives {(0 1 2) list:firstRest (0 (1 2))}] - [ a r:Fact; r:gives {(() (0 1 2)) list:append (0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 1)]; - 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_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4476 a r:Inference; - r:gives { - (2 (0 2 2)) :split ((0 2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 2) list:firstRest (0 (2 2))}] - [ a r:Fact; r:gives {(0 2 2) list:firstRest (0 (2 2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 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_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4477 a r:Inference; - r:gives { - (0 2 2) :sort (0 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 2) list:firstRest (0 (2 2))}] - skolem:lemma5960 - skolem:lemma4395 - skolem:lemma4822 - [ a r:Fact; r:gives {(0 2 2) list:firstRest (0 (2 2))}] - [ a r:Fact; r:gives {(() (0 2 2)) list:append (0 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 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_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4478 a r:Inference; - r:gives { - (2 (0 2 3)) :split ((0 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 3) list:firstRest (0 (2 3))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 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_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4479 a r:Inference; - r:gives { - (0 2) :sort (0 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - skolem:lemma5962 - skolem:lemma4395 - skolem:lemma4833 - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {(() (0 2)) list:append (0 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4480 a r:Inference; - r:gives { - (2 (0 2 4)) :split ((0 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 4) list:firstRest (0 (2 4))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 4)]; - 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_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4481 a r:Inference; - r:gives { - 3996 :numberToDigits (3 9 9 6). - }; - r:evidence ( - [ 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 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:lemma4392. - -skolem:lemma4482 a r:Inference; - r:gives { - (3 9 9 6) :sort (3 6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 9 6) list:firstRest (3 (9 9 6))}] - skolem:lemma5964 - skolem:lemma4395 - skolem:lemma5891 - [ a r:Fact; r:gives {(3 6 9 9) list:firstRest (3 (6 9 9))}] - [ a r:Fact; r:gives {(() (3 6 9 9)) list:append (3 6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4483 a r:Inference; - r:gives { - (3 6 9 9) :digitsToNumber 3699 . - }; - r:evidence ( - [ 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 {(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 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 3699]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4484 a r:Inference; - r:gives { - (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 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]; - 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 9963]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma4397. - -skolem:lemma4485 a r:Inference; - r:gives { - (2 (0 2 5)) :split ((0 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 5) list:firstRest (0 (2 5))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 5)]; - 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_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4486 a r:Inference; - r:gives { - 4995 :numberToDigits (4 9 9 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4995 1000) math:integerQuotient 4}] - [ a r:Fact; r:gives {(4995 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4995]; - 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:lemma4392. - -skolem:lemma4487 a r:Inference; - r:gives { - (4 9 9 5) :sort (4 5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 9 5) list:firstRest (4 (9 9 5))}] - skolem:lemma5966 - skolem:lemma4395 - skolem:lemma5889 - [ a r:Fact; r:gives {(4 5 9 9) list:firstRest (4 (5 9 9))}] - [ a r:Fact; r:gives {(() (4 5 9 9)) list:append (4 5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4488 a r:Inference; - r:gives { - (4 5 9 9) :digitsToNumber 4599 . - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ 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 {(4000 500 90 9) math:sum 4599}] - ); - 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 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 4599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4489 a r:Inference; - r:gives { - (9 9 5 4) :digitsToNumber 9954 . - }; - 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 4) math:sum 9954}] - ); - 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 9954]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma4397. - -skolem:lemma4490 a r:Inference; - r:gives { - (2 (0 2 6)) :split ((0 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 6) list:firstRest (0 (2 6))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 6)]; - 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_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4491 a r:Inference; - r:gives { - 5994 :numberToDigits (5 9 9 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(5994 1000) math:integerQuotient 5}] - [ a r:Fact; r:gives {(5994 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5994]; - 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:lemma4392. - -skolem:lemma4492 a r:Inference; - r:gives { - (5 9 9 4) :sort (4 5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 9 4) list:firstRest (5 (9 9 4))}] - skolem:lemma5968 - skolem:lemma4414 - skolem:lemma4650 - [ a r:Fact; r:gives {(5 9 9) list:firstRest (5 (9 9))}] - [ a r:Fact; r:gives {((4) (5 9 9)) list:append (4 5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 4)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4493 a r:Inference; - r:gives { - (2 (0 2 7)) :split ((0 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 7) list:firstRest (0 (2 7))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 7)]; - 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_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4494 a r:Inference; - r:gives { - 6993 :numberToDigits (6 9 9 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(6993 1000) math:integerQuotient 6}] - [ a r:Fact; r:gives {(6993 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6993]; - 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:lemma4392. - -skolem:lemma4495 a r:Inference; - r:gives { - (6 9 9 3) :sort (3 6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 9 3) list:firstRest (6 (9 9 3))}] - skolem:lemma5970 - skolem:lemma4408 - skolem:lemma4650 - [ a r:Fact; r:gives {(6 9 9) list:firstRest (6 (9 9))}] - [ a r:Fact; r:gives {((3) (6 9 9)) list:append (3 6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 3)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4496 a r:Inference; - r:gives { - (2 (0 2 8)) :split ((0 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 8) list:firstRest (0 (2 8))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 8)]; - 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_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4497 a r:Inference; - r:gives { - 7992 :numberToDigits (7 9 9 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(7992 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7992 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7992]; - 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:lemma4392. - -skolem:lemma4498 a r:Inference; - r:gives { - (7 9 9 2) :sort (2 7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 9 2) list:firstRest (7 (9 9 2))}] - skolem:lemma5972 - skolem:lemma4833 - skolem:lemma4650 - [ a r:Fact; r:gives {(7 9 9) list:firstRest (7 (9 9))}] - [ a r:Fact; r:gives {((2) (7 9 9)) list:append (2 7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 2)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4499 a r:Inference; - r:gives { - (2 (0 2 9)) :split ((0 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2 9) list:firstRest (0 (2 9))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 2 9)]; - 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_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4500 a r:Inference; - r:gives { - 8991 :numberToDigits (8 9 9 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(8991 1000) math:integerQuotient 8}] - [ a r:Fact; r:gives {(8991 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8991]; - 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:lemma4392. - -skolem:lemma4501 a r:Inference; - r:gives { - (8 9 9 1) :sort (1 8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 9 1) list:firstRest (8 (9 9 1))}] - skolem:lemma5974 - skolem:lemma4705 - skolem:lemma4650 - [ a r:Fact; r:gives {(8 9 9) list:firstRest (8 (9 9))}] - [ a r:Fact; r:gives {((1) (8 9 9)) list:append (1 8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9 1)]; - 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 9)]; - 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 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4502 a r:Inference; - r:gives { - (2 (0 3 0)) :split ((0 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 0) list:firstRest (0 (3 0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 0)]; - 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_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4503 a r:Inference; - r:gives { - (2 (0 3 1)) :split ((0 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 1) list:firstRest (0 (3 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 1)]; - 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_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4504 a r:Inference; - r:gives { - (2 (0 3 2)) :split ((0 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 2) list:firstRest (0 (3 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 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_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4505 a r:Inference; - r:gives { - (2 (0 3 3)) :split ((0) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 3) list:firstRest (0 (3 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 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_2"]; r:boundTo (3 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4506 a r:Inference; - r:gives { - (0) :sort (0). - }; - r:evidence ( - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - skolem:lemma5979 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {(() (0)) list:append (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_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0)]; - r:rule skolem:lemma4396. - -skolem:lemma4507 a r:Inference; - r:gives { - (3 3) :sort (3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - skolem:lemma5980 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {((3) (3)) list:append (3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - 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_8"]; r:boundTo (3 3)]; - r:rule skolem:lemma4396. - -skolem:lemma4508 a r:Inference; - r:gives { - (2 (0 3 4)) :split ((0) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 4) list:firstRest (0 (3 4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 4)]; - 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_2"]; r:boundTo (3 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4509 a r:Inference; - r:gives { - (3 4) :sort (3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - skolem:lemma5982 - skolem:lemma4395 - skolem:lemma4414 - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(() (3 4)) list:append (3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma4510 a r:Inference; - r:gives { - (2 (0 3 5)) :split ((0) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 5) list:firstRest (0 (3 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 5)]; - 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_2"]; r:boundTo (3 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4511 a r:Inference; - r:gives { - (3 5) :sort (3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - skolem:lemma5984 - skolem:lemma4395 - skolem:lemma4416 - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(() (3 5)) list:append (3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4512 a r:Inference; - r:gives { - (2 (0 3 6)) :split ((0) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 6) list:firstRest (0 (3 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 6)]; - 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_2"]; r:boundTo (3 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4513 a r:Inference; - r:gives { - (3 6) :sort (3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - skolem:lemma5986 - skolem:lemma4395 - skolem:lemma4458 - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(() (3 6)) list:append (3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4514 a r:Inference; - r:gives { - (2 (0 3 7)) :split ((0) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 7) list:firstRest (0 (3 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 7)]; - 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_2"]; r:boundTo (3 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4515 a r:Inference; - r:gives { - (3 7) :sort (3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - skolem:lemma5988 - skolem:lemma4395 - skolem:lemma4422 - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(() (3 7)) list:append (3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4516 a r:Inference; - r:gives { - (2 (0 3 8)) :split ((0) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 8) list:firstRest (0 (3 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 8)]; - 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_2"]; r:boundTo (3 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4517 a r:Inference; - r:gives { - (3 8) :sort (3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - skolem:lemma5990 - skolem:lemma4395 - skolem:lemma4426 - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(() (3 8)) list:append (3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4518 a r:Inference; - r:gives { - (2 (0 3 9)) :split ((0) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3 9) list:firstRest (0 (3 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 3 9)]; - 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_2"]; r:boundTo (3 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4519 a r:Inference; - r:gives { - (3 9) :sort (3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - skolem:lemma5992 - skolem:lemma4395 - skolem:lemma4430 - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(() (3 9)) list:append (3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4520 a r:Inference; - r:gives { - (2 (0 4 0)) :split ((0 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 0) list:firstRest (0 (4 0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 0)]; - 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_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4521 a r:Inference; - r:gives { - (2 (0 4 1)) :split ((0 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 1) list:firstRest (0 (4 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 1)]; - 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_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4522 a r:Inference; - r:gives { - (2 (0 4 2)) :split ((0 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 2) list:firstRest (0 (4 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 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_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4523 a r:Inference; - r:gives { - (2 (0 4 3)) :split ((0) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 3) list:firstRest (0 (4 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 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_2"]; r:boundTo (4 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4524 a r:Inference; - r:gives { - (4 3) :sort (3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - skolem:lemma5997 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((3) (4)) list:append (3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma4525 a r:Inference; - r:gives { - (2 (0 4 4)) :split ((0) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 4) list:firstRest (0 (4 4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 4)]; - 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_2"]; r:boundTo (4 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4526 a r:Inference; - r:gives { - (4 4) :sort (4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - skolem:lemma5999 - skolem:lemma4414 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((4) (4)) list:append (4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma4527 a r:Inference; - r:gives { - (2 (0 4 5)) :split ((0) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 5) list:firstRest (0 (4 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 5)]; - 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_2"]; r:boundTo (4 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4528 a r:Inference; - r:gives { - (4 5) :sort (4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - skolem:lemma6001 - skolem:lemma4395 - skolem:lemma4416 - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(() (4 5)) list:append (4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4529 a r:Inference; - r:gives { - (2 (0 4 7)) :split ((0) (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 7) list:firstRest (0 (4 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 7)]; - 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_2"]; r:boundTo (4 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4530 a r:Inference; - r:gives { - (4 7) :sort (4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - skolem:lemma6003 - skolem:lemma4395 - skolem:lemma4422 - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(() (4 7)) list:append (4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4531 a r:Inference; - r:gives { - (2 (0 4 8)) :split ((0) (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 8) list:firstRest (0 (4 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 8)]; - 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_2"]; r:boundTo (4 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4532 a r:Inference; - r:gives { - (4 8) :sort (4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - skolem:lemma6005 - skolem:lemma4395 - skolem:lemma4426 - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(() (4 8)) list:append (4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4533 a r:Inference; - r:gives { - (2 (0 4 9)) :split ((0) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4 9) list:firstRest (0 (4 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4 9)]; - 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_2"]; r:boundTo (4 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4534 a r:Inference; - r:gives { - (4 9) :sort (4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - skolem:lemma6007 - skolem:lemma4395 - skolem:lemma4430 - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(() (4 9)) list:append (4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4535 a r:Inference; - r:gives { - (2 (0 5 0)) :split ((0 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 0) list:firstRest (0 (5 0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 0)]; - 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_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4536 a r:Inference; - r:gives { - (2 (0 5 1)) :split ((0 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 1) list:firstRest (0 (5 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 1)]; - 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_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4537 a r:Inference; - r:gives { - (2 (0 5 2)) :split ((0 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 2) list:firstRest (0 (5 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 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_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4538 a r:Inference; - r:gives { - (2 (0 5 3)) :split ((0) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 3) list:firstRest (0 (5 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 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_2"]; r:boundTo (5 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4539 a r:Inference; - r:gives { - (5 3) :sort (3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - skolem:lemma6012 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3) (5)) list:append (3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4540 a r:Inference; - r:gives { - (2 (0 5 4)) :split ((0) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 4) list:firstRest (0 (5 4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 4)]; - 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_2"]; r:boundTo (5 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4541 a r:Inference; - r:gives { - (5 4) :sort (4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - skolem:lemma6014 - skolem:lemma4414 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((4) (5)) list:append (4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4542 a r:Inference; - r:gives { - (2 (0 5 5)) :split ((0) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 5) list:firstRest (0 (5 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 5)]; - 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_2"]; r:boundTo (5 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4543 a r:Inference; - r:gives { - (5 5) :sort (5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - skolem:lemma6016 - skolem:lemma4416 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((5) (5)) list:append (5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4544 a r:Inference; - r:gives { - 5265 :numberToDigits (5 2 6 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5265 1000) math:integerQuotient 5}] - [ a r:Fact; r:gives {(5265 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5265]; - 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:lemma4392. - -skolem:lemma4545 a r:Inference; - r:gives { - (5 2 6 5) :sort (2 5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 6 5) list:firstRest (5 (2 6 5))}] - skolem:lemma6017 - skolem:lemma6018 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((2 5) (5 6)) list:append (2 5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4546 a r:Inference; - r:gives { - (2 (0 5 6)) :split ((0) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 6) list:firstRest (0 (5 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 6)]; - 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_2"]; r:boundTo (5 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4547 a r:Inference; - r:gives { - (5 6) :sort (5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - skolem:lemma6020 - skolem:lemma4395 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(() (5 6)) list:append (5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4548 a r:Inference; - r:gives { - 6264 :numberToDigits (6 2 6 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(6264 1000) math:integerQuotient 6}] - [ a r:Fact; r:gives {(6264 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6264]; - 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:lemma4392. - -skolem:lemma4549 a r:Inference; - r:gives { - (6 2 6 4) :sort (2 4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 6 4) list:firstRest (6 (2 6 4))}] - skolem:lemma6021 - skolem:lemma6022 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((2 4 6) (6)) list:append (2 4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4550 a r:Inference; - r:gives { - (2 (0 5 7)) :split ((0) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 7) list:firstRest (0 (5 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 7)]; - 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_2"]; r:boundTo (5 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4551 a r:Inference; - r:gives { - (5 7) :sort (5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - skolem:lemma6024 - skolem:lemma4395 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(() (5 7)) list:append (5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4552 a r:Inference; - r:gives { - 7263 :numberToDigits (7 2 6 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7263 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7263 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7263]; - 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:lemma4392. - -skolem:lemma4553 a r:Inference; - r:gives { - (7 2 6 3) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 6 3) list:firstRest (7 (2 6 3))}] - skolem:lemma6025 - skolem:lemma6026 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((2 3 6) (7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4554 a r:Inference; - r:gives { - (2 (0 5 8)) :split ((0) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 8) list:firstRest (0 (5 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 8)]; - 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_2"]; r:boundTo (5 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4555 a r:Inference; - r:gives { - (5 8) :sort (5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - skolem:lemma6028 - skolem:lemma4395 - skolem:lemma4426 - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(() (5 8)) list:append (5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4556 a r:Inference; - r:gives { - 8262 :numberToDigits (8 2 6 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(8262 1000) math:integerQuotient 8}] - [ a r:Fact; r:gives {(8262 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8262]; - 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:lemma4392. - -skolem:lemma4557 a r:Inference; - r:gives { - (8 2 6 2) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 6 2) list:firstRest (8 (2 6 2))}] - skolem:lemma6029 - skolem:lemma6030 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((2 2 6) (8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4558 a r:Inference; - r:gives { - (2 (0 5 9)) :split ((0) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5 9) list:firstRest (0 (5 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5 9)]; - 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_2"]; r:boundTo (5 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4559 a r:Inference; - r:gives { - (5 9) :sort (5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - skolem:lemma6032 - skolem:lemma4395 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(() (5 9)) list:append (5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4560 a r:Inference; - r:gives { - 9261 :numberToDigits (9 2 6 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9261 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9261 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9261]; - 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:lemma4392. - -skolem:lemma4561 a r:Inference; - r:gives { - (9 2 6 1) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 6 1) list:firstRest (9 (2 6 1))}] - skolem:lemma6033 - skolem:lemma6034 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((1 2 6) (9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4562 a r:Inference; - r:gives { - (2 (0 6 1)) :split ((0 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 1) list:firstRest (0 (6 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 1)]; - 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_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4563 a r:Inference; - r:gives { - (2 (0 6 2)) :split ((0 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 2) list:firstRest (0 (6 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 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_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4564 a r:Inference; - r:gives { - (2 (0 6 3)) :split ((0) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 3) list:firstRest (0 (6 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 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_2"]; r:boundTo (6 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4565 a r:Inference; - r:gives { - (6 3) :sort (3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - skolem:lemma6038 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3) (6)) list:append (3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4566 a r:Inference; - r:gives { - (2 (0 6 5)) :split ((0) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 5) list:firstRest (0 (6 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 5)]; - 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_2"]; r:boundTo (6 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4567 a r:Inference; - r:gives { - (6 5) :sort (5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - skolem:lemma6040 - skolem:lemma4416 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((5) (6)) list:append (5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4568 a r:Inference; - r:gives { - (2 (0 6 6)) :split ((0) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 6) list:firstRest (0 (6 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 6)]; - 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_2"]; r:boundTo (6 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4569 a r:Inference; - r:gives { - (6 6) :sort (6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - skolem:lemma6042 - skolem:lemma4458 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((6) (6)) list:append (6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4570 a r:Inference; - r:gives { - 6354 :numberToDigits (6 3 5 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(6354 1000) math:integerQuotient 6}] - [ a r:Fact; r:gives {(6354 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6354]; - 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:lemma4392. - -skolem:lemma4571 a r:Inference; - r:gives { - (6 3 5 4) :sort (3 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 5 4) list:firstRest (6 (3 5 4))}] - skolem:lemma6043 - skolem:lemma4980 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 4 5) (6)) list:append (3 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4572 a r:Inference; - r:gives { - (3 4 5 6) :digitsToNumber 3456 . - }; - r:evidence ( - [ 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 {(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 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 3456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma4397. - -skolem:lemma4573 a r:Inference; - r:gives { - (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 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]; - 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 6543]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma4397. - -skolem:lemma4574 a r:Inference; - r:gives { - (2 (0 6 7)) :split ((0) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 7) list:firstRest (0 (6 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 7)]; - 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_2"]; r:boundTo (6 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4575 a r:Inference; - r:gives { - (6 7) :sort (6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - skolem:lemma6045 - skolem:lemma4395 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(() (6 7)) list:append (6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4576 a r:Inference; - r:gives { - 7353 :numberToDigits (7 3 5 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7353 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7353 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7353]; - 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:lemma4392. - -skolem:lemma4577 a r:Inference; - r:gives { - (7 3 5 3) :sort (3 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 5 3) list:firstRest (7 (3 5 3))}] - skolem:lemma6046 - skolem:lemma4978 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 3 5) (7)) list:append (3 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4578 a r:Inference; - r:gives { - (3 3 5 7) :digitsToNumber 3357 . - }; - 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 {(5 10) math:product 50}] - [ 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 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 3357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma4397. - -skolem:lemma4579 a r:Inference; - r:gives { - (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 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]; - 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 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma4397. - -skolem:lemma4580 a r:Inference; - r:gives { - (2 (0 6 8)) :split ((0) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 8) list:firstRest (0 (6 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 8)]; - 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_2"]; r:boundTo (6 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4581 a r:Inference; - r:gives { - (6 8) :sort (6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - skolem:lemma6048 - skolem:lemma4395 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(() (6 8)) list:append (6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4582 a r:Inference; - r:gives { - (2 (0 6 9)) :split ((0) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6 9) list:firstRest (0 (6 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6 9)]; - 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_2"]; r:boundTo (6 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4583 a r:Inference; - r:gives { - (6 9) :sort (6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - skolem:lemma6050 - skolem:lemma4395 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(() (6 9)) list:append (6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4584 a r:Inference; - r:gives { - 9351 :numberToDigits (9 3 5 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9351 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9351 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9351]; - 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:lemma4392. - -skolem:lemma4585 a r:Inference; - r:gives { - (9 3 5 1) :sort (1 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 5 1) list:firstRest (9 (3 5 1))}] - skolem:lemma6051 - skolem:lemma6052 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((1 3 5) (9)) list:append (1 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4586 a r:Inference; - r:gives { - (1 3 5 9) :digitsToNumber 1359 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ 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 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 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 1359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4587 a r:Inference; - r:gives { - (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 {(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 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:lemma4397. - -skolem:lemma4588 a r:Inference; - r:gives { - (2 (0 7 0)) :split ((0 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 0) list:firstRest (0 (7 0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 0)]; - 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_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4589 a r:Inference; - r:gives { - (2 (0 7 1)) :split ((0 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 1) list:firstRest (0 (7 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 1)]; - 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_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4590 a r:Inference; - r:gives { - (2 (0 7 2)) :split ((0 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 2) list:firstRest (0 (7 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 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_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4591 a r:Inference; - r:gives { - (2 (0 7 3)) :split ((0) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 3) list:firstRest (0 (7 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 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_2"]; r:boundTo (7 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4592 a r:Inference; - r:gives { - (7 3) :sort (3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - skolem:lemma6057 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3) (7)) list:append (3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4593 a r:Inference; - r:gives { - (2 (0 7 4)) :split ((0) (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 4) list:firstRest (0 (7 4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 4)]; - 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_2"]; r:boundTo (7 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4594 a r:Inference; - r:gives { - (7 4) :sort (4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - skolem:lemma6059 - skolem:lemma4414 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4) (7)) list:append (4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4595 a r:Inference; - r:gives { - (2 (0 7 5)) :split ((0) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 5) list:firstRest (0 (7 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 5)]; - 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_2"]; r:boundTo (7 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4596 a r:Inference; - r:gives { - (7 5) :sort (5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - skolem:lemma6061 - skolem:lemma4416 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((5) (7)) list:append (5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4597 a r:Inference; - r:gives { - (2 (0 7 6)) :split ((0) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 6) list:firstRest (0 (7 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 6)]; - 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_2"]; r:boundTo (7 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4598 a r:Inference; - r:gives { - (7 6) :sort (6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - skolem:lemma6063 - skolem:lemma4458 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((6) (7)) list:append (6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4599 a r:Inference; - r:gives { - (2 (0 7 7)) :split ((0) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 7) list:firstRest (0 (7 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 7)]; - 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_2"]; r:boundTo (7 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4600 a r:Inference; - r:gives { - (7 7) :sort (7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - skolem:lemma6065 - skolem:lemma4422 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((7) (7)) list:append (7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4601 a r:Inference; - r:gives { - 7443 :numberToDigits (7 4 4 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7443 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7443 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7443]; - 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:lemma4392. - -skolem:lemma4602 a r:Inference; - r:gives { - (7 4 4 3) :sort (3 4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 4 3) list:firstRest (7 (4 4 3))}] - skolem:lemma6066 - skolem:lemma5103 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 4 4) (7)) list:append (3 4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4603 a r:Inference; - r:gives { - (3 4 4 7) :digitsToNumber 3447 . - }; - r:evidence ( - [ 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 {(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 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 3447]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma4397. - -skolem:lemma4604 a r:Inference; - r:gives { - (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 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]; - 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 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma4397. - -skolem:lemma4605 a r:Inference; - r:gives { - (2 (0 7 8)) :split ((0) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 8) list:firstRest (0 (7 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 8)]; - 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_2"]; r:boundTo (7 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4606 a r:Inference; - r:gives { - (7 8) :sort (7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - skolem:lemma6068 - skolem:lemma4395 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(() (7 8)) list:append (7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4607 a r:Inference; - r:gives { - 8442 :numberToDigits (8 4 4 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(8442 1000) math:integerQuotient 8}] - [ a r:Fact; r:gives {(8442 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8442]; - 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:lemma4392. - -skolem:lemma4608 a r:Inference; - r:gives { - (8 4 4 2) :sort (2 4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 4 2) list:firstRest (8 (4 4 2))}] - skolem:lemma6069 - skolem:lemma6070 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((2 4 4) (8)) list:append (2 4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4609 a r:Inference; - r:gives { - (2 (0 7 9)) :split ((0) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7 9) list:firstRest (0 (7 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7 9)]; - 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_2"]; r:boundTo (7 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4610 a r:Inference; - r:gives { - (7 9) :sort (7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - skolem:lemma6072 - skolem:lemma4395 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(() (7 9)) list:append (7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4611 a r:Inference; - r:gives { - 9441 :numberToDigits (9 4 4 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9441 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9441 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9441]; - 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:lemma4392. - -skolem:lemma4612 a r:Inference; - r:gives { - (9 4 4 1) :sort (1 4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 4 1) list:firstRest (9 (4 4 1))}] - skolem:lemma6073 - skolem:lemma6074 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((1 4 4) (9)) list:append (1 4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 4 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4613 a r:Inference; - r:gives { - (1 4 4 9) :digitsToNumber 1449 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ 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 {(1000 400 40 9) math:sum 1449}] - ); - 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 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 1449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4614 a r:Inference; - r:gives { - (9 4 4 1) :digitsToNumber 9441 . - }; - 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 1) math:sum 9441}] - ); - 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 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma4397. - -skolem:lemma4615 a r:Inference; - r:gives { - (2 (0 8 0)) :split ((0 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 0) list:firstRest (0 (8 0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 0)]; - 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_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4616 a r:Inference; - r:gives { - (2 (0 8 1)) :split ((0 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 1) list:firstRest (0 (8 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 1)]; - 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_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4617 a r:Inference; - r:gives { - (2 (0 8 2)) :split ((0 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 2) list:firstRest (0 (8 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 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_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4618 a r:Inference; - r:gives { - (2 (0 8 3)) :split ((0) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 3) list:firstRest (0 (8 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 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_2"]; r:boundTo (8 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4619 a r:Inference; - r:gives { - (8 3) :sort (3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - skolem:lemma6079 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3) (8)) list:append (3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4620 a r:Inference; - r:gives { - (2 (0 8 4)) :split ((0) (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 4) list:firstRest (0 (8 4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 4)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4621 a r:Inference; - r:gives { - (8 4) :sort (4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - skolem:lemma6081 - skolem:lemma4414 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4) (8)) list:append (4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4622 a r:Inference; - r:gives { - (2 (0 8 5)) :split ((0) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 5) list:firstRest (0 (8 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 5)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4623 a r:Inference; - r:gives { - (8 5) :sort (5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - skolem:lemma6083 - skolem:lemma4416 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((5) (8)) list:append (5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4624 a r:Inference; - r:gives { - (2 (0 8 6)) :split ((0) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 6) list:firstRest (0 (8 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 6)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4625 a r:Inference; - r:gives { - (8 6) :sort (6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - skolem:lemma6085 - skolem:lemma4458 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((6) (8)) list:append (6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4626 a r:Inference; - r:gives { - (2 (0 8 7)) :split ((0) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 7) list:firstRest (0 (8 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 7)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4627 a r:Inference; - r:gives { - (8 7) :sort (7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - skolem:lemma6087 - skolem:lemma4422 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((7) (8)) list:append (7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4628 a r:Inference; - r:gives { - (2 (0 8 8)) :split ((0) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 8) list:firstRest (0 (8 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 8)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4629 a r:Inference; - r:gives { - (8 8) :sort (8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - skolem:lemma6089 - skolem:lemma4426 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((8) (8)) list:append (8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4630 a r:Inference; - r:gives { - (2 (0 8 9)) :split ((0) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 9) list:firstRest (0 (8 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 9)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4631 a r:Inference; - r:gives { - (8 9) :sort (8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - skolem:lemma6091 - skolem:lemma4395 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(() (8 9)) list:append (8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4632 a r:Inference; - r:gives { - 9531 :numberToDigits (9 5 3 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9531 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9531 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9531]; - 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:lemma4392. - -skolem:lemma4633 a r:Inference; - r:gives { - (9 5 3 1) :sort (1 3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 3 1) list:firstRest (9 (5 3 1))}] - skolem:lemma6092 - skolem:lemma6093 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((1 3 5) (9)) list:append (1 3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4634 a r:Inference; - r:gives { - (2 (0 9 0)) :split ((0 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 0) list:firstRest (0 (9 0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 0)]; - 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_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4635 a r:Inference; - r:gives { - (2 (0 9 1)) :split ((0 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 1) list:firstRest (0 (9 1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 1)]; - 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_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4636 a r:Inference; - r:gives { - (2 (0 9 2)) :split ((0 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 2) list:firstRest (0 (9 2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 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_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4637 a r:Inference; - r:gives { - (2 (0 9 3)) :split ((0) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 3) list:firstRest (0 (9 3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 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_2"]; r:boundTo (9 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4638 a r:Inference; - r:gives { - (9 3) :sort (3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - skolem:lemma6098 - skolem:lemma4408 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3) (9)) list:append (3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4639 a r:Inference; - r:gives { - (2 (0 9 4)) :split ((0) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 4) list:firstRest (0 (9 4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 4)]; - 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_2"]; r:boundTo (9 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4640 a r:Inference; - r:gives { - (9 4) :sort (4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - skolem:lemma6100 - skolem:lemma4414 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4) (9)) list:append (4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4641 a r:Inference; - r:gives { - (2 (0 9 5)) :split ((0) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 5) list:firstRest (0 (9 5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 5)]; - 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_2"]; r:boundTo (9 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4642 a r:Inference; - r:gives { - (9 5) :sort (5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - skolem:lemma6102 - skolem:lemma4416 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5) (9)) list:append (5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4643 a r:Inference; - r:gives { - (2 (0 9 6)) :split ((0) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 6) list:firstRest (0 (9 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 6)]; - 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_2"]; r:boundTo (9 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4644 a r:Inference; - r:gives { - (9 6) :sort (6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - skolem:lemma6104 - skolem:lemma4458 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6) (9)) list:append (6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4645 a r:Inference; - r:gives { - (2 (0 9 7)) :split ((0) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 7) list:firstRest (0 (9 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 7)]; - 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_2"]; r:boundTo (9 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4646 a r:Inference; - r:gives { - (9 7) :sort (7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - skolem:lemma6106 - skolem:lemma4422 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((7) (9)) list:append (7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4647 a r:Inference; - r:gives { - (2 (0 9 8)) :split ((0) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 8) list:firstRest (0 (9 8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 8)]; - 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_2"]; r:boundTo (9 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4648 a r:Inference; - r:gives { - (9 8) :sort (8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - skolem:lemma6108 - skolem:lemma4426 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((8) (9)) list:append (8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4649 a r:Inference; - r:gives { - (2 (0 9 9)) :split ((0) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 9) list:firstRest (0 (9 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 9)]; - 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_2"]; r:boundTo (9 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4650 a r:Inference; - r:gives { - (9 9) :sort (9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - skolem:lemma6110 - skolem:lemma4430 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((9) (9)) list:append (9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4651 a r:Inference; - r:gives { - 9621 :numberToDigits (9 6 2 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(9621 1000) math:integerQuotient 9}] - [ a r:Fact; r:gives {(9621 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9621]; - 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:lemma4392. - -skolem:lemma4652 a r:Inference; - r:gives { - (9 6 2 1) :sort (1 2 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 2 1) list:firstRest (9 (6 2 1))}] - skolem:lemma6111 - skolem:lemma6112 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((1 2 6) (9)) list:append (1 2 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4653 a r:Inference; - r:gives { - (2 (1 0 0)) :split ((1 0 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 0) list:firstRest (1 (0 0))}] - [ a r:Fact; r:gives {(1 0 0) list:firstRest (1 (0 0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4654 a r:Inference; - r:gives { - (1 0 0) :sort (0 0 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 0) list:firstRest (1 (0 0))}] - skolem:lemma6113 - skolem:lemma4407 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {((0 0) (1)) list:append (0 0 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 0 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4655 a r:Inference; - r:gives { - (2 (1 0 1)) :split ((1 0 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 1) list:firstRest (1 (0 1))}] - [ a r:Fact; r:gives {(1 0 1) list:firstRest (1 (0 1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4656 a r:Inference; - r:gives { - (1 0 1) :sort (0 1 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 1) list:firstRest (1 (0 1))}] - skolem:lemma6114 - skolem:lemma4442 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {((0 1) (1)) list:append (0 1 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4657 a r:Inference; - r:gives { - (2 (1 0 2)) :split ((1 0 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 2) list:firstRest (1 (0 2))}] - [ a r:Fact; r:gives {(1 0 2) list:firstRest (1 (0 2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4658 a r:Inference; - r:gives { - (1 0 2) :sort (0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 2) list:firstRest (1 (0 2))}] - skolem:lemma6115 - skolem:lemma4506 - skolem:lemma4833 - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {((0) (1 2)) list:append (0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 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:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4659 a r:Inference; - r:gives { - (2 (1 0 3)) :split ((1 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 3) list:firstRest (1 (0 3))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4660 a r:Inference; - r:gives { - (1 0) :sort (0 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - skolem:lemma6116 - skolem:lemma4506 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {((0) (1)) list:append (0 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4661 a r:Inference; - r:gives { - (2 (1 0 4)) :split ((1 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 4) list:firstRest (1 (0 4))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4662 a r:Inference; - r:gives { - (2 (1 0 5)) :split ((1 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 5) list:firstRest (1 (0 5))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4663 a r:Inference; - r:gives { - (2 (1 0 6)) :split ((1 0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 6) list:firstRest (1 (0 6))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4664 a r:Inference; - r:gives { - (2 (1 0 7)) :split ((1 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 7) list:firstRest (1 (0 7))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4665 a r:Inference; - r:gives { - (2 (1 0 8)) :split ((1 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 8) list:firstRest (1 (0 8))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4666 a r:Inference; - r:gives { - (2 (1 0 9)) :split ((1 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 9) list:firstRest (1 (0 9))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4667 a r:Inference; - r:gives { - (2 (1 1 0)) :split ((1 1 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 0) list:firstRest (1 (1 0))}] - [ a r:Fact; r:gives {(1 1 0) list:firstRest (1 (1 0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4668 a r:Inference; - r:gives { - (1 1 0) :sort (0 1 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 0) list:firstRest (1 (1 0))}] - skolem:lemma6118 - skolem:lemma4660 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {((0 1) (1)) list:append (0 1 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4669 a r:Inference; - r:gives { - (2 (1 1 1)) :split ((1 1 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 1) list:firstRest (1 (1 1))}] - [ a r:Fact; r:gives {(1 1 1) list:firstRest (1 (1 1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4670 a r:Inference; - r:gives { - (1 1 1) :sort (1 1 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 1) list:firstRest (1 (1 1))}] - skolem:lemma6119 - skolem:lemma4680 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {((1 1) (1)) list:append (1 1 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4671 a r:Inference; - r:gives { - 999 :numberToDigits (0 9 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(999 1000) math:integerQuotient 0}] - [ a r:Fact; r:gives {(999 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 0]; - 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_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:lemma4392. - -skolem:lemma4672 a r:Inference; - r:gives { - (0 9 9 9) :sort (0 9 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9 9 9) list:firstRest (0 (9 9 9))}] - skolem:lemma6120 - skolem:lemma4395 - skolem:lemma5897 - [ a r:Fact; r:gives {(0 9 9 9) list:firstRest (0 (9 9 9))}] - [ a r:Fact; r:gives {(() (0 9 9 9)) list:append (0 9 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9 9 9)]; - 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_2"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 9 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4673 a r:Inference; - r:gives { - (0 9 9 9) :digitsToNumber 999 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ 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 {(0 900 90 9) math:sum 999}] - ); - 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 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 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma4397. - -skolem:lemma4674 a r:Inference; - r:gives { - (9 9 9 0) :digitsToNumber 9990 . - }; - 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 0) math:sum 9990}] - ); - 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 9990]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma4397. - -skolem:lemma4675 a r:Inference; - r:gives { - (2 (1 1 2)) :split ((1 1 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 2) list:firstRest (1 (1 2))}] - [ a r:Fact; r:gives {(1 1 2) list:firstRest (1 (1 2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4676 a r:Inference; - r:gives { - (1 1 2) :sort (1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 2) list:firstRest (1 (1 2))}] - skolem:lemma6121 - skolem:lemma4705 - skolem:lemma4833 - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {((1) (1 2)) list:append (1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4677 a r:Inference; - r:gives { - 1089 :numberToDigits (1 0 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(1089 1000) math:integerQuotient 1}] - [ a r:Fact; r:gives {(1089 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 1]; - 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_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:lemma4392. - -skolem:lemma4678 a r:Inference; - r:gives { - (1 0 8 9) :sort (0 1 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0 8 9) list:firstRest (1 (0 8 9))}] - skolem:lemma6122 - skolem:lemma4506 - skolem:lemma4631 - [ a r:Fact; r:gives {(1 8 9) list:firstRest (1 (8 9))}] - [ a r:Fact; r:gives {((0) (1 8 9)) list:append (0 1 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8 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 (8 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 (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4679 a r:Inference; - r:gives { - (2 (1 1 3)) :split ((1 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 3) list:firstRest (1 (1 3))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4680 a r:Inference; - r:gives { - (1 1) :sort (1 1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - skolem:lemma6123 - skolem:lemma4705 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {((1) (1)) list:append (1 1)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1)]; - r:rule skolem:lemma4396. - -skolem:lemma4681 a r:Inference; - r:gives { - (2 (1 1 4)) :split ((1 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 4) list:firstRest (1 (1 4))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4682 a r:Inference; - r:gives { - (2 (1 1 5)) :split ((1 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 5) list:firstRest (1 (1 5))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4683 a r:Inference; - r:gives { - (2 (1 1 6)) :split ((1 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 6) list:firstRest (1 (1 6))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4684 a r:Inference; - r:gives { - (2 (1 1 7)) :split ((1 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 7) list:firstRest (1 (1 7))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4685 a r:Inference; - r:gives { - (2 (1 1 8)) :split ((1 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 8) list:firstRest (1 (1 8))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4686 a r:Inference; - r:gives { - (2 (1 1 9)) :split ((1 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1 9) list:firstRest (1 (1 9))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4687 a r:Inference; - r:gives { - (2 (1 2 0)) :split ((1 2 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 0) list:firstRest (1 (2 0))}] - [ a r:Fact; r:gives {(1 2 0) list:firstRest (1 (2 0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4688 a r:Inference; - r:gives { - (1 2 0) :sort (0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 0) list:firstRest (1 (2 0))}] - skolem:lemma6124 - skolem:lemma4506 - skolem:lemma4833 - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {((0) (1 2)) list:append (0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 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 (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:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4689 a r:Inference; - r:gives { - (2 (1 2 1)) :split ((1 2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 1) list:firstRest (1 (2 1))}] - [ a r:Fact; r:gives {(1 2 1) list:firstRest (1 (2 1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4690 a r:Inference; - r:gives { - (1 2 1) :sort (1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 1) list:firstRest (1 (2 1))}] - skolem:lemma6125 - skolem:lemma4705 - skolem:lemma4833 - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {((1) (1 2)) list:append (1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4691 a r:Inference; - r:gives { - (2 (1 2 2)) :split ((1 2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 2) list:firstRest (1 (2 2))}] - [ a r:Fact; r:gives {(1 2 2) list:firstRest (1 (2 2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4692 a r:Inference; - r:gives { - (1 2 2) :sort (1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 2) list:firstRest (1 (2 2))}] - skolem:lemma6126 - skolem:lemma4395 - skolem:lemma4822 - [ a r:Fact; r:gives {(1 2 2) list:firstRest (1 (2 2))}] - [ a r:Fact; r:gives {(() (1 2 2)) list:append (1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4693 a r:Inference; - r:gives { - (2 (1 2 3)) :split ((1 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 3) list:firstRest (1 (2 3))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4694 a r:Inference; - r:gives { - (1 2) :sort (1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - skolem:lemma6127 - skolem:lemma4395 - skolem:lemma4833 - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {(() (1 2)) list:append (1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4695 a r:Inference; - r:gives { - (2 (1 2 4)) :split ((1 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 4) list:firstRest (1 (2 4))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4696 a r:Inference; - r:gives { - (2 (1 2 5)) :split ((1 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 5) list:firstRest (1 (2 5))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4697 a r:Inference; - r:gives { - (2 (1 2 6)) :split ((1 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 6) list:firstRest (1 (2 6))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4698 a r:Inference; - r:gives { - (2 (1 2 7)) :split ((1 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 7) list:firstRest (1 (2 7))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4699 a r:Inference; - r:gives { - (2 (1 2 8)) :split ((1 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 8) list:firstRest (1 (2 8))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4700 a r:Inference; - r:gives { - (2 (1 2 9)) :split ((1 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2 9) list:firstRest (1 (2 9))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4701 a r:Inference; - r:gives { - (2 (1 3 0)) :split ((1 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 0) list:firstRest (1 (3 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4702 a r:Inference; - r:gives { - (2 (1 3 1)) :split ((1 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 1) list:firstRest (1 (3 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4703 a r:Inference; - r:gives { - (2 (1 3 2)) :split ((1 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 2) list:firstRest (1 (3 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4704 a r:Inference; - r:gives { - (2 (1 3 3)) :split ((1) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 3) list:firstRest (1 (3 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4705 a r:Inference; - r:gives { - (1) :sort (1). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - skolem:lemma6128 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(() (1)) list:append (1)}] - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1)]; - r:rule skolem:lemma4396. - -skolem:lemma4706 a r:Inference; - r:gives { - (2 (1 3 4)) :split ((1) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 4) list:firstRest (1 (3 4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4707 a r:Inference; - r:gives { - (2 (1 3 5)) :split ((1) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 5) list:firstRest (1 (3 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4708 a r:Inference; - r:gives { - (2 (1 3 6)) :split ((1) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 6) list:firstRest (1 (3 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4709 a r:Inference; - r:gives { - (2 (1 3 7)) :split ((1) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 7) list:firstRest (1 (3 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4710 a r:Inference; - r:gives { - (2 (1 3 8)) :split ((1) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 8) list:firstRest (1 (3 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4711 a r:Inference; - r:gives { - (2 (1 3 9)) :split ((1) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3 9) list:firstRest (1 (3 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4712 a r:Inference; - r:gives { - (2 (1 4 0)) :split ((1 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 0) list:firstRest (1 (4 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4713 a r:Inference; - r:gives { - (2 (1 4 1)) :split ((1 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 1) list:firstRest (1 (4 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4714 a r:Inference; - r:gives { - (2 (1 4 2)) :split ((1 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 2) list:firstRest (1 (4 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4715 a r:Inference; - r:gives { - (2 (1 4 3)) :split ((1) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 3) list:firstRest (1 (4 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4716 a r:Inference; - r:gives { - (2 (1 4 4)) :split ((1) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 4) list:firstRest (1 (4 4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4717 a r:Inference; - r:gives { - (2 (1 4 5)) :split ((1) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 5) list:firstRest (1 (4 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4718 a r:Inference; - r:gives { - (2 (1 4 6)) :split ((1) (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 6) list:firstRest (1 (4 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4719 a r:Inference; - r:gives { - (4 6) :sort (4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - skolem:lemma6130 - skolem:lemma4395 - skolem:lemma4458 - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(() (4 6)) list:append (4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4720 a r:Inference; - r:gives { - (2 (1 4 8)) :split ((1) (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 8) list:firstRest (1 (4 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4721 a r:Inference; - r:gives { - (2 (1 4 9)) :split ((1) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4 9) list:firstRest (1 (4 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4722 a r:Inference; - r:gives { - (2 (1 5 0)) :split ((1 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 0) list:firstRest (1 (5 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4723 a r:Inference; - r:gives { - (2 (1 5 1)) :split ((1 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 1) list:firstRest (1 (5 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4724 a r:Inference; - r:gives { - (2 (1 5 2)) :split ((1 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 2) list:firstRest (1 (5 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4725 a r:Inference; - r:gives { - (2 (1 5 3)) :split ((1) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 3) list:firstRest (1 (5 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4726 a r:Inference; - r:gives { - (2 (1 5 4)) :split ((1) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 4) list:firstRest (1 (5 4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4727 a r:Inference; - r:gives { - (2 (1 5 5)) :split ((1) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 5) list:firstRest (1 (5 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4728 a r:Inference; - r:gives { - 4266 :numberToDigits (4 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4266 1000) math:integerQuotient 4}] - [ a r:Fact; r:gives {(4266 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4266]; - 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:lemma4392. - -skolem:lemma4729 a r:Inference; - r:gives { - (4 2 6 6) :sort (2 4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 6 6) list:firstRest (4 (2 6 6))}] - skolem:lemma6131 - skolem:lemma4833 - skolem:lemma4569 - [ a r:Fact; r:gives {(4 6 6) list:firstRest (4 (6 6))}] - [ a r:Fact; r:gives {((2) (4 6 6)) list:append (2 4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4730 a r:Inference; - r:gives { - (2 (1 5 6)) :split ((1) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 6) list:firstRest (1 (5 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4731 a r:Inference; - r:gives { - (2 (1 5 7)) :split ((1) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 7) list:firstRest (1 (5 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4732 a r:Inference; - r:gives { - (2 (1 5 8)) :split ((1) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 8) list:firstRest (1 (5 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4733 a r:Inference; - r:gives { - (2 (1 5 9)) :split ((1) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5 9) list:firstRest (1 (5 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4734 a r:Inference; - r:gives { - (2 (1 6 0)) :split ((1 0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 0) list:firstRest (1 (6 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4735 a r:Inference; - r:gives { - (2 (1 6 1)) :split ((1 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 1) list:firstRest (1 (6 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4736 a r:Inference; - r:gives { - (2 (1 6 2)) :split ((1 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 2) list:firstRest (1 (6 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4737 a r:Inference; - r:gives { - (2 (1 6 3)) :split ((1) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 3) list:firstRest (1 (6 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4738 a r:Inference; - r:gives { - (2 (1 6 4)) :split ((1) (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 4) list:firstRest (1 (6 4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4739 a r:Inference; - r:gives { - (6 4) :sort (4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - skolem:lemma6134 - skolem:lemma4414 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4) (6)) list:append (4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4740 a r:Inference; - r:gives { - (2 (1 6 5)) :split ((1) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 5) list:firstRest (1 (6 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4741 a r:Inference; - r:gives { - (2 (1 6 6)) :split ((1) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 6) list:firstRest (1 (6 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4742 a r:Inference; - r:gives { - 5355 :numberToDigits (5 3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5355 1000) math:integerQuotient 5}] - [ a r:Fact; r:gives {(5355 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5355]; - 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:lemma4392. - -skolem:lemma4743 a r:Inference; - r:gives { - (5 3 5 5) :sort (3 5 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 5 5) list:firstRest (5 (3 5 5))}] - skolem:lemma6135 - skolem:lemma4982 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3 5 5) (5)) list:append (3 5 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4744 a r:Inference; - r:gives { - (3 5 5 5) :digitsToNumber 3555 . - }; - r:evidence ( - [ 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 {(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 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 3555]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma4397. - -skolem:lemma4745 a r:Inference; - r:gives { - (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 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]; - 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 5553]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma4397. - -skolem:lemma4746 a r:Inference; - r:gives { - (2 (1 6 7)) :split ((1) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 7) list:firstRest (1 (6 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4747 a r:Inference; - r:gives { - (2 (1 6 8)) :split ((1) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 8) list:firstRest (1 (6 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4748 a r:Inference; - r:gives { - (2 (1 6 9)) :split ((1) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6 9) list:firstRest (1 (6 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4749 a r:Inference; - r:gives { - (2 (1 7 0)) :split ((1 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 0) list:firstRest (1 (7 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4750 a r:Inference; - r:gives { - (2 (1 7 1)) :split ((1 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 1) list:firstRest (1 (7 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4751 a r:Inference; - r:gives { - (2 (1 7 2)) :split ((1 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 2) list:firstRest (1 (7 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4752 a r:Inference; - r:gives { - (2 (1 7 3)) :split ((1) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 3) list:firstRest (1 (7 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4753 a r:Inference; - r:gives { - (2 (1 7 5)) :split ((1) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 5) list:firstRest (1 (7 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4754 a r:Inference; - r:gives { - (2 (1 7 6)) :split ((1) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 6) list:firstRest (1 (7 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4755 a r:Inference; - r:gives { - (2 (1 7 7)) :split ((1) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 7) list:firstRest (1 (7 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4756 a r:Inference; - r:gives { - 6444 :numberToDigits (6 4 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(6444 1000) math:integerQuotient 6}] - [ a r:Fact; r:gives {(6444 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6444]; - 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:lemma4392. - -skolem:lemma4757 a r:Inference; - r:gives { - (6 4 4 4) :sort (4 4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 4 4) list:firstRest (6 (4 4 4))}] - skolem:lemma6136 - skolem:lemma5105 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4 4 4) (6)) list:append (4 4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4758 a r:Inference; - r:gives { - (4 4 4 6) :digitsToNumber 4446 . - }; - 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 6) math:sum 4446}] - ); - 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 4446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma4397. - -skolem:lemma4759 a r:Inference; - r:gives { - (6 4 4 4) :digitsToNumber 6444 . - }; - 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 4) math:sum 6444}] - ); - 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 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma4397. - -skolem:lemma4760 a r:Inference; - r:gives { - (2 (1 7 8)) :split ((1) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 8) list:firstRest (1 (7 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4761 a r:Inference; - r:gives { - (2 (1 7 9)) :split ((1) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 9) list:firstRest (1 (7 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4762 a r:Inference; - r:gives { - (2 (1 8 0)) :split ((1 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 0) list:firstRest (1 (8 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4763 a r:Inference; - r:gives { - (2 (1 8 1)) :split ((1 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 1) list:firstRest (1 (8 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4764 a r:Inference; - r:gives { - (2 (1 8 2)) :split ((1 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 2) list:firstRest (1 (8 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4765 a r:Inference; - r:gives { - (2 (1 8 3)) :split ((1) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 3) list:firstRest (1 (8 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4766 a r:Inference; - r:gives { - (2 (1 8 4)) :split ((1) (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 4) list:firstRest (1 (8 4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4767 a r:Inference; - r:gives { - (2 (1 8 5)) :split ((1) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 5) list:firstRest (1 (8 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4768 a r:Inference; - r:gives { - (2 (1 8 6)) :split ((1) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 6) list:firstRest (1 (8 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4769 a r:Inference; - r:gives { - (2 (1 8 7)) :split ((1) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 7) list:firstRest (1 (8 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4770 a r:Inference; - r:gives { - (2 (1 8 8)) :split ((1) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 8) list:firstRest (1 (8 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4771 a r:Inference; - r:gives { - 7533 :numberToDigits (7 5 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7533 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7533 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7533]; - 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:lemma4392. - -skolem:lemma4772 a r:Inference; - r:gives { - (7 5 3 3) :sort (3 3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 3 3) list:firstRest (7 (5 3 3))}] - skolem:lemma6137 - skolem:lemma5228 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 3 5) (7)) list:append (3 3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4773 a r:Inference; - r:gives { - (2 (1 8 9)) :split ((1) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8 9) list:firstRest (1 (8 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4774 a r:Inference; - r:gives { - (2 (1 9 0)) :split ((1 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 0) list:firstRest (1 (9 0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4775 a r:Inference; - r:gives { - (2 (1 9 1)) :split ((1 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 1) list:firstRest (1 (9 1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4776 a r:Inference; - r:gives { - (2 (1 9 2)) :split ((1 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 2) list:firstRest (1 (9 2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4777 a r:Inference; - r:gives { - (2 (1 9 3)) :split ((1) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 3) list:firstRest (1 (9 3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4778 a r:Inference; - r:gives { - (2 (1 9 4)) :split ((1) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 4) list:firstRest (1 (9 4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4779 a r:Inference; - r:gives { - (2 (1 9 5)) :split ((1) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 5) list:firstRest (1 (9 5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4780 a r:Inference; - r:gives { - (2 (1 9 6)) :split ((1) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 6) list:firstRest (1 (9 6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4781 a r:Inference; - r:gives { - (2 (1 9 7)) :split ((1) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 7) list:firstRest (1 (9 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4782 a r:Inference; - r:gives { - (2 (1 9 8)) :split ((1) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 8) list:firstRest (1 (9 8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4783 a r:Inference; - r:gives { - (2 (1 9 9)) :split ((1) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9 9) list:firstRest (1 (9 9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4784 a r:Inference; - r:gives { - 8622 :numberToDigits (8 6 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(8622 1000) math:integerQuotient 8}] - [ a r:Fact; r:gives {(8622 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8622]; - 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:lemma4392. - -skolem:lemma4785 a r:Inference; - r:gives { - (8 6 2 2) :sort (2 2 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 2 2) list:firstRest (8 (6 2 2))}] - skolem:lemma6138 - skolem:lemma6139 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((2 2 6) (8)) list:append (2 2 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4786 a r:Inference; - r:gives { - (2 (2 0 0)) :split ((2 0 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0) list:firstRest (2 (0 0))}] - [ a r:Fact; r:gives {(2 0 0) list:firstRest (2 (0 0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4787 a r:Inference; - r:gives { - (2 0 0) :sort (0 0 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 0) list:firstRest (2 (0 0))}] - skolem:lemma5898 - skolem:lemma4407 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 0) (2)) list:append (0 0 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 0 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4788 a r:Inference; - r:gives { - (2 (2 0 1)) :split ((2 0 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1) list:firstRest (2 (0 1))}] - [ a r:Fact; r:gives {(2 0 1) list:firstRest (2 (0 1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4789 a r:Inference; - r:gives { - (2 0 1) :sort (0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 1) list:firstRest (2 (0 1))}] - skolem:lemma5902 - skolem:lemma4442 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1) (2)) list:append (0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4790 a r:Inference; - r:gives { - (2 (2 0 2)) :split ((2 0 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2) list:firstRest (2 (0 2))}] - [ a r:Fact; r:gives {(2 0 2) list:firstRest (2 (0 2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (0 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4791 a r:Inference; - r:gives { - (2 0 2) :sort (0 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 2) list:firstRest (2 (0 2))}] - skolem:lemma5904 - skolem:lemma4479 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 2) (2)) list:append (0 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4792 a r:Inference; - r:gives { - (2 (2 0 3)) :split ((2 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 3) list:firstRest (2 (0 3))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4793 a r:Inference; - r:gives { - (2 0) :sort (0 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - skolem:lemma6140 - skolem:lemma4506 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0) (2)) list:append (0 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_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 ()]; - 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 ()]; - 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_8"]; r:boundTo (0 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4794 a r:Inference; - r:gives { - (2 (2 0 4)) :split ((2 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 4) list:firstRest (2 (0 4))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4795 a r:Inference; - r:gives { - (2 (2 0 5)) :split ((2 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 5) list:firstRest (2 (0 5))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4796 a r:Inference; - r:gives { - (2 (2 0 6)) :split ((2 0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 6) list:firstRest (2 (0 6))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4797 a r:Inference; - r:gives { - (2 (2 0 7)) :split ((2 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 7) list:firstRest (2 (0 7))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4798 a r:Inference; - r:gives { - (2 (2 0 8)) :split ((2 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 8) list:firstRest (2 (0 8))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4799 a r:Inference; - r:gives { - (2 (2 0 9)) :split ((2 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0 9) list:firstRest (2 (0 9))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 0 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_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4800 a r:Inference; - r:gives { - (2 (2 1 0)) :split ((2 1 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0) list:firstRest (2 (1 0))}] - [ a r:Fact; r:gives {(2 1 0) list:firstRest (2 (1 0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4801 a r:Inference; - r:gives { - (2 1 0) :sort (0 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 0) list:firstRest (2 (1 0))}] - skolem:lemma5928 - skolem:lemma4660 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 1) (2)) list:append (0 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4802 a r:Inference; - r:gives { - (2 (2 1 1)) :split ((2 1 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1) list:firstRest (2 (1 1))}] - [ a r:Fact; r:gives {(2 1 1) list:firstRest (2 (1 1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4803 a r:Inference; - r:gives { - (2 1 1) :sort (1 1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 1) list:firstRest (2 (1 1))}] - skolem:lemma5930 - skolem:lemma4680 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 1) (2)) list:append (1 1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4804 a r:Inference; - r:gives { - (2 (2 1 2)) :split ((2 1 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2) list:firstRest (2 (1 2))}] - [ a r:Fact; r:gives {(2 1 2) list:firstRest (2 (1 2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (1 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4805 a r:Inference; - r:gives { - (2 1 2) :sort (1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 2) list:firstRest (2 (1 2))}] - skolem:lemma5932 - skolem:lemma4694 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 2) (2)) list:append (1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4806 a r:Inference; - r:gives { - (2 (2 1 3)) :split ((2 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 3) list:firstRest (2 (1 3))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4807 a r:Inference; - r:gives { - (2 1) :sort (1 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - skolem:lemma6141 - skolem:lemma4705 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1) (2)) list:append (1 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (1)]; - 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 ()]; - 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 ()]; - 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_8"]; r:boundTo (1 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4808 a r:Inference; - r:gives { - (2 (2 1 4)) :split ((2 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 4) list:firstRest (2 (1 4))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4809 a r:Inference; - r:gives { - (2 (2 1 5)) :split ((2 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 5) list:firstRest (2 (1 5))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4810 a r:Inference; - r:gives { - (2 (2 1 6)) :split ((2 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 6) list:firstRest (2 (1 6))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4811 a r:Inference; - r:gives { - (2 (2 1 7)) :split ((2 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 7) list:firstRest (2 (1 7))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4812 a r:Inference; - r:gives { - (2 (2 1 8)) :split ((2 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 8) list:firstRest (2 (1 8))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4813 a r:Inference; - r:gives { - (2 (2 1 9)) :split ((2 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1 9) list:firstRest (2 (1 9))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 1 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_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4814 a r:Inference; - r:gives { - (2 (2 2 0)) :split ((2 2 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0) list:firstRest (2 (2 0))}] - [ a r:Fact; r:gives {(2 2 0) list:firstRest (2 (2 0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 0)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4815 a r:Inference; - r:gives { - (2 2 0) :sort (0 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 0) list:firstRest (2 (2 0))}] - skolem:lemma5955 - skolem:lemma4793 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((0 2) (2)) list:append (0 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (0 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4816 a r:Inference; - r:gives { - (2 (2 2 1)) :split ((2 2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1) list:firstRest (2 (2 1))}] - [ a r:Fact; r:gives {(2 2 1) list:firstRest (2 (2 1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4817 a r:Inference; - r:gives { - (2 2 1) :sort (1 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 1) list:firstRest (2 (2 1))}] - skolem:lemma5957 - skolem:lemma4807 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((1 2) (2)) list:append (1 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (1 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4818 a r:Inference; - r:gives { - (2 (2 2 2)) :split ((2 2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2) list:firstRest (2 (2 2))}] - [ a r:Fact; r:gives {(2 2 2) list:firstRest (2 (2 2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma4819 a r:Inference; - r:gives { - (2 2 2) :sort (2 2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 2) list:firstRest (2 (2 2))}] - skolem:lemma5959 - skolem:lemma4822 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((2 2) (2)) list:append (2 2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (2 2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4820 a r:Extraction; - r:gives { - { - 0 :kaprekar 0. - } <= { - true log:callWithCut true. - }. - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma4821 a r:Inference; - r:gives { - (2 (2 2 3)) :split ((2 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 3) list:firstRest (2 (2 3))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4822 a r:Inference; - r:gives { - (2 2) :sort (2 2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - skolem:lemma6142 - skolem:lemma4833 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {((2) (2)) list:append (2 2)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (2)]; - 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 ()]; - 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 ()]; - 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_8"]; r:boundTo (2 2)]; - r:rule skolem:lemma4396. - -skolem:lemma4823 a r:Inference; - r:gives { - (2 (2 2 4)) :split ((2 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 4) list:firstRest (2 (2 4))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4824 a r:Inference; - r:gives { - (2 (2 2 5)) :split ((2 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 5) list:firstRest (2 (2 5))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4825 a r:Inference; - r:gives { - (2 (2 2 6)) :split ((2 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 6) list:firstRest (2 (2 6))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4826 a r:Inference; - r:gives { - (2 (2 2 7)) :split ((2 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 7) list:firstRest (2 (2 7))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4827 a r:Inference; - r:gives { - (2 (2 2 8)) :split ((2 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 8) list:firstRest (2 (2 8))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4828 a r:Inference; - r:gives { - (2 (2 2 9)) :split ((2 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2 9) list:firstRest (2 (2 9))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 2 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_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4829 a r:Inference; - r:gives { - (2 (2 3 0)) :split ((2 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 0) list:firstRest (2 (3 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4830 a r:Inference; - r:gives { - (2 (2 3 1)) :split ((2 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 1) list:firstRest (2 (3 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4831 a r:Inference; - r:gives { - (2 (2 3 2)) :split ((2 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 2) list:firstRest (2 (3 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma5899. - -skolem:lemma4832 a r:Inference; - r:gives { - (2 (2 3 3)) :split ((2) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 3) list:firstRest (2 (3 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4833 a r:Inference; - r:gives { - (2) :sort (2). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - skolem:lemma6143 - skolem:lemma4395 - skolem:lemma4395 - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(() (2)) list:append (2)}] - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (2)]; - r:rule skolem:lemma4396. - -skolem:lemma4834 a r:Inference; - r:gives { - (2 (2 3 4)) :split ((2) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 4) list:firstRest (2 (3 4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4835 a r:Inference; - r:gives { - (2 (2 3 5)) :split ((2) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 5) list:firstRest (2 (3 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4836 a r:Inference; - r:gives { - (2 (2 3 6)) :split ((2) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4837 a r:Inference; - r:gives { - (2 (2 3 7)) :split ((2) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 7) list:firstRest (2 (3 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4838 a r:Inference; - r:gives { - (2 (2 3 8)) :split ((2) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 8) list:firstRest (2 (3 8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4839 a r:Inference; - r:gives { - (2 (2 3 9)) :split ((2) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3 9) list:firstRest (2 (3 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 3 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_2"]; r:boundTo (3 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4840 a r:Inference; - r:gives { - (2 (2 4 0)) :split ((2 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 0) list:firstRest (2 (4 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4841 a r:Inference; - r:gives { - (2 (2 4 1)) :split ((2 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 1) list:firstRest (2 (4 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4842 a r:Inference; - r:gives { - (2 (2 4 2)) :split ((2 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 2) list:firstRest (2 (4 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma5899. - -skolem:lemma4843 a r:Inference; - r:gives { - (2 (2 4 3)) :split ((2) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 3) list:firstRest (2 (4 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4844 a r:Inference; - r:gives { - (2 (2 4 4)) :split ((2) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 4) list:firstRest (2 (4 4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4845 a r:Inference; - r:gives { - (2 (2 4 5)) :split ((2) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 5) list:firstRest (2 (4 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4846 a r:Inference; - r:gives { - (2 (2 4 6)) :split ((2) (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4847 a r:Inference; - r:gives { - (2 (2 4 7)) :split ((2) (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 7) list:firstRest (2 (4 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4848 a r:Inference; - r:gives { - (2 (2 4 9)) :split ((2) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4 9) list:firstRest (2 (4 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 4 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_2"]; r:boundTo (4 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4849 a r:Inference; - r:gives { - (2 (2 5 0)) :split ((2 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 0) list:firstRest (2 (5 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4850 a r:Inference; - r:gives { - (2 (2 5 1)) :split ((2 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 1) list:firstRest (2 (5 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4851 a r:Inference; - r:gives { - (2 (2 5 2)) :split ((2 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 2) list:firstRest (2 (5 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:rule skolem:lemma5899. - -skolem:lemma4852 a r:Inference; - r:gives { - (2 (2 5 3)) :split ((2) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 3) list:firstRest (2 (5 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4853 a r:Inference; - r:gives { - (2 (2 5 4)) :split ((2) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 4) list:firstRest (2 (5 4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4854 a r:Inference; - r:gives { - (2 (2 5 5)) :split ((2) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 5) list:firstRest (2 (5 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4855 a r:Inference; - r:gives { - 3267 :numberToDigits (3 2 6 7). - }; - r:evidence ( - [ 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 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:lemma4392. - -skolem:lemma4856 a r:Inference; - r:gives { - (3 2 6 7) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 6 7) list:firstRest (3 (2 6 7))}] - skolem:lemma6144 - skolem:lemma4833 - skolem:lemma4575 - [ a r:Fact; r:gives {(3 6 7) list:firstRest (3 (6 7))}] - [ a r:Fact; r:gives {((2) (3 6 7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7)]; - 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 7)]; - 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 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4857 a r:Inference; - r:gives { - (2 (2 5 6)) :split ((2) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 6) list:firstRest (2 (5 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4858 a r:Inference; - r:gives { - (2 (2 5 7)) :split ((2) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 7) list:firstRest (2 (5 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4859 a r:Inference; - r:gives { - (2 (2 5 8)) :split ((2) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 8) list:firstRest (2 (5 8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4860 a r:Inference; - r:gives { - (2 (2 5 9)) :split ((2) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5 9) list:firstRest (2 (5 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 5 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_2"]; r:boundTo (5 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4861 a r:Inference; - r:gives { - (2 (2 6 0)) :split ((2 0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 0) list:firstRest (2 (6 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4862 a r:Inference; - r:gives { - (2 (2 6 1)) :split ((2 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1) list:firstRest (2 (6 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4863 a r:Inference; - r:gives { - (2 (2 6 2)) :split ((2 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2) list:firstRest (2 (6 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma4864 a r:Inference; - r:gives { - (2 (2 6 3)) :split ((2) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3) list:firstRest (2 (6 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4865 a r:Inference; - r:gives { - (2 (2 6 4)) :split ((2) (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4) list:firstRest (2 (6 4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4866 a r:Inference; - r:gives { - (2 (2 6 5)) :split ((2) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5) list:firstRest (2 (6 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4867 a r:Inference; - r:gives { - (2 (2 6 6)) :split ((2) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4868 a r:Inference; - r:gives { - 4356 :numberToDigits (4 3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4356 1000) math:integerQuotient 4}] - [ a r:Fact; r:gives {(4356 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4356]; - 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:lemma4392. - -skolem:lemma4869 a r:Inference; - r:gives { - (4 3 5 6) :sort (3 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 5 6) list:firstRest (4 (3 5 6))}] - skolem:lemma6145 - skolem:lemma4408 - skolem:lemma4547 - [ a r:Fact; r:gives {(4 5 6) list:firstRest (4 (5 6))}] - [ a r:Fact; r:gives {((3) (4 5 6)) list:append (3 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6)]; - 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 6)]; - 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 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4870 a r:Inference; - r:gives { - (2 (2 6 7)) :split ((2) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4871 a r:Inference; - r:gives { - (2 (2 6 8)) :split ((2) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 8) list:firstRest (2 (6 8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4872 a r:Inference; - r:gives { - (2 (2 6 9)) :split ((2) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 9) list:firstRest (2 (6 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4873 a r:Inference; - r:gives { - (2 (2 7 0)) :split ((2 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 0) list:firstRest (2 (7 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4874 a r:Inference; - r:gives { - (2 (2 7 1)) :split ((2 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 1) list:firstRest (2 (7 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4875 a r:Inference; - r:gives { - (2 (2 7 2)) :split ((2 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 2) list:firstRest (2 (7 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma4876 a r:Inference; - r:gives { - (2 (2 7 3)) :split ((2) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 3) list:firstRest (2 (7 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4877 a r:Inference; - r:gives { - (2 (2 7 4)) :split ((2) (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 4) list:firstRest (2 (7 4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4878 a r:Inference; - r:gives { - (2 (2 7 5)) :split ((2) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 5) list:firstRest (2 (7 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4879 a r:Inference; - r:gives { - (2 (2 7 6)) :split ((2) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 6) list:firstRest (2 (7 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4880 a r:Inference; - r:gives { - (2 (2 7 7)) :split ((2) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 7) list:firstRest (2 (7 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4881 a r:Inference; - r:gives { - 5445 :numberToDigits (5 4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5445 1000) math:integerQuotient 5}] - [ a r:Fact; r:gives {(5445 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5445]; - 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:lemma4392. - -skolem:lemma4882 a r:Inference; - r:gives { - (5 4 4 5) :sort (4 4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 4 5) list:firstRest (5 (4 4 5))}] - skolem:lemma6146 - skolem:lemma5107 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((4 4 5) (5)) list:append (4 4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4883 a r:Inference; - r:gives { - (4 4 5 5) :digitsToNumber 4455 . - }; - 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 {(5 10) math:product 50}] - [ a r:Fact; r:gives {(4000 400 50 5) math:sum 4455}] - ); - 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 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 4455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma4397. - -skolem:lemma4884 a r:Inference; - r:gives { - (5 5 4 4) :digitsToNumber 5544 . - }; - 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 4) math:sum 5544}] - ); - 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 5544]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma4397. - -skolem:lemma4885 a r:Inference; - r:gives { - (2 (2 7 8)) :split ((2) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 8) list:firstRest (2 (7 8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4886 a r:Inference; - r:gives { - (2 (2 7 9)) :split ((2) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7 9) list:firstRest (2 (7 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 7 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_2"]; r:boundTo (7 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4887 a r:Inference; - r:gives { - (2 (2 8 0)) :split ((2 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 0) list:firstRest (2 (8 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4888 a r:Inference; - r:gives { - (2 (2 8 1)) :split ((2 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 1) list:firstRest (2 (8 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4889 a r:Inference; - r:gives { - (2 (2 8 2)) :split ((2 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 2) list:firstRest (2 (8 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma4890 a r:Inference; - r:gives { - (2 (2 8 3)) :split ((2) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 3) list:firstRest (2 (8 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4891 a r:Inference; - r:gives { - (2 (2 8 5)) :split ((2) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 5) list:firstRest (2 (8 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4892 a r:Inference; - r:gives { - (2 (2 8 6)) :split ((2) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 6) list:firstRest (2 (8 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4893 a r:Inference; - r:gives { - (2 (2 8 7)) :split ((2) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 7) list:firstRest (2 (8 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4894 a r:Inference; - r:gives { - (2 (2 8 8)) :split ((2) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 8) list:firstRest (2 (8 8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4895 a r:Inference; - r:gives { - 6534 :numberToDigits (6 5 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(6534 1000) math:integerQuotient 6}] - [ a r:Fact; r:gives {(6534 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6534]; - 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:lemma4392. - -skolem:lemma4896 a r:Inference; - r:gives { - (6 5 3 4) :sort (3 4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 3 4) list:firstRest (6 (5 3 4))}] - skolem:lemma6147 - skolem:lemma5230 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 4 5) (6)) list:append (3 4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4897 a r:Inference; - r:gives { - (2 (2 8 9)) :split ((2) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8 9) list:firstRest (2 (8 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 8 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_2"]; r:boundTo (8 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4898 a r:Inference; - r:gives { - (2 (2 9 0)) :split ((2 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 0) list:firstRest (2 (9 0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4899 a r:Inference; - r:gives { - (2 (2 9 1)) :split ((2 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 1) list:firstRest (2 (9 1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4900 a r:Inference; - r:gives { - (2 (2 9 2)) :split ((2 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 2) list:firstRest (2 (9 2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:rule skolem:lemma5899. - -skolem:lemma4901 a r:Inference; - r:gives { - (2 (2 9 3)) :split ((2) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 3) list:firstRest (2 (9 3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 3)]; - 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 ()]; - 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 3)]; - r:rule skolem:lemma5899. - -skolem:lemma4902 a r:Inference; - r:gives { - (2 (2 9 4)) :split ((2) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 4) list:firstRest (2 (9 4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 4)]; - 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 ()]; - 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 4)]; - r:rule skolem:lemma5899. - -skolem:lemma4903 a r:Inference; - r:gives { - (2 (2 9 5)) :split ((2) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 5) list:firstRest (2 (9 5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 5)]; - 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 ()]; - 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 5)]; - r:rule skolem:lemma5899. - -skolem:lemma4904 a r:Inference; - r:gives { - (2 (2 9 6)) :split ((2) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 6) list:firstRest (2 (9 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma4905 a r:Inference; - r:gives { - (2 (2 9 7)) :split ((2) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 7) list:firstRest (2 (9 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma4906 a r:Inference; - r:gives { - (2 (2 9 8)) :split ((2) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 8) list:firstRest (2 (9 8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 8)]; - 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 ()]; - 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 8)]; - r:rule skolem:lemma5899. - -skolem:lemma4907 a r:Inference; - r:gives { - (2 (2 9 9)) :split ((2) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9 9) list:firstRest (2 (9 9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 9 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_2"]; r:boundTo (9 9)]; - 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma4908 a r:Inference; - r:gives { - 7623 :numberToDigits (7 6 2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(7623 1000) math:integerQuotient 7}] - [ a r:Fact; r:gives {(7623 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7623]; - 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:lemma4392. - -skolem:lemma4909 a r:Inference; - r:gives { - (7 6 2 3) :sort (2 3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 2 3) list:firstRest (7 (6 2 3))}] - skolem:lemma6148 - skolem:lemma6149 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((2 3 6) (7)) list:append (2 3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4910 a r:Inference; - r:gives { - (2 (3 0 0)) :split ((0 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 0) list:firstRest (3 (0 0))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma4911 a r:Inference; - r:gives { - (2 (3 0 1)) :split ((0 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 1) list:firstRest (3 (0 1))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma4912 a r:Inference; - r:gives { - (2 (3 0 2)) :split ((0 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 2) list:firstRest (3 (0 2))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 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_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma4913 a r:Inference; - r:gives { - (2 (3 0 3)) :split ((0) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 3) list:firstRest (3 (0 3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4914 a r:Inference; - r:gives { - (2 (3 0 4)) :split ((0) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 4) list:firstRest (3 (0 4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4915 a r:Inference; - r:gives { - (2 (3 0 5)) :split ((0) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 5) list:firstRest (3 (0 5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 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_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4916 a r:Inference; - r:gives { - (2 (3 0 6)) :split ((0) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 6) list:firstRest (3 (0 6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4917 a r:Inference; - r:gives { - (2 (3 0 7)) :split ((0) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 7) list:firstRest (3 (0 7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4918 a r:Inference; - r:gives { - (2 (3 0 8)) :split ((0) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 8) list:firstRest (3 (0 8))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4919 a r:Inference; - r:gives { - (2 (3 0 9)) :split ((0) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0 9) list:firstRest (3 (0 9))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4920 a r:Inference; - r:gives { - (2 (3 1 0)) :split ((1 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 0) list:firstRest (3 (1 0))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma4921 a r:Inference; - r:gives { - (2 (3 1 1)) :split ((1 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 1) list:firstRest (3 (1 1))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma4922 a r:Inference; - r:gives { - (2 (3 1 2)) :split ((1 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 2) list:firstRest (3 (1 2))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 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_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma4923 a r:Inference; - r:gives { - (2 (3 1 3)) :split ((1) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 3) list:firstRest (3 (1 3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4924 a r:Inference; - r:gives { - (2 (3 1 4)) :split ((1) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 4) list:firstRest (3 (1 4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4925 a r:Inference; - r:gives { - (2 (3 1 5)) :split ((1) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 5) list:firstRest (3 (1 5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 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_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4926 a r:Inference; - r:gives { - (2 (3 1 6)) :split ((1) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 6) list:firstRest (3 (1 6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4927 a r:Inference; - r:gives { - (2 (3 1 7)) :split ((1) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 7) list:firstRest (3 (1 7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4928 a r:Inference; - r:gives { - (2 (3 1 8)) :split ((1) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 8) list:firstRest (3 (1 8))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4929 a r:Inference; - r:gives { - (2 (3 1 9)) :split ((1) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1 9) list:firstRest (3 (1 9))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4930 a r:Inference; - r:gives { - (2 (3 2 0)) :split ((2 0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 0) list:firstRest (3 (2 0))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma4931 a r:Inference; - r:gives { - (2 (3 2 1)) :split ((2 1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 1) list:firstRest (3 (2 1))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma4932 a r:Inference; - r:gives { - (2 (3 2 2)) :split ((2 2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 2) list:firstRest (3 (2 2))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 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_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma4933 a r:Inference; - r:gives { - (2 (3 2 3)) :split ((2) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 3) list:firstRest (3 (2 3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4934 a r:Inference; - r:gives { - (2 (3 2 4)) :split ((2) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 4) list:firstRest (3 (2 4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4935 a r:Inference; - r:gives { - (2 (3 2 5)) :split ((2) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 5) list:firstRest (3 (2 5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 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_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4936 a r:Inference; - r:gives { - (2 (3 2 6)) :split ((2) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 6) list:firstRest (3 (2 6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4937 a r:Inference; - r:gives { - (2 (3 2 7)) :split ((2) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 7) list:firstRest (3 (2 7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4938 a r:Inference; - r:gives { - (2 (3 2 8)) :split ((2) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 8) list:firstRest (3 (2 8))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4939 a r:Inference; - r:gives { - (2 (3 2 9)) :split ((2) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2 9) list:firstRest (3 (2 9))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4940 a r:Inference; - r:gives { - (2 (3 3 0)) :split ((0) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 0) list:firstRest (3 (3 0))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4941 a r:Inference; - r:gives { - (2 (3 3 1)) :split ((1) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 1) list:firstRest (3 (3 1))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4942 a r:Inference; - r:gives { - (2 (3 3 2)) :split ((2) (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 2) list:firstRest (3 (3 2))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 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_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4943 a r:Inference; - r:gives { - (2 (3 3 3)) :split (() (3 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 3) list:firstRest (3 (3 3))}] - [ a r:Fact; r:gives {(3 3 3) list:firstRest (3 (3 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4944 a r:Inference; - r:gives { - (3 3 3) :sort (3 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 3) list:firstRest (3 (3 3))}] - skolem:lemma6151 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {((3 3) (3)) list:append (3 3 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - 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_8"]; r:boundTo (3 3 3)]; - r:rule skolem:lemma4396. - -skolem:lemma4945 a r:Inference; - r:gives { - (2 (3 3 4)) :split (() (3 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 4) list:firstRest (3 (3 4))}] - [ a r:Fact; r:gives {(3 3 4) list:firstRest (3 (3 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4946 a r:Inference; - r:gives { - (3 3 4) :sort (3 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 4) list:firstRest (3 (3 4))}] - skolem:lemma6152 - skolem:lemma4408 - skolem:lemma4414 - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {((3) (3 4)) list:append (3 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma4947 a r:Inference; - r:gives { - (2 (3 3 5)) :split (() (3 3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 5) list:firstRest (3 (3 5))}] - [ a r:Fact; r:gives {(3 3 5) list:firstRest (3 (3 5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 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_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4948 a r:Inference; - r:gives { - (3 3 5) :sort (3 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 5) list:firstRest (3 (3 5))}] - skolem:lemma6153 - skolem:lemma4408 - skolem:lemma4416 - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {((3) (3 5)) list:append (3 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 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_2"]; r:boundTo (3 5)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4949 a r:Inference; - r:gives { - (2 (3 3 6)) :split (() (3 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 6) list:firstRest (3 (3 6))}] - [ a r:Fact; r:gives {(3 3 6) list:firstRest (3 (3 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4950 a r:Inference; - r:gives { - (3 3 6) :sort (3 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 6) list:firstRest (3 (3 6))}] - skolem:lemma6154 - skolem:lemma4408 - skolem:lemma4458 - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {((3) (3 6)) list:append (3 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4951 a r:Inference; - r:gives { - (2 (3 3 7)) :split (() (3 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 7) list:firstRest (3 (3 7))}] - [ a r:Fact; r:gives {(3 3 7) list:firstRest (3 (3 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4952 a r:Inference; - r:gives { - (3 3 7) :sort (3 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 7) list:firstRest (3 (3 7))}] - skolem:lemma6155 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {((3) (3 7)) list:append (3 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4953 a r:Inference; - r:gives { - (2 (3 3 8)) :split (() (3 3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 8) list:firstRest (3 (3 8))}] - [ a r:Fact; r:gives {(3 3 8) list:firstRest (3 (3 8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4954 a r:Inference; - r:gives { - (3 3 8) :sort (3 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 8) list:firstRest (3 (3 8))}] - skolem:lemma6156 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {((3) (3 8)) list:append (3 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4955 a r:Inference; - r:gives { - (2 (3 3 9)) :split (() (3 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 9) list:firstRest (3 (3 9))}] - [ a r:Fact; r:gives {(3 3 9) list:firstRest (3 (3 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4956 a r:Inference; - r:gives { - (3 3 9) :sort (3 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3 9) list:firstRest (3 (3 9))}] - skolem:lemma6157 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {((3) (3 9)) list:append (3 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4957 a r:Inference; - r:gives { - (2 (3 4 0)) :split ((0) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 0) list:firstRest (3 (4 0))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4958 a r:Inference; - r:gives { - (2 (3 4 1)) :split ((1) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 1) list:firstRest (3 (4 1))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4959 a r:Inference; - r:gives { - (2 (3 4 2)) :split ((2) (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 2) list:firstRest (3 (4 2))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 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_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4960 a r:Inference; - r:gives { - (2 (3 4 3)) :split (() (3 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 3) list:firstRest (3 (4 3))}] - [ a r:Fact; r:gives {(3 4 3) list:firstRest (3 (4 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4961 a r:Inference; - r:gives { - (3 4 3) :sort (3 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 3) list:firstRest (3 (4 3))}] - skolem:lemma6158 - skolem:lemma4408 - skolem:lemma4414 - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {((3) (3 4)) list:append (3 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma4962 a r:Inference; - r:gives { - (2 (3 4 4)) :split (() (3 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 4) list:firstRest (3 (4 4))}] - [ a r:Fact; r:gives {(3 4 4) list:firstRest (3 (4 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4963 a r:Inference; - r:gives { - (3 4 4) :sort (3 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 4) list:firstRest (3 (4 4))}] - skolem:lemma6159 - skolem:lemma4395 - skolem:lemma4526 - [ a r:Fact; r:gives {(3 4 4) list:firstRest (3 (4 4))}] - [ a r:Fact; r:gives {(() (3 4 4)) list:append (3 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma4964 a r:Inference; - r:gives { - (2 (3 4 5)) :split (() (3 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 5) list:firstRest (3 (4 5))}] - [ a r:Fact; r:gives {(3 4 5) list:firstRest (3 (4 5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 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_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4965 a r:Inference; - r:gives { - (3 4 5) :sort (3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 5) list:firstRest (3 (4 5))}] - skolem:lemma6160 - skolem:lemma4395 - skolem:lemma4528 - [ a r:Fact; r:gives {(3 4 5) list:firstRest (3 (4 5))}] - [ a r:Fact; r:gives {(() (3 4 5)) list:append (3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 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_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4966 a r:Inference; - r:gives { - (2 (3 4 6)) :split (() (3 4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 6) list:firstRest (3 (4 6))}] - [ a r:Fact; r:gives {(3 4 6) list:firstRest (3 (4 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4967 a r:Inference; - r:gives { - (3 4 6) :sort (3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 6) list:firstRest (3 (4 6))}] - skolem:lemma6161 - skolem:lemma4395 - skolem:lemma4719 - [ a r:Fact; r:gives {(3 4 6) list:firstRest (3 (4 6))}] - [ a r:Fact; r:gives {(() (3 4 6)) list:append (3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4968 a r:Inference; - r:gives { - (2 (3 4 7)) :split (() (3 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 7) list:firstRest (3 (4 7))}] - [ a r:Fact; r:gives {(3 4 7) list:firstRest (3 (4 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4969 a r:Inference; - r:gives { - (3 4 7) :sort (3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 7) list:firstRest (3 (4 7))}] - skolem:lemma6162 - skolem:lemma4395 - skolem:lemma4530 - [ a r:Fact; r:gives {(3 4 7) list:firstRest (3 (4 7))}] - [ a r:Fact; r:gives {(() (3 4 7)) list:append (3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4970 a r:Inference; - r:gives { - (2 (3 4 8)) :split (() (3 4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 8) list:firstRest (3 (4 8))}] - [ a r:Fact; r:gives {(3 4 8) list:firstRest (3 (4 8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4971 a r:Inference; - r:gives { - (3 4 8) :sort (3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 8) list:firstRest (3 (4 8))}] - skolem:lemma6163 - skolem:lemma4395 - skolem:lemma4532 - [ a r:Fact; r:gives {(3 4 8) list:firstRest (3 (4 8))}] - [ a r:Fact; r:gives {(() (3 4 8)) list:append (3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma4972 a r:Inference; - r:gives { - (2 (3 4 9)) :split (() (3 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 9) list:firstRest (3 (4 9))}] - [ a r:Fact; r:gives {(3 4 9) list:firstRest (3 (4 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4973 a r:Inference; - r:gives { - (3 4 9) :sort (3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4 9) list:firstRest (3 (4 9))}] - skolem:lemma6164 - skolem:lemma4395 - skolem:lemma4534 - [ a r:Fact; r:gives {(3 4 9) list:firstRest (3 (4 9))}] - [ a r:Fact; r:gives {(() (3 4 9)) list:append (3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4974 a r:Inference; - r:gives { - (2 (3 5 0)) :split ((0) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 0) list:firstRest (3 (5 0))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4975 a r:Inference; - r:gives { - (2 (3 5 1)) :split ((1) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 1) list:firstRest (3 (5 1))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4976 a r:Inference; - r:gives { - (2 (3 5 2)) :split ((2) (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 2) list:firstRest (3 (5 2))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 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_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4977 a r:Inference; - r:gives { - (2 (3 5 3)) :split (() (3 5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 3) list:firstRest (3 (5 3))}] - [ a r:Fact; r:gives {(3 5 3) list:firstRest (3 (5 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4978 a r:Inference; - r:gives { - (3 5 3) :sort (3 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 3) list:firstRest (3 (5 3))}] - skolem:lemma6165 - skolem:lemma4408 - skolem:lemma4416 - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {((3) (3 5)) list:append (3 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4979 a r:Inference; - r:gives { - (2 (3 5 4)) :split (() (3 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 4) list:firstRest (3 (5 4))}] - [ a r:Fact; r:gives {(3 5 4) list:firstRest (3 (5 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4980 a r:Inference; - r:gives { - (3 5 4) :sort (3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 4) list:firstRest (3 (5 4))}] - skolem:lemma6166 - skolem:lemma4395 - skolem:lemma4541 - [ a r:Fact; r:gives {(3 4 5) list:firstRest (3 (4 5))}] - [ a r:Fact; r:gives {(() (3 4 5)) list:append (3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4981 a r:Inference; - r:gives { - (2 (3 5 5)) :split (() (3 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 5) list:firstRest (3 (5 5))}] - [ a r:Fact; r:gives {(3 5 5) list:firstRest (3 (5 5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 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_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4982 a r:Inference; - r:gives { - (3 5 5) :sort (3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 5) list:firstRest (3 (5 5))}] - skolem:lemma6167 - skolem:lemma4395 - skolem:lemma4543 - [ a r:Fact; r:gives {(3 5 5) list:firstRest (3 (5 5))}] - [ a r:Fact; r:gives {(() (3 5 5)) list:append (3 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 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_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma4983 a r:Inference; - r:gives { - (2 (3 5 6)) :split (() (3 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 6) list:firstRest (3 (5 6))}] - [ a r:Fact; r:gives {(3 5 6) list:firstRest (3 (5 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4984 a r:Inference; - r:gives { - (3 5 6) :sort (3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 6) list:firstRest (3 (5 6))}] - skolem:lemma6168 - skolem:lemma4395 - skolem:lemma4547 - [ a r:Fact; r:gives {(3 5 6) list:firstRest (3 (5 6))}] - [ a r:Fact; r:gives {(() (3 5 6)) list:append (3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4985 a r:Inference; - r:gives { - (2 (3 5 7)) :split (() (3 5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 7) list:firstRest (3 (5 7))}] - [ a r:Fact; r:gives {(3 5 7) list:firstRest (3 (5 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4986 a r:Inference; - r:gives { - (3 5 7) :sort (3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 7) list:firstRest (3 (5 7))}] - skolem:lemma6169 - skolem:lemma4395 - skolem:lemma4551 - [ a r:Fact; r:gives {(3 5 7) list:firstRest (3 (5 7))}] - [ a r:Fact; r:gives {(() (3 5 7)) list:append (3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma4987 a r:Inference; - r:gives { - (2 (3 5 9)) :split (() (3 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 9) list:firstRest (3 (5 9))}] - [ a r:Fact; r:gives {(3 5 9) list:firstRest (3 (5 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4988 a r:Inference; - r:gives { - (3 5 9) :sort (3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 9) list:firstRest (3 (5 9))}] - skolem:lemma6170 - skolem:lemma4395 - skolem:lemma4559 - [ a r:Fact; r:gives {(3 5 9) list:firstRest (3 (5 9))}] - [ a r:Fact; r:gives {(() (3 5 9)) list:append (3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma4989 a r:Inference; - r:gives { - (2 (3 6 0)) :split ((0) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 0) list:firstRest (3 (6 0))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma4990 a r:Inference; - r:gives { - (2 (3 6 1)) :split ((1) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 1) list:firstRest (3 (6 1))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma4991 a r:Inference; - r:gives { - (2 (3 6 2)) :split ((2) (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 2) list:firstRest (3 (6 2))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 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_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma4992 a r:Inference; - r:gives { - (2 (3 6 3)) :split (() (3 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 3) list:firstRest (3 (6 3))}] - [ a r:Fact; r:gives {(3 6 3) list:firstRest (3 (6 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4993 a r:Inference; - r:gives { - (3 6 3) :sort (3 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 3) list:firstRest (3 (6 3))}] - skolem:lemma6171 - skolem:lemma4408 - skolem:lemma4458 - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {((3) (3 6)) list:append (3 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4994 a r:Inference; - r:gives { - (2 (3 6 4)) :split (() (3 6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 4) list:firstRest (3 (6 4))}] - [ a r:Fact; r:gives {(3 6 4) list:firstRest (3 (6 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4995 a r:Inference; - r:gives { - (3 6 4) :sort (3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 4) list:firstRest (3 (6 4))}] - skolem:lemma6172 - skolem:lemma4395 - skolem:lemma4739 - [ a r:Fact; r:gives {(3 4 6) list:firstRest (3 (4 6))}] - [ a r:Fact; r:gives {(() (3 4 6)) list:append (3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4996 a r:Inference; - r:gives { - (2 (3 6 5)) :split (() (3 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 5) list:firstRest (3 (6 5))}] - [ a r:Fact; r:gives {(3 6 5) list:firstRest (3 (6 5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 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_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4997 a r:Inference; - r:gives { - (3 6 5) :sort (3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 5) list:firstRest (3 (6 5))}] - skolem:lemma6173 - skolem:lemma4395 - skolem:lemma4567 - [ a r:Fact; r:gives {(3 5 6) list:firstRest (3 (5 6))}] - [ a r:Fact; r:gives {(() (3 5 6)) list:append (3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 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_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma4998 a r:Inference; - r:gives { - (2 (3 6 6)) :split (() (3 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 6) list:firstRest (3 (6 6))}] - [ a r:Fact; r:gives {(3 6 6) list:firstRest (3 (6 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma4999 a r:Inference; - r:gives { - (3 6 6) :sort (3 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 6) list:firstRest (3 (6 6))}] - skolem:lemma6174 - skolem:lemma4395 - skolem:lemma4569 - [ a r:Fact; r:gives {(3 6 6) list:firstRest (3 (6 6))}] - [ a r:Fact; r:gives {(() (3 6 6)) list:append (3 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5000 a r:Inference; - r:gives { - (2 (3 6 7)) :split (() (3 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 7) list:firstRest (3 (6 7))}] - [ a r:Fact; r:gives {(3 6 7) list:firstRest (3 (6 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5001 a r:Inference; - r:gives { - (3 6 7) :sort (3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 7) list:firstRest (3 (6 7))}] - skolem:lemma6175 - skolem:lemma4395 - skolem:lemma4575 - [ a r:Fact; r:gives {(3 6 7) list:firstRest (3 (6 7))}] - [ a r:Fact; r:gives {(() (3 6 7)) list:append (3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5002 a r:Inference; - r:gives { - (2 (3 6 8)) :split (() (3 6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 8) list:firstRest (3 (6 8))}] - [ a r:Fact; r:gives {(3 6 8) list:firstRest (3 (6 8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5003 a r:Inference; - r:gives { - (3 6 8) :sort (3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 8) list:firstRest (3 (6 8))}] - skolem:lemma6176 - skolem:lemma4395 - skolem:lemma4581 - [ a r:Fact; r:gives {(3 6 8) list:firstRest (3 (6 8))}] - [ a r:Fact; r:gives {(() (3 6 8)) list:append (3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5004 a r:Inference; - r:gives { - (2 (3 6 9)) :split (() (3 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 9) list:firstRest (3 (6 9))}] - [ a r:Fact; r:gives {(3 6 9) list:firstRest (3 (6 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5005 a r:Inference; - r:gives { - (3 6 9) :sort (3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6 9) list:firstRest (3 (6 9))}] - skolem:lemma6177 - skolem:lemma4395 - skolem:lemma4583 - [ a r:Fact; r:gives {(3 6 9) list:firstRest (3 (6 9))}] - [ a r:Fact; r:gives {(() (3 6 9)) list:append (3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5006 a r:Inference; - r:gives { - (2 (3 7 0)) :split ((0) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 0) list:firstRest (3 (7 0))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5007 a r:Inference; - r:gives { - (2 (3 7 1)) :split ((1) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 1) list:firstRest (3 (7 1))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5008 a r:Inference; - r:gives { - (2 (3 7 2)) :split ((2) (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 2) list:firstRest (3 (7 2))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 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_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5009 a r:Inference; - r:gives { - (2 (3 7 3)) :split (() (3 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 3) list:firstRest (3 (7 3))}] - [ a r:Fact; r:gives {(3 7 3) list:firstRest (3 (7 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5010 a r:Inference; - r:gives { - (3 7 3) :sort (3 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 3) list:firstRest (3 (7 3))}] - skolem:lemma6178 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {((3) (3 7)) list:append (3 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5011 a r:Inference; - r:gives { - (2 (3 7 4)) :split (() (3 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 4) list:firstRest (3 (7 4))}] - [ a r:Fact; r:gives {(3 7 4) list:firstRest (3 (7 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5012 a r:Inference; - r:gives { - (3 7 4) :sort (3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 4) list:firstRest (3 (7 4))}] - skolem:lemma6179 - skolem:lemma4395 - skolem:lemma4594 - [ a r:Fact; r:gives {(3 4 7) list:firstRest (3 (4 7))}] - [ a r:Fact; r:gives {(() (3 4 7)) list:append (3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5013 a r:Inference; - r:gives { - (2 (3 7 5)) :split (() (3 7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 5) list:firstRest (3 (7 5))}] - [ a r:Fact; r:gives {(3 7 5) list:firstRest (3 (7 5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 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_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5014 a r:Inference; - r:gives { - (3 7 5) :sort (3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 5) list:firstRest (3 (7 5))}] - skolem:lemma6180 - skolem:lemma4395 - skolem:lemma4596 - [ a r:Fact; r:gives {(3 5 7) list:firstRest (3 (5 7))}] - [ a r:Fact; r:gives {(() (3 5 7)) list:append (3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 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_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5015 a r:Inference; - r:gives { - (2 (3 7 6)) :split (() (3 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 6) list:firstRest (3 (7 6))}] - [ a r:Fact; r:gives {(3 7 6) list:firstRest (3 (7 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5016 a r:Inference; - r:gives { - (3 7 6) :sort (3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 6) list:firstRest (3 (7 6))}] - skolem:lemma6181 - skolem:lemma4395 - skolem:lemma4598 - [ a r:Fact; r:gives {(3 6 7) list:firstRest (3 (6 7))}] - [ a r:Fact; r:gives {(() (3 6 7)) list:append (3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5017 a r:Inference; - r:gives { - (2 (3 7 7)) :split (() (3 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 7) list:firstRest (3 (7 7))}] - [ a r:Fact; r:gives {(3 7 7) list:firstRest (3 (7 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5018 a r:Inference; - r:gives { - (3 7 7) :sort (3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 7) list:firstRest (3 (7 7))}] - skolem:lemma6182 - skolem:lemma4395 - skolem:lemma4600 - [ a r:Fact; r:gives {(3 7 7) list:firstRest (3 (7 7))}] - [ a r:Fact; r:gives {(() (3 7 7)) list:append (3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5019 a r:Inference; - r:gives { - (2 (3 7 8)) :split (() (3 7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 8) list:firstRest (3 (7 8))}] - [ a r:Fact; r:gives {(3 7 8) list:firstRest (3 (7 8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5020 a r:Inference; - r:gives { - (3 7 8) :sort (3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 8) list:firstRest (3 (7 8))}] - skolem:lemma6183 - skolem:lemma4395 - skolem:lemma4606 - [ a r:Fact; r:gives {(3 7 8) list:firstRest (3 (7 8))}] - [ a r:Fact; r:gives {(() (3 7 8)) list:append (3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5021 a r:Inference; - r:gives { - (2 (3 7 9)) :split (() (3 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 9) list:firstRest (3 (7 9))}] - [ a r:Fact; r:gives {(3 7 9) list:firstRest (3 (7 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5022 a r:Inference; - r:gives { - (3 7 9) :sort (3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7 9) list:firstRest (3 (7 9))}] - skolem:lemma6184 - skolem:lemma4395 - skolem:lemma4610 - [ a r:Fact; r:gives {(3 7 9) list:firstRest (3 (7 9))}] - [ a r:Fact; r:gives {(() (3 7 9)) list:append (3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5023 a r:Inference; - r:gives { - (2 (3 8 0)) :split ((0) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 0) list:firstRest (3 (8 0))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5024 a r:Inference; - r:gives { - (2 (3 8 1)) :split ((1) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 1) list:firstRest (3 (8 1))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5025 a r:Inference; - r:gives { - (2 (3 8 2)) :split ((2) (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 2) list:firstRest (3 (8 2))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 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_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5026 a r:Inference; - r:gives { - (2 (3 8 3)) :split (() (3 8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 3) list:firstRest (3 (8 3))}] - [ a r:Fact; r:gives {(3 8 3) list:firstRest (3 (8 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5027 a r:Inference; - r:gives { - (3 8 3) :sort (3 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 3) list:firstRest (3 (8 3))}] - skolem:lemma6185 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {((3) (3 8)) list:append (3 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5028 a r:Inference; - r:gives { - (2 (3 8 4)) :split (() (3 8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 4) list:firstRest (3 (8 4))}] - [ a r:Fact; r:gives {(3 8 4) list:firstRest (3 (8 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5029 a r:Inference; - r:gives { - (3 8 4) :sort (3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 4) list:firstRest (3 (8 4))}] - skolem:lemma6186 - skolem:lemma4395 - skolem:lemma4621 - [ a r:Fact; r:gives {(3 4 8) list:firstRest (3 (4 8))}] - [ a r:Fact; r:gives {(() (3 4 8)) list:append (3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5030 a r:Inference; - r:gives { - (2 (3 8 6)) :split (() (3 8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 6) list:firstRest (3 (8 6))}] - [ a r:Fact; r:gives {(3 8 6) list:firstRest (3 (8 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5031 a r:Inference; - r:gives { - (3 8 6) :sort (3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 6) list:firstRest (3 (8 6))}] - skolem:lemma6187 - skolem:lemma4395 - skolem:lemma4625 - [ a r:Fact; r:gives {(3 6 8) list:firstRest (3 (6 8))}] - [ a r:Fact; r:gives {(() (3 6 8)) list:append (3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5032 a r:Inference; - r:gives { - (2 (3 8 7)) :split (() (3 8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 7) list:firstRest (3 (8 7))}] - [ a r:Fact; r:gives {(3 8 7) list:firstRest (3 (8 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5033 a r:Inference; - r:gives { - (3 8 7) :sort (3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 7) list:firstRest (3 (8 7))}] - skolem:lemma6188 - skolem:lemma4395 - skolem:lemma4627 - [ a r:Fact; r:gives {(3 7 8) list:firstRest (3 (7 8))}] - [ a r:Fact; r:gives {(() (3 7 8)) list:append (3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5034 a r:Inference; - r:gives { - (2 (3 8 8)) :split (() (3 8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 8) list:firstRest (3 (8 8))}] - [ a r:Fact; r:gives {(3 8 8) list:firstRest (3 (8 8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5035 a r:Inference; - r:gives { - (3 8 8) :sort (3 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 8) list:firstRest (3 (8 8))}] - skolem:lemma6189 - skolem:lemma4395 - skolem:lemma4629 - [ a r:Fact; r:gives {(3 8 8) list:firstRest (3 (8 8))}] - [ a r:Fact; r:gives {(() (3 8 8)) list:append (3 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5036 a r:Inference; - r:gives { - (2 (3 8 9)) :split (() (3 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 9) list:firstRest (3 (8 9))}] - [ a r:Fact; r:gives {(3 8 9) list:firstRest (3 (8 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5037 a r:Inference; - r:gives { - (3 8 9) :sort (3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8 9) list:firstRest (3 (8 9))}] - skolem:lemma6190 - skolem:lemma4395 - skolem:lemma4631 - [ a r:Fact; r:gives {(3 8 9) list:firstRest (3 (8 9))}] - [ a r:Fact; r:gives {(() (3 8 9)) list:append (3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5038 a r:Inference; - r:gives { - (2 (3 9 0)) :split ((0) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 0) list:firstRest (3 (9 0))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5039 a r:Inference; - r:gives { - (2 (3 9 1)) :split ((1) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 1) list:firstRest (3 (9 1))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5040 a r:Inference; - r:gives { - (2 (3 9 2)) :split ((2) (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 2) list:firstRest (3 (9 2))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 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_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5041 a r:Inference; - r:gives { - (2 (3 9 3)) :split (() (3 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 3) list:firstRest (3 (9 3))}] - [ a r:Fact; r:gives {(3 9 3) list:firstRest (3 (9 3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5042 a r:Inference; - r:gives { - (3 9 3) :sort (3 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 3) list:firstRest (3 (9 3))}] - skolem:lemma6191 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {((3) (3 9)) list:append (3 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5043 a r:Inference; - r:gives { - (2 (3 9 4)) :split (() (3 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 4) list:firstRest (3 (9 4))}] - [ a r:Fact; r:gives {(3 9 4) list:firstRest (3 (9 4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5044 a r:Inference; - r:gives { - (3 9 4) :sort (3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 4) list:firstRest (3 (9 4))}] - skolem:lemma6192 - skolem:lemma4395 - skolem:lemma4640 - [ a r:Fact; r:gives {(3 4 9) list:firstRest (3 (4 9))}] - [ a r:Fact; r:gives {(() (3 4 9)) list:append (3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5045 a r:Inference; - r:gives { - (2 (3 9 5)) :split (() (3 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 5) list:firstRest (3 (9 5))}] - [ a r:Fact; r:gives {(3 9 5) list:firstRest (3 (9 5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 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_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5046 a r:Inference; - r:gives { - (3 9 5) :sort (3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 5) list:firstRest (3 (9 5))}] - skolem:lemma6193 - skolem:lemma4395 - skolem:lemma4642 - [ a r:Fact; r:gives {(3 5 9) list:firstRest (3 (5 9))}] - [ a r:Fact; r:gives {(() (3 5 9)) list:append (3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 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_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5047 a r:Inference; - r:gives { - (2 (3 9 6)) :split (() (3 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 6) list:firstRest (3 (9 6))}] - [ a r:Fact; r:gives {(3 9 6) list:firstRest (3 (9 6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5048 a r:Inference; - r:gives { - (3 9 6) :sort (3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 6) list:firstRest (3 (9 6))}] - skolem:lemma6194 - skolem:lemma4395 - skolem:lemma4644 - [ a r:Fact; r:gives {(3 6 9) list:firstRest (3 (6 9))}] - [ a r:Fact; r:gives {(() (3 6 9)) list:append (3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5049 a r:Inference; - r:gives { - (2 (3 9 7)) :split (() (3 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 7) list:firstRest (3 (9 7))}] - [ a r:Fact; r:gives {(3 9 7) list:firstRest (3 (9 7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5050 a r:Inference; - r:gives { - (3 9 7) :sort (3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 7) list:firstRest (3 (9 7))}] - skolem:lemma6195 - skolem:lemma4395 - skolem:lemma4646 - [ a r:Fact; r:gives {(3 7 9) list:firstRest (3 (7 9))}] - [ a r:Fact; r:gives {(() (3 7 9)) list:append (3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5051 a r:Inference; - r:gives { - (2 (3 9 8)) :split (() (3 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 8) list:firstRest (3 (9 8))}] - [ a r:Fact; r:gives {(3 9 8) list:firstRest (3 (9 8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5052 a r:Inference; - r:gives { - (3 9 8) :sort (3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 8) list:firstRest (3 (9 8))}] - skolem:lemma6196 - skolem:lemma4395 - skolem:lemma4648 - [ a r:Fact; r:gives {(3 8 9) list:firstRest (3 (8 9))}] - [ a r:Fact; r:gives {(() (3 8 9)) list:append (3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5053 a r:Inference; - r:gives { - (2 (3 9 9)) :split (() (3 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 9) list:firstRest (3 (9 9))}] - [ a r:Fact; r:gives {(3 9 9) list:firstRest (3 (9 9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5054 a r:Inference; - r:gives { - (3 9 9) :sort (3 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9 9) list:firstRest (3 (9 9))}] - skolem:lemma6197 - skolem:lemma4395 - skolem:lemma4650 - [ a r:Fact; r:gives {(3 9 9) list:firstRest (3 (9 9))}] - [ a r:Fact; r:gives {(() (3 9 9)) list:append (3 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5055 a r:Inference; - r:gives { - (2 (4 0 0)) :split ((0 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 0) list:firstRest (4 (0 0))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5056 a r:Inference; - r:gives { - (2 (4 0 1)) :split ((0 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 1) list:firstRest (4 (0 1))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5057 a r:Inference; - r:gives { - (2 (4 0 2)) :split ((0 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 2) list:firstRest (4 (0 2))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5058 a r:Inference; - r:gives { - (2 (4 0 3)) :split ((0) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 3) list:firstRest (4 (0 3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5059 a r:Inference; - r:gives { - (2 (4 0 4)) :split ((0) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 4) list:firstRest (4 (0 4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5060 a r:Inference; - r:gives { - (2 (4 0 5)) :split ((0) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 5) list:firstRest (4 (0 5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5061 a r:Inference; - r:gives { - (2 (4 0 7)) :split ((0) (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 7) list:firstRest (4 (0 7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5062 a r:Inference; - r:gives { - (2 (4 0 8)) :split ((0) (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 8) list:firstRest (4 (0 8))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5063 a r:Inference; - r:gives { - (2 (4 0 9)) :split ((0) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0 9) list:firstRest (4 (0 9))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5064 a r:Inference; - r:gives { - (2 (4 1 0)) :split ((1 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 0) list:firstRest (4 (1 0))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5065 a r:Inference; - r:gives { - (2 (4 1 1)) :split ((1 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 1) list:firstRest (4 (1 1))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5066 a r:Inference; - r:gives { - (2 (4 1 2)) :split ((1 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 2) list:firstRest (4 (1 2))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5067 a r:Inference; - r:gives { - (2 (4 1 3)) :split ((1) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 3) list:firstRest (4 (1 3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5068 a r:Inference; - r:gives { - (2 (4 1 4)) :split ((1) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 4) list:firstRest (4 (1 4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5069 a r:Inference; - r:gives { - (2 (4 1 5)) :split ((1) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 5) list:firstRest (4 (1 5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5070 a r:Inference; - r:gives { - (2 (4 1 6)) :split ((1) (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 6) list:firstRest (4 (1 6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5071 a r:Inference; - r:gives { - (2 (4 1 8)) :split ((1) (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 8) list:firstRest (4 (1 8))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5072 a r:Inference; - r:gives { - (2 (4 1 9)) :split ((1) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1 9) list:firstRest (4 (1 9))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5073 a r:Inference; - r:gives { - (2 (4 2 0)) :split ((2 0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 0) list:firstRest (4 (2 0))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5074 a r:Inference; - r:gives { - (2 (4 2 1)) :split ((2 1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 1) list:firstRest (4 (2 1))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5075 a r:Inference; - r:gives { - (2 (4 2 2)) :split ((2 2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 2) list:firstRest (4 (2 2))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5076 a r:Inference; - r:gives { - (2 (4 2 3)) :split ((2) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 3) list:firstRest (4 (2 3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5077 a r:Inference; - r:gives { - (2 (4 2 4)) :split ((2) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 4) list:firstRest (4 (2 4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5078 a r:Inference; - r:gives { - (2 (4 2 5)) :split ((2) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 5) list:firstRest (4 (2 5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5079 a r:Inference; - r:gives { - (2 (4 2 6)) :split ((2) (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 6) list:firstRest (4 (2 6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5080 a r:Inference; - r:gives { - (2 (4 2 7)) :split ((2) (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 7) list:firstRest (4 (2 7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5081 a r:Inference; - r:gives { - (2 (4 2 9)) :split ((2) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2 9) list:firstRest (4 (2 9))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5082 a r:Inference; - r:gives { - (2 (4 3 0)) :split ((0) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 0) list:firstRest (4 (3 0))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5083 a r:Inference; - r:gives { - (2 (4 3 1)) :split ((1) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 1) list:firstRest (4 (3 1))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5084 a r:Inference; - r:gives { - (2 (4 3 2)) :split ((2) (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 2) list:firstRest (4 (3 2))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5085 a r:Inference; - r:gives { - (2 (4 3 3)) :split (() (4 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 3) list:firstRest (4 (3 3))}] - [ a r:Fact; r:gives {(4 3 3) list:firstRest (4 (3 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5086 a r:Inference; - r:gives { - (4 3 3) :sort (3 3 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 3) list:firstRest (4 (3 3))}] - skolem:lemma6198 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((3 3) (4)) list:append (3 3 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 4)]; - r:rule skolem:lemma4396. - -skolem:lemma5087 a r:Inference; - r:gives { - (2 (4 3 4)) :split (() (4 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 4) list:firstRest (4 (3 4))}] - [ a r:Fact; r:gives {(4 3 4) list:firstRest (4 (3 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5088 a r:Inference; - r:gives { - (4 3 4) :sort (3 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 4) list:firstRest (4 (3 4))}] - skolem:lemma6199 - skolem:lemma4509 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((3 4) (4)) list:append (3 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma5089 a r:Inference; - r:gives { - (2 (4 3 5)) :split (() (4 3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 5) list:firstRest (4 (3 5))}] - [ a r:Fact; r:gives {(4 3 5) list:firstRest (4 (3 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5090 a r:Inference; - r:gives { - (4 3 5) :sort (3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 5) list:firstRest (4 (3 5))}] - skolem:lemma6200 - skolem:lemma4408 - skolem:lemma4416 - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {((3) (4 5)) list:append (3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5091 a r:Inference; - r:gives { - (2 (4 3 6)) :split (() (4 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 6) list:firstRest (4 (3 6))}] - [ a r:Fact; r:gives {(4 3 6) list:firstRest (4 (3 6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5092 a r:Inference; - r:gives { - (4 3 6) :sort (3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 6) list:firstRest (4 (3 6))}] - skolem:lemma6201 - skolem:lemma4408 - skolem:lemma4458 - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {((3) (4 6)) list:append (3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5093 a r:Inference; - r:gives { - (2 (4 3 7)) :split (() (4 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 7) list:firstRest (4 (3 7))}] - [ a r:Fact; r:gives {(4 3 7) list:firstRest (4 (3 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5094 a r:Inference; - r:gives { - (4 3 7) :sort (3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 7) list:firstRest (4 (3 7))}] - skolem:lemma6202 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {((3) (4 7)) list:append (3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5095 a r:Inference; - r:gives { - (2 (4 3 8)) :split (() (4 3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 8) list:firstRest (4 (3 8))}] - [ a r:Fact; r:gives {(4 3 8) list:firstRest (4 (3 8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5096 a r:Inference; - r:gives { - (4 3 8) :sort (3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 8) list:firstRest (4 (3 8))}] - skolem:lemma6203 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {((3) (4 8)) list:append (3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5097 a r:Inference; - r:gives { - (2 (4 3 9)) :split (() (4 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 9) list:firstRest (4 (3 9))}] - [ a r:Fact; r:gives {(4 3 9) list:firstRest (4 (3 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5098 a r:Inference; - r:gives { - (4 3 9) :sort (3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3 9) list:firstRest (4 (3 9))}] - skolem:lemma6204 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {((3) (4 9)) list:append (3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5099 a r:Inference; - r:gives { - (2 (4 4 0)) :split ((0) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 0) list:firstRest (4 (4 0))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5100 a r:Inference; - r:gives { - (2 (4 4 1)) :split ((1) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 1) list:firstRest (4 (4 1))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5101 a r:Inference; - r:gives { - (2 (4 4 2)) :split ((2) (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 2) list:firstRest (4 (4 2))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5102 a r:Inference; - r:gives { - (2 (4 4 3)) :split (() (4 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 3) list:firstRest (4 (4 3))}] - [ a r:Fact; r:gives {(4 4 3) list:firstRest (4 (4 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5103 a r:Inference; - r:gives { - (4 4 3) :sort (3 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 3) list:firstRest (4 (4 3))}] - skolem:lemma6205 - skolem:lemma4524 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((3 4) (4)) list:append (3 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma5104 a r:Inference; - r:gives { - (2 (4 4 4)) :split (() (4 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 4) list:firstRest (4 (4 4))}] - [ a r:Fact; r:gives {(4 4 4) list:firstRest (4 (4 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5105 a r:Inference; - r:gives { - (4 4 4) :sort (4 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 4) list:firstRest (4 (4 4))}] - skolem:lemma6206 - skolem:lemma4526 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((4 4) (4)) list:append (4 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma5106 a r:Inference; - r:gives { - (2 (4 4 5)) :split (() (4 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 5) list:firstRest (4 (4 5))}] - [ a r:Fact; r:gives {(4 4 5) list:firstRest (4 (4 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5107 a r:Inference; - r:gives { - (4 4 5) :sort (4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 5) list:firstRest (4 (4 5))}] - skolem:lemma6207 - skolem:lemma4414 - skolem:lemma4416 - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {((4) (4 5)) list:append (4 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5108 a r:Inference; - r:gives { - (2 (4 4 6)) :split (() (4 4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 6) list:firstRest (4 (4 6))}] - [ a r:Fact; r:gives {(4 4 6) list:firstRest (4 (4 6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5109 a r:Inference; - r:gives { - (4 4 6) :sort (4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 6) list:firstRest (4 (4 6))}] - skolem:lemma6208 - skolem:lemma4414 - skolem:lemma4458 - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {((4) (4 6)) list:append (4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5110 a r:Inference; - r:gives { - (2 (4 4 7)) :split (() (4 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 7) list:firstRest (4 (4 7))}] - [ a r:Fact; r:gives {(4 4 7) list:firstRest (4 (4 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5111 a r:Inference; - r:gives { - (4 4 7) :sort (4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 7) list:firstRest (4 (4 7))}] - skolem:lemma6209 - skolem:lemma4414 - skolem:lemma4422 - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {((4) (4 7)) list:append (4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5112 a r:Inference; - r:gives { - (2 (4 4 8)) :split (() (4 4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 8) list:firstRest (4 (4 8))}] - [ a r:Fact; r:gives {(4 4 8) list:firstRest (4 (4 8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5113 a r:Inference; - r:gives { - (4 4 8) :sort (4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 8) list:firstRest (4 (4 8))}] - skolem:lemma6210 - skolem:lemma4414 - skolem:lemma4426 - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {((4) (4 8)) list:append (4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5114 a r:Inference; - r:gives { - (2 (4 4 9)) :split (() (4 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 9) list:firstRest (4 (4 9))}] - [ a r:Fact; r:gives {(4 4 9) list:firstRest (4 (4 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5115 a r:Inference; - r:gives { - (4 4 9) :sort (4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 9) list:firstRest (4 (4 9))}] - skolem:lemma6211 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {((4) (4 9)) list:append (4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5116 a r:Inference; - r:gives { - (2 (4 5 0)) :split ((0) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 0) list:firstRest (4 (5 0))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5117 a r:Inference; - r:gives { - (2 (4 5 1)) :split ((1) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 1) list:firstRest (4 (5 1))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5118 a r:Inference; - r:gives { - (2 (4 5 2)) :split ((2) (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 2) list:firstRest (4 (5 2))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5119 a r:Inference; - r:gives { - (2 (4 5 3)) :split (() (4 5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 3) list:firstRest (4 (5 3))}] - [ a r:Fact; r:gives {(4 5 3) list:firstRest (4 (5 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5120 a r:Inference; - r:gives { - (4 5 3) :sort (3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 3) list:firstRest (4 (5 3))}] - skolem:lemma6212 - skolem:lemma4408 - skolem:lemma4416 - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {((3) (4 5)) list:append (3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5121 a r:Inference; - r:gives { - (2 (4 5 4)) :split (() (4 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 4) list:firstRest (4 (5 4))}] - [ a r:Fact; r:gives {(4 5 4) list:firstRest (4 (5 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5122 a r:Inference; - r:gives { - (4 5 4) :sort (4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 4) list:firstRest (4 (5 4))}] - skolem:lemma6213 - skolem:lemma4414 - skolem:lemma4416 - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {((4) (4 5)) list:append (4 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5123 a r:Inference; - r:gives { - (2 (4 5 5)) :split (() (4 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 5) list:firstRest (4 (5 5))}] - [ a r:Fact; r:gives {(4 5 5) list:firstRest (4 (5 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5124 a r:Inference; - r:gives { - (4 5 5) :sort (4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 5) list:firstRest (4 (5 5))}] - skolem:lemma6214 - skolem:lemma4395 - skolem:lemma4543 - [ a r:Fact; r:gives {(4 5 5) list:firstRest (4 (5 5))}] - [ a r:Fact; r:gives {(() (4 5 5)) list:append (4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5125 a r:Inference; - r:gives { - (2 (4 5 6)) :split (() (4 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 6) list:firstRest (4 (5 6))}] - [ a r:Fact; r:gives {(4 5 6) list:firstRest (4 (5 6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5126 a r:Inference; - r:gives { - (4 5 6) :sort (4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 6) list:firstRest (4 (5 6))}] - skolem:lemma6215 - skolem:lemma4395 - skolem:lemma4547 - [ a r:Fact; r:gives {(4 5 6) list:firstRest (4 (5 6))}] - [ a r:Fact; r:gives {(() (4 5 6)) list:append (4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5127 a r:Inference; - r:gives { - (2 (4 5 7)) :split (() (4 5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 7) list:firstRest (4 (5 7))}] - [ a r:Fact; r:gives {(4 5 7) list:firstRest (4 (5 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5128 a r:Inference; - r:gives { - (4 5 7) :sort (4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 7) list:firstRest (4 (5 7))}] - skolem:lemma6216 - skolem:lemma4395 - skolem:lemma4551 - [ a r:Fact; r:gives {(4 5 7) list:firstRest (4 (5 7))}] - [ a r:Fact; r:gives {(() (4 5 7)) list:append (4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5129 a r:Inference; - r:gives { - (2 (4 5 8)) :split (() (4 5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 8) list:firstRest (4 (5 8))}] - [ a r:Fact; r:gives {(4 5 8) list:firstRest (4 (5 8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5130 a r:Inference; - r:gives { - (4 5 8) :sort (4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 8) list:firstRest (4 (5 8))}] - skolem:lemma6217 - skolem:lemma4395 - skolem:lemma4555 - [ a r:Fact; r:gives {(4 5 8) list:firstRest (4 (5 8))}] - [ a r:Fact; r:gives {(() (4 5 8)) list:append (4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5131 a r:Inference; - r:gives { - (2 (4 5 9)) :split (() (4 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 9) list:firstRest (4 (5 9))}] - [ a r:Fact; r:gives {(4 5 9) list:firstRest (4 (5 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5132 a r:Inference; - r:gives { - (4 5 9) :sort (4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5 9) list:firstRest (4 (5 9))}] - skolem:lemma6218 - skolem:lemma4395 - skolem:lemma4559 - [ a r:Fact; r:gives {(4 5 9) list:firstRest (4 (5 9))}] - [ a r:Fact; r:gives {(() (4 5 9)) list:append (4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5133 a r:Inference; - r:gives { - (2 (4 6 1)) :split ((1) (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 1) list:firstRest (4 (6 1))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5134 a r:Inference; - r:gives { - (2 (4 6 2)) :split ((2) (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 2) list:firstRest (4 (6 2))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5135 a r:Inference; - r:gives { - (2 (4 6 3)) :split (() (4 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 3) list:firstRest (4 (6 3))}] - [ a r:Fact; r:gives {(4 6 3) list:firstRest (4 (6 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5136 a r:Inference; - r:gives { - (4 6 3) :sort (3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 3) list:firstRest (4 (6 3))}] - skolem:lemma6219 - skolem:lemma4408 - skolem:lemma4458 - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {((3) (4 6)) list:append (3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5137 a r:Inference; - r:gives { - (2 (4 6 4)) :split (() (4 6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 4) list:firstRest (4 (6 4))}] - [ a r:Fact; r:gives {(4 6 4) list:firstRest (4 (6 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5138 a r:Inference; - r:gives { - (4 6 4) :sort (4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 4) list:firstRest (4 (6 4))}] - skolem:lemma6220 - skolem:lemma4414 - skolem:lemma4458 - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {((4) (4 6)) list:append (4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5139 a r:Inference; - r:gives { - (2 (4 6 5)) :split (() (4 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 5) list:firstRest (4 (6 5))}] - [ a r:Fact; r:gives {(4 6 5) list:firstRest (4 (6 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5140 a r:Inference; - r:gives { - (4 6 5) :sort (4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 5) list:firstRest (4 (6 5))}] - skolem:lemma6221 - skolem:lemma4395 - skolem:lemma4567 - [ a r:Fact; r:gives {(4 5 6) list:firstRest (4 (5 6))}] - [ a r:Fact; r:gives {(() (4 5 6)) list:append (4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5141 a r:Inference; - r:gives { - (2 (4 6 6)) :split (() (4 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 6) list:firstRest (4 (6 6))}] - [ a r:Fact; r:gives {(4 6 6) list:firstRest (4 (6 6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5142 a r:Inference; - r:gives { - (4 6 6) :sort (4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 6) list:firstRest (4 (6 6))}] - skolem:lemma6222 - skolem:lemma4395 - skolem:lemma4569 - [ a r:Fact; r:gives {(4 6 6) list:firstRest (4 (6 6))}] - [ a r:Fact; r:gives {(() (4 6 6)) list:append (4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5143 a r:Inference; - r:gives { - (2 (4 6 7)) :split (() (4 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 7) list:firstRest (4 (6 7))}] - [ a r:Fact; r:gives {(4 6 7) list:firstRest (4 (6 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5144 a r:Inference; - r:gives { - (4 6 7) :sort (4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 7) list:firstRest (4 (6 7))}] - skolem:lemma6223 - skolem:lemma4395 - skolem:lemma4575 - [ a r:Fact; r:gives {(4 6 7) list:firstRest (4 (6 7))}] - [ a r:Fact; r:gives {(() (4 6 7)) list:append (4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5145 a r:Inference; - r:gives { - (2 (4 6 9)) :split (() (4 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 9) list:firstRest (4 (6 9))}] - [ a r:Fact; r:gives {(4 6 9) list:firstRest (4 (6 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5146 a r:Inference; - r:gives { - (4 6 9) :sort (4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6 9) list:firstRest (4 (6 9))}] - skolem:lemma6224 - skolem:lemma4395 - skolem:lemma4583 - [ a r:Fact; r:gives {(4 6 9) list:firstRest (4 (6 9))}] - [ a r:Fact; r:gives {(() (4 6 9)) list:append (4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5147 a r:Inference; - r:gives { - (2 (4 7 0)) :split ((0) (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 0) list:firstRest (4 (7 0))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5148 a r:Inference; - r:gives { - (2 (4 7 2)) :split ((2) (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 2) list:firstRest (4 (7 2))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5149 a r:Inference; - r:gives { - (2 (4 7 3)) :split (() (4 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 3) list:firstRest (4 (7 3))}] - [ a r:Fact; r:gives {(4 7 3) list:firstRest (4 (7 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5150 a r:Inference; - r:gives { - (4 7 3) :sort (3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 3) list:firstRest (4 (7 3))}] - skolem:lemma6225 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {((3) (4 7)) list:append (3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5151 a r:Inference; - r:gives { - (2 (4 7 4)) :split (() (4 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 4) list:firstRest (4 (7 4))}] - [ a r:Fact; r:gives {(4 7 4) list:firstRest (4 (7 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5152 a r:Inference; - r:gives { - (4 7 4) :sort (4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 4) list:firstRest (4 (7 4))}] - skolem:lemma6226 - skolem:lemma4414 - skolem:lemma4422 - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {((4) (4 7)) list:append (4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5153 a r:Inference; - r:gives { - (2 (4 7 5)) :split (() (4 7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 5) list:firstRest (4 (7 5))}] - [ a r:Fact; r:gives {(4 7 5) list:firstRest (4 (7 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5154 a r:Inference; - r:gives { - (4 7 5) :sort (4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 5) list:firstRest (4 (7 5))}] - skolem:lemma6227 - skolem:lemma4395 - skolem:lemma4596 - [ a r:Fact; r:gives {(4 5 7) list:firstRest (4 (5 7))}] - [ a r:Fact; r:gives {(() (4 5 7)) list:append (4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5155 a r:Inference; - r:gives { - (2 (4 7 6)) :split (() (4 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 6) list:firstRest (4 (7 6))}] - [ a r:Fact; r:gives {(4 7 6) list:firstRest (4 (7 6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5156 a r:Inference; - r:gives { - (4 7 6) :sort (4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 6) list:firstRest (4 (7 6))}] - skolem:lemma6228 - skolem:lemma4395 - skolem:lemma4598 - [ a r:Fact; r:gives {(4 6 7) list:firstRest (4 (6 7))}] - [ a r:Fact; r:gives {(() (4 6 7)) list:append (4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5157 a r:Inference; - r:gives { - (2 (4 7 7)) :split (() (4 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 7) list:firstRest (4 (7 7))}] - [ a r:Fact; r:gives {(4 7 7) list:firstRest (4 (7 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5158 a r:Inference; - r:gives { - (4 7 7) :sort (4 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 7) list:firstRest (4 (7 7))}] - skolem:lemma6229 - skolem:lemma4395 - skolem:lemma4600 - [ a r:Fact; r:gives {(4 7 7) list:firstRest (4 (7 7))}] - [ a r:Fact; r:gives {(() (4 7 7)) list:append (4 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5159 a r:Inference; - r:gives { - (2 (4 7 8)) :split (() (4 7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 8) list:firstRest (4 (7 8))}] - [ a r:Fact; r:gives {(4 7 8) list:firstRest (4 (7 8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5160 a r:Inference; - r:gives { - (4 7 8) :sort (4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 8) list:firstRest (4 (7 8))}] - skolem:lemma6230 - skolem:lemma4395 - skolem:lemma4606 - [ a r:Fact; r:gives {(4 7 8) list:firstRest (4 (7 8))}] - [ a r:Fact; r:gives {(() (4 7 8)) list:append (4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5161 a r:Inference; - r:gives { - (2 (4 7 9)) :split (() (4 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 9) list:firstRest (4 (7 9))}] - [ a r:Fact; r:gives {(4 7 9) list:firstRest (4 (7 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5162 a r:Inference; - r:gives { - (4 7 9) :sort (4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7 9) list:firstRest (4 (7 9))}] - skolem:lemma6231 - skolem:lemma4395 - skolem:lemma4610 - [ a r:Fact; r:gives {(4 7 9) list:firstRest (4 (7 9))}] - [ a r:Fact; r:gives {(() (4 7 9)) list:append (4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5163 a r:Inference; - r:gives { - (2 (4 8 0)) :split ((0) (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 0) list:firstRest (4 (8 0))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5164 a r:Inference; - r:gives { - (2 (4 8 1)) :split ((1) (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 1) list:firstRest (4 (8 1))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5165 a r:Inference; - r:gives { - (2 (4 8 3)) :split (() (4 8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 3) list:firstRest (4 (8 3))}] - [ a r:Fact; r:gives {(4 8 3) list:firstRest (4 (8 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5166 a r:Inference; - r:gives { - (4 8 3) :sort (3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 3) list:firstRest (4 (8 3))}] - skolem:lemma6232 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {((3) (4 8)) list:append (3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5167 a r:Inference; - r:gives { - (2 (4 8 4)) :split (() (4 8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 4) list:firstRest (4 (8 4))}] - [ a r:Fact; r:gives {(4 8 4) list:firstRest (4 (8 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5168 a r:Inference; - r:gives { - (4 8 4) :sort (4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 4) list:firstRest (4 (8 4))}] - skolem:lemma6233 - skolem:lemma4414 - skolem:lemma4426 - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {((4) (4 8)) list:append (4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5169 a r:Inference; - r:gives { - (2 (4 8 5)) :split (() (4 8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 5) list:firstRest (4 (8 5))}] - [ a r:Fact; r:gives {(4 8 5) list:firstRest (4 (8 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5170 a r:Inference; - r:gives { - (4 8 5) :sort (4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 5) list:firstRest (4 (8 5))}] - skolem:lemma6234 - skolem:lemma4395 - skolem:lemma4623 - [ a r:Fact; r:gives {(4 5 8) list:firstRest (4 (5 8))}] - [ a r:Fact; r:gives {(() (4 5 8)) list:append (4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5171 a r:Inference; - r:gives { - (2 (4 8 7)) :split (() (4 8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 7) list:firstRest (4 (8 7))}] - [ a r:Fact; r:gives {(4 8 7) list:firstRest (4 (8 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5172 a r:Inference; - r:gives { - (4 8 7) :sort (4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 7) list:firstRest (4 (8 7))}] - skolem:lemma6235 - skolem:lemma4395 - skolem:lemma4627 - [ a r:Fact; r:gives {(4 7 8) list:firstRest (4 (7 8))}] - [ a r:Fact; r:gives {(() (4 7 8)) list:append (4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5173 a r:Inference; - r:gives { - (2 (4 8 8)) :split (() (4 8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 8) list:firstRest (4 (8 8))}] - [ a r:Fact; r:gives {(4 8 8) list:firstRest (4 (8 8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5174 a r:Inference; - r:gives { - (4 8 8) :sort (4 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 8) list:firstRest (4 (8 8))}] - skolem:lemma6236 - skolem:lemma4395 - skolem:lemma4629 - [ a r:Fact; r:gives {(4 8 8) list:firstRest (4 (8 8))}] - [ a r:Fact; r:gives {(() (4 8 8)) list:append (4 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5175 a r:Inference; - r:gives { - (2 (4 8 9)) :split (() (4 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 9) list:firstRest (4 (8 9))}] - [ a r:Fact; r:gives {(4 8 9) list:firstRest (4 (8 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5176 a r:Inference; - r:gives { - (4 8 9) :sort (4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8 9) list:firstRest (4 (8 9))}] - skolem:lemma6237 - skolem:lemma4395 - skolem:lemma4631 - [ a r:Fact; r:gives {(4 8 9) list:firstRest (4 (8 9))}] - [ a r:Fact; r:gives {(() (4 8 9)) list:append (4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5177 a r:Inference; - r:gives { - (2 (4 9 0)) :split ((0) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 0) list:firstRest (4 (9 0))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5178 a r:Inference; - r:gives { - (2 (4 9 1)) :split ((1) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 1) list:firstRest (4 (9 1))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5179 a r:Inference; - r:gives { - (2 (4 9 2)) :split ((2) (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 2) list:firstRest (4 (9 2))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5180 a r:Inference; - r:gives { - (2 (4 9 3)) :split (() (4 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 3) list:firstRest (4 (9 3))}] - [ a r:Fact; r:gives {(4 9 3) list:firstRest (4 (9 3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5181 a r:Inference; - r:gives { - (4 9 3) :sort (3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 3) list:firstRest (4 (9 3))}] - skolem:lemma6238 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {((3) (4 9)) list:append (3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5182 a r:Inference; - r:gives { - (2 (4 9 4)) :split (() (4 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 4) list:firstRest (4 (9 4))}] - [ a r:Fact; r:gives {(4 9 4) list:firstRest (4 (9 4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5183 a r:Inference; - r:gives { - (4 9 4) :sort (4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 4) list:firstRest (4 (9 4))}] - skolem:lemma6239 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {((4) (4 9)) list:append (4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5184 a r:Inference; - r:gives { - (2 (4 9 5)) :split (() (4 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 5) list:firstRest (4 (9 5))}] - [ a r:Fact; r:gives {(4 9 5) list:firstRest (4 (9 5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5185 a r:Inference; - r:gives { - (4 9 5) :sort (4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 5) list:firstRest (4 (9 5))}] - skolem:lemma6240 - skolem:lemma4395 - skolem:lemma4642 - [ a r:Fact; r:gives {(4 5 9) list:firstRest (4 (5 9))}] - [ a r:Fact; r:gives {(() (4 5 9)) list:append (4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5186 a r:Inference; - r:gives { - (2 (4 9 6)) :split (() (4 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 6) list:firstRest (4 (9 6))}] - [ a r:Fact; r:gives {(4 9 6) list:firstRest (4 (9 6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5187 a r:Inference; - r:gives { - (4 9 6) :sort (4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 6) list:firstRest (4 (9 6))}] - skolem:lemma6241 - skolem:lemma4395 - skolem:lemma4644 - [ a r:Fact; r:gives {(4 6 9) list:firstRest (4 (6 9))}] - [ a r:Fact; r:gives {(() (4 6 9)) list:append (4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5188 a r:Inference; - r:gives { - (2 (4 9 7)) :split (() (4 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 7) list:firstRest (4 (9 7))}] - [ a r:Fact; r:gives {(4 9 7) list:firstRest (4 (9 7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5189 a r:Inference; - r:gives { - (4 9 7) :sort (4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 7) list:firstRest (4 (9 7))}] - skolem:lemma6242 - skolem:lemma4395 - skolem:lemma4646 - [ a r:Fact; r:gives {(4 7 9) list:firstRest (4 (7 9))}] - [ a r:Fact; r:gives {(() (4 7 9)) list:append (4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5190 a r:Inference; - r:gives { - (2 (4 9 8)) :split (() (4 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 8) list:firstRest (4 (9 8))}] - [ a r:Fact; r:gives {(4 9 8) list:firstRest (4 (9 8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5191 a r:Inference; - r:gives { - (4 9 8) :sort (4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 8) list:firstRest (4 (9 8))}] - skolem:lemma6243 - skolem:lemma4395 - skolem:lemma4648 - [ a r:Fact; r:gives {(4 8 9) list:firstRest (4 (8 9))}] - [ a r:Fact; r:gives {(() (4 8 9)) list:append (4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5192 a r:Inference; - r:gives { - (2 (4 9 9)) :split (() (4 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 9) list:firstRest (4 (9 9))}] - [ a r:Fact; r:gives {(4 9 9) list:firstRest (4 (9 9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5193 a r:Inference; - r:gives { - (4 9 9) :sort (4 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9 9) list:firstRest (4 (9 9))}] - skolem:lemma6244 - skolem:lemma4395 - skolem:lemma4650 - [ a r:Fact; r:gives {(4 9 9) list:firstRest (4 (9 9))}] - [ a r:Fact; r:gives {(() (4 9 9)) list:append (4 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5194 a r:Inference; - r:gives { - (2 (5 0 0)) :split ((0 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 0) list:firstRest (5 (0 0))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5195 a r:Inference; - r:gives { - (2 (5 0 1)) :split ((0 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 1) list:firstRest (5 (0 1))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5196 a r:Inference; - r:gives { - (2 (5 0 2)) :split ((0 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 2) list:firstRest (5 (0 2))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5197 a r:Inference; - r:gives { - (2 (5 0 3)) :split ((0) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 3) list:firstRest (5 (0 3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5198 a r:Inference; - r:gives { - (2 (5 0 4)) :split ((0) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 4) list:firstRest (5 (0 4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5199 a r:Inference; - r:gives { - (2 (5 0 5)) :split ((0) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 5) list:firstRest (5 (0 5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5200 a r:Inference; - r:gives { - (2 (5 0 6)) :split ((0) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 6) list:firstRest (5 (0 6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5201 a r:Inference; - r:gives { - (2 (5 0 7)) :split ((0) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 7) list:firstRest (5 (0 7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5202 a r:Inference; - r:gives { - (2 (5 0 8)) :split ((0) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 8) list:firstRest (5 (0 8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5203 a r:Inference; - r:gives { - (2 (5 0 9)) :split ((0) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0 9) list:firstRest (5 (0 9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5204 a r:Inference; - r:gives { - (2 (5 1 0)) :split ((1 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 0) list:firstRest (5 (1 0))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5205 a r:Inference; - r:gives { - (2 (5 1 1)) :split ((1 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 1) list:firstRest (5 (1 1))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5206 a r:Inference; - r:gives { - (2 (5 1 2)) :split ((1 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 2) list:firstRest (5 (1 2))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5207 a r:Inference; - r:gives { - (2 (5 1 3)) :split ((1) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 3) list:firstRest (5 (1 3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5208 a r:Inference; - r:gives { - (2 (5 1 4)) :split ((1) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 4) list:firstRest (5 (1 4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5209 a r:Inference; - r:gives { - (2 (5 1 5)) :split ((1) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 5) list:firstRest (5 (1 5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5210 a r:Inference; - r:gives { - (2 (5 1 6)) :split ((1) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 6) list:firstRest (5 (1 6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5211 a r:Inference; - r:gives { - (2 (5 1 7)) :split ((1) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 7) list:firstRest (5 (1 7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5212 a r:Inference; - r:gives { - (2 (5 1 8)) :split ((1) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 8) list:firstRest (5 (1 8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5213 a r:Inference; - r:gives { - (2 (5 1 9)) :split ((1) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1 9) list:firstRest (5 (1 9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5214 a r:Inference; - r:gives { - (2 (5 2 0)) :split ((2 0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 0) list:firstRest (5 (2 0))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5215 a r:Inference; - r:gives { - (2 (5 2 1)) :split ((2 1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 1) list:firstRest (5 (2 1))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5216 a r:Inference; - r:gives { - (2 (5 2 2)) :split ((2 2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 2) list:firstRest (5 (2 2))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5217 a r:Inference; - r:gives { - (2 (5 2 3)) :split ((2) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 3) list:firstRest (5 (2 3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5218 a r:Inference; - r:gives { - (2 (5 2 4)) :split ((2) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 4) list:firstRest (5 (2 4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5219 a r:Inference; - r:gives { - (2 (5 2 5)) :split ((2) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 5) list:firstRest (5 (2 5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5220 a r:Inference; - r:gives { - (2 (5 2 6)) :split ((2) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 6) list:firstRest (5 (2 6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5221 a r:Inference; - r:gives { - (2 (5 2 7)) :split ((2) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 7) list:firstRest (5 (2 7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5222 a r:Inference; - r:gives { - (2 (5 2 8)) :split ((2) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 8) list:firstRest (5 (2 8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5223 a r:Inference; - r:gives { - (2 (5 2 9)) :split ((2) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2 9) list:firstRest (5 (2 9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5224 a r:Inference; - r:gives { - (2 (5 3 0)) :split ((0) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 0) list:firstRest (5 (3 0))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5225 a r:Inference; - r:gives { - (2 (5 3 1)) :split ((1) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 1) list:firstRest (5 (3 1))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5226 a r:Inference; - r:gives { - (2 (5 3 2)) :split ((2) (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 2) list:firstRest (5 (3 2))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5227 a r:Inference; - r:gives { - (2 (5 3 3)) :split (() (5 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 3) list:firstRest (5 (3 3))}] - [ a r:Fact; r:gives {(5 3 3) list:firstRest (5 (3 3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5228 a r:Inference; - r:gives { - (5 3 3) :sort (3 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 3) list:firstRest (5 (3 3))}] - skolem:lemma6245 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3 3) (5)) list:append (3 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5229 a r:Inference; - r:gives { - (2 (5 3 4)) :split (() (5 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 4) list:firstRest (5 (3 4))}] - [ a r:Fact; r:gives {(5 3 4) list:firstRest (5 (3 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5230 a r:Inference; - r:gives { - (5 3 4) :sort (3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 4) list:firstRest (5 (3 4))}] - skolem:lemma6246 - skolem:lemma4509 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3 4) (5)) list:append (3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5231 a r:Inference; - r:gives { - (2 (5 3 5)) :split (() (5 3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 5) list:firstRest (5 (3 5))}] - [ a r:Fact; r:gives {(5 3 5) list:firstRest (5 (3 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5232 a r:Inference; - r:gives { - (5 3 5) :sort (3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 5) list:firstRest (5 (3 5))}] - skolem:lemma6247 - skolem:lemma4511 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3 5) (5)) list:append (3 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5233 a r:Inference; - r:gives { - (2 (5 3 6)) :split (() (5 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 6) list:firstRest (5 (3 6))}] - [ a r:Fact; r:gives {(5 3 6) list:firstRest (5 (3 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5234 a r:Inference; - r:gives { - (5 3 6) :sort (3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 6) list:firstRest (5 (3 6))}] - skolem:lemma6248 - skolem:lemma4408 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((3) (5 6)) list:append (3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5235 a r:Inference; - r:gives { - (2 (5 3 7)) :split (() (5 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 7) list:firstRest (5 (3 7))}] - [ a r:Fact; r:gives {(5 3 7) list:firstRest (5 (3 7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5236 a r:Inference; - r:gives { - (5 3 7) :sort (3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 7) list:firstRest (5 (3 7))}] - skolem:lemma6249 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((3) (5 7)) list:append (3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5237 a r:Inference; - r:gives { - (2 (5 3 9)) :split (() (5 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 9) list:firstRest (5 (3 9))}] - [ a r:Fact; r:gives {(5 3 9) list:firstRest (5 (3 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5238 a r:Inference; - r:gives { - (5 3 9) :sort (3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 9) list:firstRest (5 (3 9))}] - skolem:lemma6250 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {((3) (5 9)) list:append (3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5239 a r:Inference; - r:gives { - (2 (5 4 0)) :split ((0) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 0) list:firstRest (5 (4 0))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5240 a r:Inference; - r:gives { - (2 (5 4 1)) :split ((1) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 1) list:firstRest (5 (4 1))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5241 a r:Inference; - r:gives { - (2 (5 4 2)) :split ((2) (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 2) list:firstRest (5 (4 2))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5242 a r:Inference; - r:gives { - (2 (5 4 3)) :split (() (5 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 3) list:firstRest (5 (4 3))}] - [ a r:Fact; r:gives {(5 4 3) list:firstRest (5 (4 3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5243 a r:Inference; - r:gives { - (5 4 3) :sort (3 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 3) list:firstRest (5 (4 3))}] - skolem:lemma6251 - skolem:lemma4524 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3 4) (5)) list:append (3 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5244 a r:Inference; - r:gives { - (2 (5 4 4)) :split (() (5 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 4) list:firstRest (5 (4 4))}] - [ a r:Fact; r:gives {(5 4 4) list:firstRest (5 (4 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5245 a r:Inference; - r:gives { - (5 4 4) :sort (4 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 4) list:firstRest (5 (4 4))}] - skolem:lemma6252 - skolem:lemma4526 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((4 4) (5)) list:append (4 4 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5246 a r:Inference; - r:gives { - (2 (5 4 5)) :split (() (5 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 5) list:firstRest (5 (4 5))}] - [ a r:Fact; r:gives {(5 4 5) list:firstRest (5 (4 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5247 a r:Inference; - r:gives { - (5 4 5) :sort (4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 5) list:firstRest (5 (4 5))}] - skolem:lemma6253 - skolem:lemma4528 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((4 5) (5)) list:append (4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5248 a r:Inference; - r:gives { - (2 (5 4 6)) :split (() (5 4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 6) list:firstRest (5 (4 6))}] - [ a r:Fact; r:gives {(5 4 6) list:firstRest (5 (4 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5249 a r:Inference; - r:gives { - (5 4 6) :sort (4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 6) list:firstRest (5 (4 6))}] - skolem:lemma6254 - skolem:lemma4414 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((4) (5 6)) list:append (4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5250 a r:Inference; - r:gives { - (2 (5 4 7)) :split (() (5 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 7) list:firstRest (5 (4 7))}] - [ a r:Fact; r:gives {(5 4 7) list:firstRest (5 (4 7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5251 a r:Inference; - r:gives { - (5 4 7) :sort (4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 7) list:firstRest (5 (4 7))}] - skolem:lemma6255 - skolem:lemma4414 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((4) (5 7)) list:append (4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5252 a r:Inference; - r:gives { - (2 (5 4 8)) :split (() (5 4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 8) list:firstRest (5 (4 8))}] - [ a r:Fact; r:gives {(5 4 8) list:firstRest (5 (4 8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5253 a r:Inference; - r:gives { - (5 4 8) :sort (4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 8) list:firstRest (5 (4 8))}] - skolem:lemma6256 - skolem:lemma4414 - skolem:lemma4426 - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {((4) (5 8)) list:append (4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5254 a r:Inference; - r:gives { - (2 (5 4 9)) :split (() (5 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 9) list:firstRest (5 (4 9))}] - [ a r:Fact; r:gives {(5 4 9) list:firstRest (5 (4 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5255 a r:Inference; - r:gives { - (5 4 9) :sort (4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4 9) list:firstRest (5 (4 9))}] - skolem:lemma6257 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {((4) (5 9)) list:append (4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5256 a r:Inference; - r:gives { - (2 (5 5 0)) :split ((0) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 0) list:firstRest (5 (5 0))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5257 a r:Inference; - r:gives { - (2 (5 5 1)) :split ((1) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 1) list:firstRest (5 (5 1))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5258 a r:Inference; - r:gives { - (2 (5 5 2)) :split ((2) (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 2) list:firstRest (5 (5 2))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5259 a r:Inference; - r:gives { - (2 (5 5 3)) :split (() (5 5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 3) list:firstRest (5 (5 3))}] - [ a r:Fact; r:gives {(5 5 3) list:firstRest (5 (5 3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5260 a r:Inference; - r:gives { - (5 5 3) :sort (3 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 3) list:firstRest (5 (5 3))}] - skolem:lemma6258 - skolem:lemma4539 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((3 5) (5)) list:append (3 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5261 a r:Inference; - r:gives { - (2 (5 5 4)) :split (() (5 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 4) list:firstRest (5 (5 4))}] - [ a r:Fact; r:gives {(5 5 4) list:firstRest (5 (5 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5262 a r:Inference; - r:gives { - (5 5 4) :sort (4 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 4) list:firstRest (5 (5 4))}] - skolem:lemma6259 - skolem:lemma4541 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((4 5) (5)) list:append (4 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5263 a r:Inference; - r:gives { - (2 (5 5 5)) :split (() (5 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 5) list:firstRest (5 (5 5))}] - [ a r:Fact; r:gives {(5 5 5) list:firstRest (5 (5 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5264 a r:Inference; - r:gives { - (5 5 5) :sort (5 5 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 5) list:firstRest (5 (5 5))}] - skolem:lemma6260 - skolem:lemma4543 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((5 5) (5)) list:append (5 5 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5265 a r:Inference; - r:gives { - (2 (5 5 6)) :split (() (5 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 6) list:firstRest (5 (5 6))}] - [ a r:Fact; r:gives {(5 5 6) list:firstRest (5 (5 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5266 a r:Inference; - r:gives { - (5 5 6) :sort (5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 6) list:firstRest (5 (5 6))}] - skolem:lemma6261 - skolem:lemma4416 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((5) (5 6)) list:append (5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5267 a r:Inference; - r:gives { - (2 (5 5 7)) :split (() (5 5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 7) list:firstRest (5 (5 7))}] - [ a r:Fact; r:gives {(5 5 7) list:firstRest (5 (5 7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5268 a r:Inference; - r:gives { - (5 5 7) :sort (5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 7) list:firstRest (5 (5 7))}] - skolem:lemma6262 - skolem:lemma4416 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((5) (5 7)) list:append (5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5269 a r:Inference; - r:gives { - (2 (5 5 8)) :split (() (5 5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 8) list:firstRest (5 (5 8))}] - [ a r:Fact; r:gives {(5 5 8) list:firstRest (5 (5 8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5270 a r:Inference; - r:gives { - (5 5 8) :sort (5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 8) list:firstRest (5 (5 8))}] - skolem:lemma6263 - skolem:lemma4416 - skolem:lemma4426 - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {((5) (5 8)) list:append (5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5271 a r:Inference; - r:gives { - (2 (5 5 9)) :split (() (5 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 9) list:firstRest (5 (5 9))}] - [ a r:Fact; r:gives {(5 5 9) list:firstRest (5 (5 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5272 a r:Inference; - r:gives { - (5 5 9) :sort (5 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5 9) list:firstRest (5 (5 9))}] - skolem:lemma6264 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {((5) (5 9)) list:append (5 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5273 a r:Inference; - r:gives { - (2 (5 6 0)) :split ((0) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 0) list:firstRest (5 (6 0))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5274 a r:Inference; - r:gives { - (2 (5 6 1)) :split ((1) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 1) list:firstRest (5 (6 1))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5275 a r:Inference; - r:gives { - (2 (5 6 2)) :split ((2) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 2) list:firstRest (5 (6 2))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5276 a r:Inference; - r:gives { - (2 (5 6 3)) :split (() (5 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 3) list:firstRest (5 (6 3))}] - [ a r:Fact; r:gives {(5 6 3) list:firstRest (5 (6 3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5277 a r:Inference; - r:gives { - (5 6 3) :sort (3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 3) list:firstRest (5 (6 3))}] - skolem:lemma6265 - skolem:lemma4408 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((3) (5 6)) list:append (3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5278 a r:Inference; - r:gives { - (2 (5 6 4)) :split (() (5 6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 4) list:firstRest (5 (6 4))}] - [ a r:Fact; r:gives {(5 6 4) list:firstRest (5 (6 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5279 a r:Inference; - r:gives { - (5 6 4) :sort (4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 4) list:firstRest (5 (6 4))}] - skolem:lemma6266 - skolem:lemma4414 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((4) (5 6)) list:append (4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5280 a r:Inference; - r:gives { - (2 (5 6 5)) :split (() (5 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 5) list:firstRest (5 (6 5))}] - [ a r:Fact; r:gives {(5 6 5) list:firstRest (5 (6 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5281 a r:Inference; - r:gives { - (5 6 5) :sort (5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 5) list:firstRest (5 (6 5))}] - skolem:lemma6267 - skolem:lemma4416 - skolem:lemma4458 - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {((5) (5 6)) list:append (5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5282 a r:Inference; - r:gives { - (2 (5 6 6)) :split (() (5 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 6) list:firstRest (5 (6 6))}] - [ a r:Fact; r:gives {(5 6 6) list:firstRest (5 (6 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5283 a r:Inference; - r:gives { - (5 6 6) :sort (5 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 6) list:firstRest (5 (6 6))}] - skolem:lemma6268 - skolem:lemma4395 - skolem:lemma4569 - [ a r:Fact; r:gives {(5 6 6) list:firstRest (5 (6 6))}] - [ a r:Fact; r:gives {(() (5 6 6)) list:append (5 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5284 a r:Inference; - r:gives { - (2 (5 6 7)) :split (() (5 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 7) list:firstRest (5 (6 7))}] - [ a r:Fact; r:gives {(5 6 7) list:firstRest (5 (6 7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5285 a r:Inference; - r:gives { - (5 6 7) :sort (5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 7) list:firstRest (5 (6 7))}] - skolem:lemma6269 - skolem:lemma4395 - skolem:lemma4575 - [ a r:Fact; r:gives {(5 6 7) list:firstRest (5 (6 7))}] - [ a r:Fact; r:gives {(() (5 6 7)) list:append (5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5286 a r:Inference; - r:gives { - (2 (5 6 8)) :split (() (5 6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 8) list:firstRest (5 (6 8))}] - [ a r:Fact; r:gives {(5 6 8) list:firstRest (5 (6 8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5287 a r:Inference; - r:gives { - (5 6 8) :sort (5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 8) list:firstRest (5 (6 8))}] - skolem:lemma6270 - skolem:lemma4395 - skolem:lemma4581 - [ a r:Fact; r:gives {(5 6 8) list:firstRest (5 (6 8))}] - [ a r:Fact; r:gives {(() (5 6 8)) list:append (5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5288 a r:Inference; - r:gives { - (2 (5 6 9)) :split (() (5 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 9) list:firstRest (5 (6 9))}] - [ a r:Fact; r:gives {(5 6 9) list:firstRest (5 (6 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5289 a r:Inference; - r:gives { - (5 6 9) :sort (5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6 9) list:firstRest (5 (6 9))}] - skolem:lemma6271 - skolem:lemma4395 - skolem:lemma4583 - [ a r:Fact; r:gives {(5 6 9) list:firstRest (5 (6 9))}] - [ a r:Fact; r:gives {(() (5 6 9)) list:append (5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5290 a r:Inference; - r:gives { - (2 (5 7 0)) :split ((0) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 0) list:firstRest (5 (7 0))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5291 a r:Inference; - r:gives { - (2 (5 7 1)) :split ((1) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 1) list:firstRest (5 (7 1))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5292 a r:Inference; - r:gives { - (2 (5 7 2)) :split ((2) (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 2) list:firstRest (5 (7 2))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5293 a r:Inference; - r:gives { - (2 (5 7 3)) :split (() (5 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 3) list:firstRest (5 (7 3))}] - [ a r:Fact; r:gives {(5 7 3) list:firstRest (5 (7 3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5294 a r:Inference; - r:gives { - (5 7 3) :sort (3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 3) list:firstRest (5 (7 3))}] - skolem:lemma6272 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((3) (5 7)) list:append (3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5295 a r:Inference; - r:gives { - (2 (5 7 4)) :split (() (5 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 4) list:firstRest (5 (7 4))}] - [ a r:Fact; r:gives {(5 7 4) list:firstRest (5 (7 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5296 a r:Inference; - r:gives { - (5 7 4) :sort (4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 4) list:firstRest (5 (7 4))}] - skolem:lemma6273 - skolem:lemma4414 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((4) (5 7)) list:append (4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5297 a r:Inference; - r:gives { - (2 (5 7 5)) :split (() (5 7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 5) list:firstRest (5 (7 5))}] - [ a r:Fact; r:gives {(5 7 5) list:firstRest (5 (7 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5298 a r:Inference; - r:gives { - (5 7 5) :sort (5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 5) list:firstRest (5 (7 5))}] - skolem:lemma6274 - skolem:lemma4416 - skolem:lemma4422 - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {((5) (5 7)) list:append (5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5299 a r:Inference; - r:gives { - (2 (5 7 6)) :split (() (5 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 6) list:firstRest (5 (7 6))}] - [ a r:Fact; r:gives {(5 7 6) list:firstRest (5 (7 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5300 a r:Inference; - r:gives { - (5 7 6) :sort (5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 6) list:firstRest (5 (7 6))}] - skolem:lemma6275 - skolem:lemma4395 - skolem:lemma4598 - [ a r:Fact; r:gives {(5 6 7) list:firstRest (5 (6 7))}] - [ a r:Fact; r:gives {(() (5 6 7)) list:append (5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5301 a r:Inference; - r:gives { - (2 (5 7 7)) :split (() (5 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 7) list:firstRest (5 (7 7))}] - [ a r:Fact; r:gives {(5 7 7) list:firstRest (5 (7 7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5302 a r:Inference; - r:gives { - (5 7 7) :sort (5 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 7) list:firstRest (5 (7 7))}] - skolem:lemma6276 - skolem:lemma4395 - skolem:lemma4600 - [ a r:Fact; r:gives {(5 7 7) list:firstRest (5 (7 7))}] - [ a r:Fact; r:gives {(() (5 7 7)) list:append (5 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5303 a r:Inference; - r:gives { - (2 (5 7 9)) :split (() (5 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 9) list:firstRest (5 (7 9))}] - [ a r:Fact; r:gives {(5 7 9) list:firstRest (5 (7 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5304 a r:Inference; - r:gives { - (5 7 9) :sort (5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7 9) list:firstRest (5 (7 9))}] - skolem:lemma6277 - skolem:lemma4395 - skolem:lemma4610 - [ a r:Fact; r:gives {(5 7 9) list:firstRest (5 (7 9))}] - [ a r:Fact; r:gives {(() (5 7 9)) list:append (5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5305 a r:Inference; - r:gives { - (2 (5 8 0)) :split ((0) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 0) list:firstRest (5 (8 0))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5306 a r:Inference; - r:gives { - (2 (5 8 1)) :split ((1) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 1) list:firstRest (5 (8 1))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5307 a r:Inference; - r:gives { - (2 (5 8 2)) :split ((2) (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 2) list:firstRest (5 (8 2))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5308 a r:Inference; - r:gives { - (2 (5 8 4)) :split (() (5 8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 4) list:firstRest (5 (8 4))}] - [ a r:Fact; r:gives {(5 8 4) list:firstRest (5 (8 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5309 a r:Inference; - r:gives { - (5 8 4) :sort (4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 4) list:firstRest (5 (8 4))}] - skolem:lemma6278 - skolem:lemma4414 - skolem:lemma4426 - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {((4) (5 8)) list:append (4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5310 a r:Inference; - r:gives { - (2 (5 8 5)) :split (() (5 8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 5) list:firstRest (5 (8 5))}] - [ a r:Fact; r:gives {(5 8 5) list:firstRest (5 (8 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5311 a r:Inference; - r:gives { - (5 8 5) :sort (5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 5) list:firstRest (5 (8 5))}] - skolem:lemma6279 - skolem:lemma4416 - skolem:lemma4426 - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {((5) (5 8)) list:append (5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5312 a r:Inference; - r:gives { - (2 (5 8 6)) :split (() (5 8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 6) list:firstRest (5 (8 6))}] - [ a r:Fact; r:gives {(5 8 6) list:firstRest (5 (8 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5313 a r:Inference; - r:gives { - (5 8 6) :sort (5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 6) list:firstRest (5 (8 6))}] - skolem:lemma6280 - skolem:lemma4395 - skolem:lemma4625 - [ a r:Fact; r:gives {(5 6 8) list:firstRest (5 (6 8))}] - [ a r:Fact; r:gives {(() (5 6 8)) list:append (5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5314 a r:Inference; - r:gives { - (2 (5 8 8)) :split (() (5 8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 8) list:firstRest (5 (8 8))}] - [ a r:Fact; r:gives {(5 8 8) list:firstRest (5 (8 8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5315 a r:Inference; - r:gives { - (5 8 8) :sort (5 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 8) list:firstRest (5 (8 8))}] - skolem:lemma6281 - skolem:lemma4395 - skolem:lemma4629 - [ a r:Fact; r:gives {(5 8 8) list:firstRest (5 (8 8))}] - [ a r:Fact; r:gives {(() (5 8 8)) list:append (5 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5316 a r:Inference; - r:gives { - (2 (5 8 9)) :split (() (5 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 9) list:firstRest (5 (8 9))}] - [ a r:Fact; r:gives {(5 8 9) list:firstRest (5 (8 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5317 a r:Inference; - r:gives { - (5 8 9) :sort (5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8 9) list:firstRest (5 (8 9))}] - skolem:lemma6282 - skolem:lemma4395 - skolem:lemma4631 - [ a r:Fact; r:gives {(5 8 9) list:firstRest (5 (8 9))}] - [ a r:Fact; r:gives {(() (5 8 9)) list:append (5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5318 a r:Inference; - r:gives { - (2 (5 9 0)) :split ((0) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 0) list:firstRest (5 (9 0))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5319 a r:Inference; - r:gives { - (2 (5 9 1)) :split ((1) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 1) list:firstRest (5 (9 1))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5320 a r:Inference; - r:gives { - (2 (5 9 2)) :split ((2) (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 2) list:firstRest (5 (9 2))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5321 a r:Inference; - r:gives { - (2 (5 9 3)) :split (() (5 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 3) list:firstRest (5 (9 3))}] - [ a r:Fact; r:gives {(5 9 3) list:firstRest (5 (9 3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5322 a r:Inference; - r:gives { - (5 9 3) :sort (3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 3) list:firstRest (5 (9 3))}] - skolem:lemma6283 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {((3) (5 9)) list:append (3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5323 a r:Inference; - r:gives { - (2 (5 9 4)) :split (() (5 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 4) list:firstRest (5 (9 4))}] - [ a r:Fact; r:gives {(5 9 4) list:firstRest (5 (9 4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5324 a r:Inference; - r:gives { - (5 9 4) :sort (4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 4) list:firstRest (5 (9 4))}] - skolem:lemma6284 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {((4) (5 9)) list:append (4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5325 a r:Inference; - r:gives { - (2 (5 9 5)) :split (() (5 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 5) list:firstRest (5 (9 5))}] - [ a r:Fact; r:gives {(5 9 5) list:firstRest (5 (9 5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5326 a r:Inference; - r:gives { - (5 9 5) :sort (5 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 5) list:firstRest (5 (9 5))}] - skolem:lemma6285 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {((5) (5 9)) list:append (5 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5327 a r:Inference; - r:gives { - (2 (5 9 6)) :split (() (5 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 6) list:firstRest (5 (9 6))}] - [ a r:Fact; r:gives {(5 9 6) list:firstRest (5 (9 6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5328 a r:Inference; - r:gives { - (5 9 6) :sort (5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 6) list:firstRest (5 (9 6))}] - skolem:lemma6286 - skolem:lemma4395 - skolem:lemma4644 - [ a r:Fact; r:gives {(5 6 9) list:firstRest (5 (6 9))}] - [ a r:Fact; r:gives {(() (5 6 9)) list:append (5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5329 a r:Inference; - r:gives { - (2 (5 9 7)) :split (() (5 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 7) list:firstRest (5 (9 7))}] - [ a r:Fact; r:gives {(5 9 7) list:firstRest (5 (9 7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5330 a r:Inference; - r:gives { - (5 9 7) :sort (5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 7) list:firstRest (5 (9 7))}] - skolem:lemma6287 - skolem:lemma4395 - skolem:lemma4646 - [ a r:Fact; r:gives {(5 7 9) list:firstRest (5 (7 9))}] - [ a r:Fact; r:gives {(() (5 7 9)) list:append (5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5331 a r:Inference; - r:gives { - (2 (5 9 8)) :split (() (5 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 8) list:firstRest (5 (9 8))}] - [ a r:Fact; r:gives {(5 9 8) list:firstRest (5 (9 8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5332 a r:Inference; - r:gives { - (5 9 8) :sort (5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 8) list:firstRest (5 (9 8))}] - skolem:lemma6288 - skolem:lemma4395 - skolem:lemma4648 - [ a r:Fact; r:gives {(5 8 9) list:firstRest (5 (8 9))}] - [ a r:Fact; r:gives {(() (5 8 9)) list:append (5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5333 a r:Inference; - r:gives { - (2 (5 9 9)) :split (() (5 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 9) list:firstRest (5 (9 9))}] - [ a r:Fact; r:gives {(5 9 9) list:firstRest (5 (9 9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5334 a r:Inference; - r:gives { - (5 9 9) :sort (5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9 9) list:firstRest (5 (9 9))}] - skolem:lemma6289 - skolem:lemma4395 - skolem:lemma4650 - [ a r:Fact; r:gives {(5 9 9) list:firstRest (5 (9 9))}] - [ a r:Fact; r:gives {(() (5 9 9)) list:append (5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5335 a r:Inference; - r:gives { - (2 (6 0 1)) :split ((0 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 1) list:firstRest (6 (0 1))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5336 a r:Inference; - r:gives { - (2 (6 0 2)) :split ((0 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 2) list:firstRest (6 (0 2))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5337 a r:Inference; - r:gives { - (2 (6 0 3)) :split ((0) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 3) list:firstRest (6 (0 3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5338 a r:Inference; - r:gives { - (2 (6 0 5)) :split ((0) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 5) list:firstRest (6 (0 5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5339 a r:Inference; - r:gives { - (2 (6 0 6)) :split ((0) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 6) list:firstRest (6 (0 6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5340 a r:Inference; - r:gives { - (2 (6 0 7)) :split ((0) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 7) list:firstRest (6 (0 7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5341 a r:Inference; - r:gives { - (2 (6 0 8)) :split ((0) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 8) list:firstRest (6 (0 8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5342 a r:Inference; - r:gives { - (2 (6 0 9)) :split ((0) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0 9) list:firstRest (6 (0 9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5343 a r:Inference; - r:gives { - (2 (6 1 0)) :split ((1 0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 0) list:firstRest (6 (1 0))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5344 a r:Inference; - r:gives { - (2 (6 1 1)) :split ((1 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 1) list:firstRest (6 (1 1))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5345 a r:Inference; - r:gives { - (2 (6 1 2)) :split ((1 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 2) list:firstRest (6 (1 2))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5346 a r:Inference; - r:gives { - (2 (6 1 3)) :split ((1) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 3) list:firstRest (6 (1 3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5347 a r:Inference; - r:gives { - (2 (6 1 4)) :split ((1) (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 4) list:firstRest (6 (1 4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5348 a r:Inference; - r:gives { - (2 (6 1 5)) :split ((1) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 5) list:firstRest (6 (1 5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5349 a r:Inference; - r:gives { - (2 (6 1 6)) :split ((1) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 6) list:firstRest (6 (1 6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5350 a r:Inference; - r:gives { - (2 (6 1 7)) :split ((1) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 7) list:firstRest (6 (1 7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5351 a r:Inference; - r:gives { - (2 (6 1 8)) :split ((1) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 8) list:firstRest (6 (1 8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5352 a r:Inference; - r:gives { - (2 (6 1 9)) :split ((1) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1 9) list:firstRest (6 (1 9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5353 a r:Inference; - r:gives { - (2 (6 2 0)) :split ((2 0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 0) list:firstRest (6 (2 0))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5354 a r:Inference; - r:gives { - (2 (6 2 1)) :split ((2 1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 1) list:firstRest (6 (2 1))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5355 a r:Inference; - r:gives { - (2 (6 2 2)) :split ((2 2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 2) list:firstRest (6 (2 2))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5356 a r:Inference; - r:gives { - (2 (6 2 3)) :split ((2) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 3) list:firstRest (6 (2 3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5357 a r:Inference; - r:gives { - (2 (6 2 4)) :split ((2) (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 4) list:firstRest (6 (2 4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5358 a r:Inference; - r:gives { - (2 (6 2 5)) :split ((2) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 5) list:firstRest (6 (2 5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5359 a r:Inference; - r:gives { - (2 (6 2 6)) :split ((2) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 6) list:firstRest (6 (2 6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5360 a r:Inference; - r:gives { - (2 (6 2 7)) :split ((2) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 7) list:firstRest (6 (2 7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5361 a r:Inference; - r:gives { - (2 (6 2 8)) :split ((2) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 8) list:firstRest (6 (2 8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5362 a r:Inference; - r:gives { - (2 (6 2 9)) :split ((2) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 9) list:firstRest (6 (2 9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5363 a r:Inference; - r:gives { - (2 (6 3 0)) :split ((0) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 0) list:firstRest (6 (3 0))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5364 a r:Inference; - r:gives { - (2 (6 3 1)) :split ((1) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 1) list:firstRest (6 (3 1))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5365 a r:Inference; - r:gives { - (2 (6 3 2)) :split ((2) (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 2) list:firstRest (6 (3 2))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5366 a r:Inference; - r:gives { - (2 (6 3 3)) :split (() (6 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 3) list:firstRest (6 (3 3))}] - [ a r:Fact; r:gives {(6 3 3) list:firstRest (6 (3 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5367 a r:Inference; - r:gives { - (6 3 3) :sort (3 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 3) list:firstRest (6 (3 3))}] - skolem:lemma6290 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 3) (6)) list:append (3 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5368 a r:Inference; - r:gives { - (2 (6 3 4)) :split (() (6 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 4) list:firstRest (6 (3 4))}] - [ a r:Fact; r:gives {(6 3 4) list:firstRest (6 (3 4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5369 a r:Inference; - r:gives { - (6 3 4) :sort (3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 4) list:firstRest (6 (3 4))}] - skolem:lemma6291 - skolem:lemma4509 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 4) (6)) list:append (3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5370 a r:Inference; - r:gives { - (2 (6 3 5)) :split (() (6 3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 5) list:firstRest (6 (3 5))}] - [ a r:Fact; r:gives {(6 3 5) list:firstRest (6 (3 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5371 a r:Inference; - r:gives { - (6 3 5) :sort (3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 5) list:firstRest (6 (3 5))}] - skolem:lemma6292 - skolem:lemma4511 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 5) (6)) list:append (3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5372 a r:Inference; - r:gives { - (2 (6 3 6)) :split (() (6 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 6) list:firstRest (6 (3 6))}] - [ a r:Fact; r:gives {(6 3 6) list:firstRest (6 (3 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5373 a r:Inference; - r:gives { - (6 3 6) :sort (3 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 6) list:firstRest (6 (3 6))}] - skolem:lemma6293 - skolem:lemma4513 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 6) (6)) list:append (3 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5374 a r:Inference; - r:gives { - (2 (6 3 7)) :split (() (6 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 7) list:firstRest (6 (3 7))}] - [ a r:Fact; r:gives {(6 3 7) list:firstRest (6 (3 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5375 a r:Inference; - r:gives { - (6 3 7) :sort (3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 7) list:firstRest (6 (3 7))}] - skolem:lemma6294 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((3) (6 7)) list:append (3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5376 a r:Inference; - r:gives { - (2 (6 3 8)) :split (() (6 3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 8) list:firstRest (6 (3 8))}] - [ a r:Fact; r:gives {(6 3 8) list:firstRest (6 (3 8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5377 a r:Inference; - r:gives { - (6 3 8) :sort (3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 8) list:firstRest (6 (3 8))}] - skolem:lemma6295 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((3) (6 8)) list:append (3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5378 a r:Inference; - r:gives { - (2 (6 3 9)) :split (() (6 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 9) list:firstRest (6 (3 9))}] - [ a r:Fact; r:gives {(6 3 9) list:firstRest (6 (3 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5379 a r:Inference; - r:gives { - (6 3 9) :sort (3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3 9) list:firstRest (6 (3 9))}] - skolem:lemma6296 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((3) (6 9)) list:append (3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5380 a r:Inference; - r:gives { - (2 (6 4 1)) :split ((1) (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 1) list:firstRest (6 (4 1))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5381 a r:Inference; - r:gives { - (2 (6 4 2)) :split ((2) (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 2) list:firstRest (6 (4 2))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5382 a r:Inference; - r:gives { - (2 (6 4 3)) :split (() (6 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 3) list:firstRest (6 (4 3))}] - [ a r:Fact; r:gives {(6 4 3) list:firstRest (6 (4 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5383 a r:Inference; - r:gives { - (6 4 3) :sort (3 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 3) list:firstRest (6 (4 3))}] - skolem:lemma6297 - skolem:lemma4524 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 4) (6)) list:append (3 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5384 a r:Inference; - r:gives { - (2 (6 4 4)) :split (() (6 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 4) list:firstRest (6 (4 4))}] - [ a r:Fact; r:gives {(6 4 4) list:firstRest (6 (4 4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5385 a r:Inference; - r:gives { - (6 4 4) :sort (4 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 4) list:firstRest (6 (4 4))}] - skolem:lemma6298 - skolem:lemma4526 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4 4) (6)) list:append (4 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5386 a r:Inference; - r:gives { - (2 (6 4 5)) :split (() (6 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 5) list:firstRest (6 (4 5))}] - [ a r:Fact; r:gives {(6 4 5) list:firstRest (6 (4 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5387 a r:Inference; - r:gives { - (6 4 5) :sort (4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 5) list:firstRest (6 (4 5))}] - skolem:lemma6299 - skolem:lemma4528 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4 5) (6)) list:append (4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5388 a r:Inference; - r:gives { - (2 (6 4 6)) :split (() (6 4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 6) list:firstRest (6 (4 6))}] - [ a r:Fact; r:gives {(6 4 6) list:firstRest (6 (4 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5389 a r:Inference; - r:gives { - (6 4 6) :sort (4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 6) list:firstRest (6 (4 6))}] - skolem:lemma6300 - skolem:lemma4719 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4 6) (6)) list:append (4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5390 a r:Inference; - r:gives { - (2 (6 4 7)) :split (() (6 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 7) list:firstRest (6 (4 7))}] - [ a r:Fact; r:gives {(6 4 7) list:firstRest (6 (4 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5391 a r:Inference; - r:gives { - (6 4 7) :sort (4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 7) list:firstRest (6 (4 7))}] - skolem:lemma6301 - skolem:lemma4414 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((4) (6 7)) list:append (4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5392 a r:Inference; - r:gives { - (2 (6 4 9)) :split (() (6 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 9) list:firstRest (6 (4 9))}] - [ a r:Fact; r:gives {(6 4 9) list:firstRest (6 (4 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5393 a r:Inference; - r:gives { - (6 4 9) :sort (4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4 9) list:firstRest (6 (4 9))}] - skolem:lemma6302 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((4) (6 9)) list:append (4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5394 a r:Inference; - r:gives { - (2 (6 5 0)) :split ((0) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 0) list:firstRest (6 (5 0))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5395 a r:Inference; - r:gives { - (2 (6 5 1)) :split ((1) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 1) list:firstRest (6 (5 1))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5396 a r:Inference; - r:gives { - (2 (6 5 2)) :split ((2) (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 2) list:firstRest (6 (5 2))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5397 a r:Inference; - r:gives { - (2 (6 5 3)) :split (() (6 5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 3) list:firstRest (6 (5 3))}] - [ a r:Fact; r:gives {(6 5 3) list:firstRest (6 (5 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5398 a r:Inference; - r:gives { - (6 5 3) :sort (3 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 3) list:firstRest (6 (5 3))}] - skolem:lemma6303 - skolem:lemma4539 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 5) (6)) list:append (3 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5399 a r:Inference; - r:gives { - (2 (6 5 4)) :split (() (6 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 4) list:firstRest (6 (5 4))}] - [ a r:Fact; r:gives {(6 5 4) list:firstRest (6 (5 4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5400 a r:Inference; - r:gives { - (6 5 4) :sort (4 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 4) list:firstRest (6 (5 4))}] - skolem:lemma6304 - skolem:lemma4541 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4 5) (6)) list:append (4 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5401 a r:Inference; - r:gives { - (2 (6 5 5)) :split (() (6 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 5) list:firstRest (6 (5 5))}] - [ a r:Fact; r:gives {(6 5 5) list:firstRest (6 (5 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5402 a r:Inference; - r:gives { - (6 5 5) :sort (5 5 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 5) list:firstRest (6 (5 5))}] - skolem:lemma6305 - skolem:lemma4543 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((5 5) (6)) list:append (5 5 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5403 a r:Inference; - r:gives { - (2 (6 5 6)) :split (() (6 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 6) list:firstRest (6 (5 6))}] - [ a r:Fact; r:gives {(6 5 6) list:firstRest (6 (5 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5404 a r:Inference; - r:gives { - (6 5 6) :sort (5 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 6) list:firstRest (6 (5 6))}] - skolem:lemma6306 - skolem:lemma4547 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((5 6) (6)) list:append (5 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5405 a r:Inference; - r:gives { - (2 (6 5 7)) :split (() (6 5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 7) list:firstRest (6 (5 7))}] - [ a r:Fact; r:gives {(6 5 7) list:firstRest (6 (5 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5406 a r:Inference; - r:gives { - (6 5 7) :sort (5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 7) list:firstRest (6 (5 7))}] - skolem:lemma6307 - skolem:lemma4416 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((5) (6 7)) list:append (5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5407 a r:Inference; - r:gives { - (2 (6 5 8)) :split (() (6 5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 8) list:firstRest (6 (5 8))}] - [ a r:Fact; r:gives {(6 5 8) list:firstRest (6 (5 8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5408 a r:Inference; - r:gives { - (6 5 8) :sort (5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 8) list:firstRest (6 (5 8))}] - skolem:lemma6308 - skolem:lemma4416 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((5) (6 8)) list:append (5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5409 a r:Inference; - r:gives { - (2 (6 5 9)) :split (() (6 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 9) list:firstRest (6 (5 9))}] - [ a r:Fact; r:gives {(6 5 9) list:firstRest (6 (5 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5410 a r:Inference; - r:gives { - (6 5 9) :sort (5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5 9) list:firstRest (6 (5 9))}] - skolem:lemma6309 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((5) (6 9)) list:append (5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5411 a r:Inference; - r:gives { - (2 (6 6 0)) :split ((0) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 0) list:firstRest (6 (6 0))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5412 a r:Inference; - r:gives { - (2 (6 6 1)) :split ((1) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 1) list:firstRest (6 (6 1))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5413 a r:Inference; - r:gives { - (2 (6 6 2)) :split ((2) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 2) list:firstRest (6 (6 2))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5414 a r:Inference; - r:gives { - (2 (6 6 3)) :split (() (6 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 3) list:firstRest (6 (6 3))}] - [ a r:Fact; r:gives {(6 6 3) list:firstRest (6 (6 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5415 a r:Inference; - r:gives { - (6 6 3) :sort (3 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 3) list:firstRest (6 (6 3))}] - skolem:lemma6310 - skolem:lemma4565 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((3 6) (6)) list:append (3 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5416 a r:Inference; - r:gives { - (2 (6 6 4)) :split (() (6 6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 4) list:firstRest (6 (6 4))}] - [ a r:Fact; r:gives {(6 6 4) list:firstRest (6 (6 4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5417 a r:Inference; - r:gives { - (6 6 4) :sort (4 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 4) list:firstRest (6 (6 4))}] - skolem:lemma6311 - skolem:lemma4739 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((4 6) (6)) list:append (4 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5418 a r:Inference; - r:gives { - (2 (6 6 5)) :split (() (6 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 5) list:firstRest (6 (6 5))}] - [ a r:Fact; r:gives {(6 6 5) list:firstRest (6 (6 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5419 a r:Inference; - r:gives { - (6 6 5) :sort (5 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 5) list:firstRest (6 (6 5))}] - skolem:lemma6312 - skolem:lemma4567 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((5 6) (6)) list:append (5 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5420 a r:Inference; - r:gives { - (2 (6 6 6)) :split (() (6 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 6) list:firstRest (6 (6 6))}] - [ a r:Fact; r:gives {(6 6 6) list:firstRest (6 (6 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5421 a r:Inference; - r:gives { - (6 6 6) :sort (6 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 6) list:firstRest (6 (6 6))}] - skolem:lemma6313 - skolem:lemma4569 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((6 6) (6)) list:append (6 6 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 6)]; - r:rule skolem:lemma4396. - -skolem:lemma5422 a r:Inference; - r:gives { - (2 (6 6 7)) :split (() (6 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 7) list:firstRest (6 (6 7))}] - [ a r:Fact; r:gives {(6 6 7) list:firstRest (6 (6 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5423 a r:Inference; - r:gives { - (6 6 7) :sort (6 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 7) list:firstRest (6 (6 7))}] - skolem:lemma6314 - skolem:lemma4458 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((6) (6 7)) list:append (6 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5424 a r:Inference; - r:gives { - (2 (6 6 8)) :split (() (6 6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 8) list:firstRest (6 (6 8))}] - [ a r:Fact; r:gives {(6 6 8) list:firstRest (6 (6 8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5425 a r:Inference; - r:gives { - (6 6 8) :sort (6 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 8) list:firstRest (6 (6 8))}] - skolem:lemma6315 - skolem:lemma4458 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((6) (6 8)) list:append (6 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5426 a r:Inference; - r:gives { - (2 (6 6 9)) :split (() (6 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 9) list:firstRest (6 (6 9))}] - [ a r:Fact; r:gives {(6 6 9) list:firstRest (6 (6 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5427 a r:Inference; - r:gives { - (6 6 9) :sort (6 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6 9) list:firstRest (6 (6 9))}] - skolem:lemma6316 - skolem:lemma4458 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((6) (6 9)) list:append (6 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5428 a r:Inference; - r:gives { - (2 (6 7 0)) :split ((0) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 0) list:firstRest (6 (7 0))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5429 a r:Inference; - r:gives { - (2 (6 7 1)) :split ((1) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 1) list:firstRest (6 (7 1))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5430 a r:Inference; - r:gives { - (2 (6 7 2)) :split ((2) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 2) list:firstRest (6 (7 2))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5431 a r:Inference; - r:gives { - (2 (6 7 3)) :split (() (6 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 3) list:firstRest (6 (7 3))}] - [ a r:Fact; r:gives {(6 7 3) list:firstRest (6 (7 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5432 a r:Inference; - r:gives { - (6 7 3) :sort (3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 3) list:firstRest (6 (7 3))}] - skolem:lemma6317 - skolem:lemma4408 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((3) (6 7)) list:append (3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5433 a r:Inference; - r:gives { - (2 (6 7 4)) :split (() (6 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 4) list:firstRest (6 (7 4))}] - [ a r:Fact; r:gives {(6 7 4) list:firstRest (6 (7 4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5434 a r:Inference; - r:gives { - (6 7 4) :sort (4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 4) list:firstRest (6 (7 4))}] - skolem:lemma6318 - skolem:lemma4414 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((4) (6 7)) list:append (4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5435 a r:Inference; - r:gives { - (2 (6 7 5)) :split (() (6 7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 5) list:firstRest (6 (7 5))}] - [ a r:Fact; r:gives {(6 7 5) list:firstRest (6 (7 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5436 a r:Inference; - r:gives { - (6 7 5) :sort (5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 5) list:firstRest (6 (7 5))}] - skolem:lemma6319 - skolem:lemma4416 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((5) (6 7)) list:append (5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5437 a r:Inference; - r:gives { - (2 (6 7 6)) :split (() (6 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 6) list:firstRest (6 (7 6))}] - [ a r:Fact; r:gives {(6 7 6) list:firstRest (6 (7 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5438 a r:Inference; - r:gives { - (6 7 6) :sort (6 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 6) list:firstRest (6 (7 6))}] - skolem:lemma6320 - skolem:lemma4458 - skolem:lemma4422 - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {((6) (6 7)) list:append (6 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5439 a r:Inference; - r:gives { - (2 (6 7 7)) :split (() (6 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 7) list:firstRest (6 (7 7))}] - [ a r:Fact; r:gives {(6 7 7) list:firstRest (6 (7 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5440 a r:Inference; - r:gives { - (6 7 7) :sort (6 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 7) list:firstRest (6 (7 7))}] - skolem:lemma6321 - skolem:lemma4395 - skolem:lemma4600 - [ a r:Fact; r:gives {(6 7 7) list:firstRest (6 (7 7))}] - [ a r:Fact; r:gives {(() (6 7 7)) list:append (6 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5441 a r:Inference; - r:gives { - (2 (6 7 8)) :split (() (6 7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 8) list:firstRest (6 (7 8))}] - [ a r:Fact; r:gives {(6 7 8) list:firstRest (6 (7 8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5442 a r:Inference; - r:gives { - (6 7 8) :sort (6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 8) list:firstRest (6 (7 8))}] - skolem:lemma6322 - skolem:lemma4395 - skolem:lemma4606 - [ a r:Fact; r:gives {(6 7 8) list:firstRest (6 (7 8))}] - [ a r:Fact; r:gives {(() (6 7 8)) list:append (6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5443 a r:Inference; - r:gives { - (2 (6 7 9)) :split (() (6 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 9) list:firstRest (6 (7 9))}] - [ a r:Fact; r:gives {(6 7 9) list:firstRest (6 (7 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5444 a r:Inference; - r:gives { - (6 7 9) :sort (6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7 9) list:firstRest (6 (7 9))}] - skolem:lemma6323 - skolem:lemma4395 - skolem:lemma4610 - [ a r:Fact; r:gives {(6 7 9) list:firstRest (6 (7 9))}] - [ a r:Fact; r:gives {(() (6 7 9)) list:append (6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5445 a r:Inference; - r:gives { - (2 (6 8 0)) :split ((0) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 0) list:firstRest (6 (8 0))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5446 a r:Inference; - r:gives { - (2 (6 8 1)) :split ((1) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 1) list:firstRest (6 (8 1))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5447 a r:Inference; - r:gives { - (2 (6 8 2)) :split ((2) (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 2) list:firstRest (6 (8 2))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5448 a r:Inference; - r:gives { - (2 (6 8 3)) :split (() (6 8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 3) list:firstRest (6 (8 3))}] - [ a r:Fact; r:gives {(6 8 3) list:firstRest (6 (8 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5449 a r:Inference; - r:gives { - (6 8 3) :sort (3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 3) list:firstRest (6 (8 3))}] - skolem:lemma6324 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((3) (6 8)) list:append (3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5450 a r:Inference; - r:gives { - (2 (6 8 5)) :split (() (6 8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 5) list:firstRest (6 (8 5))}] - [ a r:Fact; r:gives {(6 8 5) list:firstRest (6 (8 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5451 a r:Inference; - r:gives { - (6 8 5) :sort (5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 5) list:firstRest (6 (8 5))}] - skolem:lemma6325 - skolem:lemma4416 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((5) (6 8)) list:append (5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5452 a r:Inference; - r:gives { - (2 (6 8 6)) :split (() (6 8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 6) list:firstRest (6 (8 6))}] - [ a r:Fact; r:gives {(6 8 6) list:firstRest (6 (8 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5453 a r:Inference; - r:gives { - (6 8 6) :sort (6 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 6) list:firstRest (6 (8 6))}] - skolem:lemma6326 - skolem:lemma4458 - skolem:lemma4426 - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {((6) (6 8)) list:append (6 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5454 a r:Inference; - r:gives { - (2 (6 8 7)) :split (() (6 8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 7) list:firstRest (6 (8 7))}] - [ a r:Fact; r:gives {(6 8 7) list:firstRest (6 (8 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5455 a r:Inference; - r:gives { - (6 8 7) :sort (6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 7) list:firstRest (6 (8 7))}] - skolem:lemma6327 - skolem:lemma4395 - skolem:lemma4627 - [ a r:Fact; r:gives {(6 7 8) list:firstRest (6 (7 8))}] - [ a r:Fact; r:gives {(() (6 7 8)) list:append (6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5456 a r:Inference; - r:gives { - (2 (6 8 9)) :split (() (6 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 9) list:firstRest (6 (8 9))}] - [ a r:Fact; r:gives {(6 8 9) list:firstRest (6 (8 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5457 a r:Inference; - r:gives { - (6 8 9) :sort (6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8 9) list:firstRest (6 (8 9))}] - skolem:lemma6328 - skolem:lemma4395 - skolem:lemma4631 - [ a r:Fact; r:gives {(6 8 9) list:firstRest (6 (8 9))}] - [ a r:Fact; r:gives {(() (6 8 9)) list:append (6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5458 a r:Inference; - r:gives { - (2 (6 9 0)) :split ((0) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 0) list:firstRest (6 (9 0))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5459 a r:Inference; - r:gives { - (2 (6 9 1)) :split ((1) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 1) list:firstRest (6 (9 1))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5460 a r:Inference; - r:gives { - (2 (6 9 2)) :split ((2) (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 2) list:firstRest (6 (9 2))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5461 a r:Inference; - r:gives { - (2 (6 9 3)) :split (() (6 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 3) list:firstRest (6 (9 3))}] - [ a r:Fact; r:gives {(6 9 3) list:firstRest (6 (9 3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5462 a r:Inference; - r:gives { - (6 9 3) :sort (3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 3) list:firstRest (6 (9 3))}] - skolem:lemma6329 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((3) (6 9)) list:append (3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5463 a r:Inference; - r:gives { - (2 (6 9 4)) :split (() (6 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 4) list:firstRest (6 (9 4))}] - [ a r:Fact; r:gives {(6 9 4) list:firstRest (6 (9 4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5464 a r:Inference; - r:gives { - (6 9 4) :sort (4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 4) list:firstRest (6 (9 4))}] - skolem:lemma6330 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((4) (6 9)) list:append (4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5465 a r:Inference; - r:gives { - (2 (6 9 5)) :split (() (6 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 5) list:firstRest (6 (9 5))}] - [ a r:Fact; r:gives {(6 9 5) list:firstRest (6 (9 5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5466 a r:Inference; - r:gives { - (6 9 5) :sort (5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 5) list:firstRest (6 (9 5))}] - skolem:lemma6331 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((5) (6 9)) list:append (5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5467 a r:Inference; - r:gives { - (2 (6 9 6)) :split (() (6 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 6) list:firstRest (6 (9 6))}] - [ a r:Fact; r:gives {(6 9 6) list:firstRest (6 (9 6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5468 a r:Inference; - r:gives { - (6 9 6) :sort (6 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 6) list:firstRest (6 (9 6))}] - skolem:lemma6332 - skolem:lemma4458 - skolem:lemma4430 - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {((6) (6 9)) list:append (6 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5469 a r:Inference; - r:gives { - (2 (6 9 7)) :split (() (6 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 7) list:firstRest (6 (9 7))}] - [ a r:Fact; r:gives {(6 9 7) list:firstRest (6 (9 7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5470 a r:Inference; - r:gives { - (6 9 7) :sort (6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 7) list:firstRest (6 (9 7))}] - skolem:lemma6333 - skolem:lemma4395 - skolem:lemma4646 - [ a r:Fact; r:gives {(6 7 9) list:firstRest (6 (7 9))}] - [ a r:Fact; r:gives {(() (6 7 9)) list:append (6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5471 a r:Inference; - r:gives { - (2 (6 9 8)) :split (() (6 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 8) list:firstRest (6 (9 8))}] - [ a r:Fact; r:gives {(6 9 8) list:firstRest (6 (9 8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5472 a r:Inference; - r:gives { - (6 9 8) :sort (6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 8) list:firstRest (6 (9 8))}] - skolem:lemma6334 - skolem:lemma4395 - skolem:lemma4648 - [ a r:Fact; r:gives {(6 8 9) list:firstRest (6 (8 9))}] - [ a r:Fact; r:gives {(() (6 8 9)) list:append (6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5473 a r:Inference; - r:gives { - (2 (6 9 9)) :split (() (6 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 9) list:firstRest (6 (9 9))}] - [ a r:Fact; r:gives {(6 9 9) list:firstRest (6 (9 9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5474 a r:Inference; - r:gives { - (6 9 9) :sort (6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9 9) list:firstRest (6 (9 9))}] - skolem:lemma6335 - skolem:lemma4395 - skolem:lemma4650 - [ a r:Fact; r:gives {(6 9 9) list:firstRest (6 (9 9))}] - [ a r:Fact; r:gives {(() (6 9 9)) list:append (6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5475 a r:Inference; - r:gives { - (2 (7 0 0)) :split ((0 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 0) list:firstRest (7 (0 0))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5476 a r:Inference; - r:gives { - (2 (7 0 1)) :split ((0 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 1) list:firstRest (7 (0 1))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5477 a r:Inference; - r:gives { - (2 (7 0 2)) :split ((0 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 2) list:firstRest (7 (0 2))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5478 a r:Inference; - r:gives { - (2 (7 0 3)) :split ((0) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 3) list:firstRest (7 (0 3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5479 a r:Inference; - r:gives { - (2 (7 0 4)) :split ((0) (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 4) list:firstRest (7 (0 4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5480 a r:Inference; - r:gives { - (2 (7 0 5)) :split ((0) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 5) list:firstRest (7 (0 5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5481 a r:Inference; - r:gives { - (2 (7 0 6)) :split ((0) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 6) list:firstRest (7 (0 6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5482 a r:Inference; - r:gives { - (2 (7 0 7)) :split ((0) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 7) list:firstRest (7 (0 7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5483 a r:Inference; - r:gives { - (2 (7 0 8)) :split ((0) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 8) list:firstRest (7 (0 8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5484 a r:Inference; - r:gives { - (2 (7 0 9)) :split ((0) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0 9) list:firstRest (7 (0 9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5485 a r:Inference; - r:gives { - (2 (7 1 0)) :split ((1 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 0) list:firstRest (7 (1 0))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5486 a r:Inference; - r:gives { - (2 (7 1 1)) :split ((1 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 1) list:firstRest (7 (1 1))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5487 a r:Inference; - r:gives { - (2 (7 1 2)) :split ((1 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 2) list:firstRest (7 (1 2))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5488 a r:Inference; - r:gives { - (2 (7 1 3)) :split ((1) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 3) list:firstRest (7 (1 3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5489 a r:Inference; - r:gives { - (2 (7 1 5)) :split ((1) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 5) list:firstRest (7 (1 5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5490 a r:Inference; - r:gives { - (2 (7 1 6)) :split ((1) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 6) list:firstRest (7 (1 6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5491 a r:Inference; - r:gives { - (2 (7 1 7)) :split ((1) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 7) list:firstRest (7 (1 7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5492 a r:Inference; - r:gives { - (2 (7 1 8)) :split ((1) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 8) list:firstRest (7 (1 8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5493 a r:Inference; - r:gives { - (2 (7 1 9)) :split ((1) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1 9) list:firstRest (7 (1 9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5494 a r:Inference; - r:gives { - (2 (7 2 0)) :split ((2 0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 0) list:firstRest (7 (2 0))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5495 a r:Inference; - r:gives { - (2 (7 2 1)) :split ((2 1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 1) list:firstRest (7 (2 1))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5496 a r:Inference; - r:gives { - (2 (7 2 2)) :split ((2 2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 2) list:firstRest (7 (2 2))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5497 a r:Inference; - r:gives { - (2 (7 2 3)) :split ((2) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 3) list:firstRest (7 (2 3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5498 a r:Inference; - r:gives { - (2 (7 2 4)) :split ((2) (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 4) list:firstRest (7 (2 4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5499 a r:Inference; - r:gives { - (2 (7 2 5)) :split ((2) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 5) list:firstRest (7 (2 5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5500 a r:Inference; - r:gives { - (2 (7 2 6)) :split ((2) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 6) list:firstRest (7 (2 6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5501 a r:Inference; - r:gives { - (2 (7 2 7)) :split ((2) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 7) list:firstRest (7 (2 7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5502 a r:Inference; - r:gives { - (2 (7 2 8)) :split ((2) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 8) list:firstRest (7 (2 8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5503 a r:Inference; - r:gives { - (2 (7 2 9)) :split ((2) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2 9) list:firstRest (7 (2 9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5504 a r:Inference; - r:gives { - (2 (7 3 0)) :split ((0) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 0) list:firstRest (7 (3 0))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5505 a r:Inference; - r:gives { - (2 (7 3 1)) :split ((1) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 1) list:firstRest (7 (3 1))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5506 a r:Inference; - r:gives { - (2 (7 3 2)) :split ((2) (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 2) list:firstRest (7 (3 2))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5507 a r:Inference; - r:gives { - (2 (7 3 3)) :split (() (7 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 3) list:firstRest (7 (3 3))}] - [ a r:Fact; r:gives {(7 3 3) list:firstRest (7 (3 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5508 a r:Inference; - r:gives { - (7 3 3) :sort (3 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 3) list:firstRest (7 (3 3))}] - skolem:lemma6336 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 3) (7)) list:append (3 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5509 a r:Inference; - r:gives { - (2 (7 3 4)) :split (() (7 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 4) list:firstRest (7 (3 4))}] - [ a r:Fact; r:gives {(7 3 4) list:firstRest (7 (3 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5510 a r:Inference; - r:gives { - (7 3 4) :sort (3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 4) list:firstRest (7 (3 4))}] - skolem:lemma6337 - skolem:lemma4509 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 4) (7)) list:append (3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5511 a r:Inference; - r:gives { - (2 (7 3 5)) :split (() (7 3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 5) list:firstRest (7 (3 5))}] - [ a r:Fact; r:gives {(7 3 5) list:firstRest (7 (3 5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5512 a r:Inference; - r:gives { - (7 3 5) :sort (3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 5) list:firstRest (7 (3 5))}] - skolem:lemma6338 - skolem:lemma4511 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 5) (7)) list:append (3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5513 a r:Inference; - r:gives { - (2 (7 3 6)) :split (() (7 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 6) list:firstRest (7 (3 6))}] - [ a r:Fact; r:gives {(7 3 6) list:firstRest (7 (3 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5514 a r:Inference; - r:gives { - (7 3 6) :sort (3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 6) list:firstRest (7 (3 6))}] - skolem:lemma6339 - skolem:lemma4513 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 6) (7)) list:append (3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5515 a r:Inference; - r:gives { - (2 (7 3 7)) :split (() (7 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 7) list:firstRest (7 (3 7))}] - [ a r:Fact; r:gives {(7 3 7) list:firstRest (7 (3 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5516 a r:Inference; - r:gives { - (7 3 7) :sort (3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 7) list:firstRest (7 (3 7))}] - skolem:lemma6340 - skolem:lemma4515 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 7) (7)) list:append (3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5517 a r:Inference; - r:gives { - (2 (7 3 8)) :split (() (7 3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 8) list:firstRest (7 (3 8))}] - [ a r:Fact; r:gives {(7 3 8) list:firstRest (7 (3 8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5518 a r:Inference; - r:gives { - (7 3 8) :sort (3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 8) list:firstRest (7 (3 8))}] - skolem:lemma6341 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((3) (7 8)) list:append (3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5519 a r:Inference; - r:gives { - (2 (7 3 9)) :split (() (7 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 9) list:firstRest (7 (3 9))}] - [ a r:Fact; r:gives {(7 3 9) list:firstRest (7 (3 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5520 a r:Inference; - r:gives { - (7 3 9) :sort (3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3 9) list:firstRest (7 (3 9))}] - skolem:lemma6342 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((3) (7 9)) list:append (3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5521 a r:Inference; - r:gives { - (2 (7 4 0)) :split ((0) (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 0) list:firstRest (7 (4 0))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5522 a r:Inference; - r:gives { - (2 (7 4 2)) :split ((2) (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 2) list:firstRest (7 (4 2))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5523 a r:Inference; - r:gives { - (2 (7 4 3)) :split (() (7 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 3) list:firstRest (7 (4 3))}] - [ a r:Fact; r:gives {(7 4 3) list:firstRest (7 (4 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5524 a r:Inference; - r:gives { - (7 4 3) :sort (3 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 3) list:firstRest (7 (4 3))}] - skolem:lemma6343 - skolem:lemma4524 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 4) (7)) list:append (3 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5525 a r:Inference; - r:gives { - (2 (7 4 4)) :split (() (7 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 4) list:firstRest (7 (4 4))}] - [ a r:Fact; r:gives {(7 4 4) list:firstRest (7 (4 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5526 a r:Inference; - r:gives { - (7 4 4) :sort (4 4 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 4) list:firstRest (7 (4 4))}] - skolem:lemma6344 - skolem:lemma4526 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 4) (7)) list:append (4 4 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5527 a r:Inference; - r:gives { - (2 (7 4 5)) :split (() (7 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 5) list:firstRest (7 (4 5))}] - [ a r:Fact; r:gives {(7 4 5) list:firstRest (7 (4 5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5528 a r:Inference; - r:gives { - (7 4 5) :sort (4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 5) list:firstRest (7 (4 5))}] - skolem:lemma6345 - skolem:lemma4528 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 5) (7)) list:append (4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5529 a r:Inference; - r:gives { - (2 (7 4 6)) :split (() (7 4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 6) list:firstRest (7 (4 6))}] - [ a r:Fact; r:gives {(7 4 6) list:firstRest (7 (4 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5530 a r:Inference; - r:gives { - (7 4 6) :sort (4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 6) list:firstRest (7 (4 6))}] - skolem:lemma6346 - skolem:lemma4719 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 6) (7)) list:append (4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5531 a r:Inference; - r:gives { - (2 (7 4 7)) :split (() (7 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 7) list:firstRest (7 (4 7))}] - [ a r:Fact; r:gives {(7 4 7) list:firstRest (7 (4 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5532 a r:Inference; - r:gives { - (7 4 7) :sort (4 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 7) list:firstRest (7 (4 7))}] - skolem:lemma6347 - skolem:lemma4530 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 7) (7)) list:append (4 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5533 a r:Inference; - r:gives { - (2 (7 4 8)) :split (() (7 4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 8) list:firstRest (7 (4 8))}] - [ a r:Fact; r:gives {(7 4 8) list:firstRest (7 (4 8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5534 a r:Inference; - r:gives { - (7 4 8) :sort (4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 8) list:firstRest (7 (4 8))}] - skolem:lemma6348 - skolem:lemma4414 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((4) (7 8)) list:append (4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5535 a r:Inference; - r:gives { - (2 (7 4 9)) :split (() (7 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 9) list:firstRest (7 (4 9))}] - [ a r:Fact; r:gives {(7 4 9) list:firstRest (7 (4 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5536 a r:Inference; - r:gives { - (7 4 9) :sort (4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4 9) list:firstRest (7 (4 9))}] - skolem:lemma6349 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((4) (7 9)) list:append (4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5537 a r:Inference; - r:gives { - (2 (7 5 0)) :split ((0) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 0) list:firstRest (7 (5 0))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5538 a r:Inference; - r:gives { - (2 (7 5 1)) :split ((1) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 1) list:firstRest (7 (5 1))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5539 a r:Inference; - r:gives { - (2 (7 5 2)) :split ((2) (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 2) list:firstRest (7 (5 2))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5540 a r:Inference; - r:gives { - (2 (7 5 3)) :split (() (7 5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 3) list:firstRest (7 (5 3))}] - [ a r:Fact; r:gives {(7 5 3) list:firstRest (7 (5 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5541 a r:Inference; - r:gives { - (7 5 3) :sort (3 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 3) list:firstRest (7 (5 3))}] - skolem:lemma6350 - skolem:lemma4539 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 5) (7)) list:append (3 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5542 a r:Inference; - r:gives { - (2 (7 5 4)) :split (() (7 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 4) list:firstRest (7 (5 4))}] - [ a r:Fact; r:gives {(7 5 4) list:firstRest (7 (5 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5543 a r:Inference; - r:gives { - (7 5 4) :sort (4 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 4) list:firstRest (7 (5 4))}] - skolem:lemma6351 - skolem:lemma4541 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 5) (7)) list:append (4 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5544 a r:Inference; - r:gives { - (2 (7 5 5)) :split (() (7 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 5) list:firstRest (7 (5 5))}] - [ a r:Fact; r:gives {(7 5 5) list:firstRest (7 (5 5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5545 a r:Inference; - r:gives { - (7 5 5) :sort (5 5 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 5) list:firstRest (7 (5 5))}] - skolem:lemma6352 - skolem:lemma4543 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((5 5) (7)) list:append (5 5 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5546 a r:Inference; - r:gives { - (2 (7 5 6)) :split (() (7 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 6) list:firstRest (7 (5 6))}] - [ a r:Fact; r:gives {(7 5 6) list:firstRest (7 (5 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5547 a r:Inference; - r:gives { - (7 5 6) :sort (5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 6) list:firstRest (7 (5 6))}] - skolem:lemma6353 - skolem:lemma4547 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((5 6) (7)) list:append (5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5548 a r:Inference; - r:gives { - (2 (7 5 7)) :split (() (7 5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 7) list:firstRest (7 (5 7))}] - [ a r:Fact; r:gives {(7 5 7) list:firstRest (7 (5 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5549 a r:Inference; - r:gives { - (7 5 7) :sort (5 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 7) list:firstRest (7 (5 7))}] - skolem:lemma6354 - skolem:lemma4551 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((5 7) (7)) list:append (5 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5550 a r:Inference; - r:gives { - (2 (7 5 9)) :split (() (7 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 9) list:firstRest (7 (5 9))}] - [ a r:Fact; r:gives {(7 5 9) list:firstRest (7 (5 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5551 a r:Inference; - r:gives { - (7 5 9) :sort (5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5 9) list:firstRest (7 (5 9))}] - skolem:lemma6355 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((5) (7 9)) list:append (5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5552 a r:Inference; - r:gives { - (2 (7 6 0)) :split ((0) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 0) list:firstRest (7 (6 0))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5553 a r:Inference; - r:gives { - (2 (7 6 1)) :split ((1) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 1) list:firstRest (7 (6 1))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5554 a r:Inference; - r:gives { - (2 (7 6 2)) :split ((2) (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 2) list:firstRest (7 (6 2))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5555 a r:Inference; - r:gives { - (2 (7 6 3)) :split (() (7 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 3) list:firstRest (7 (6 3))}] - [ a r:Fact; r:gives {(7 6 3) list:firstRest (7 (6 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5556 a r:Inference; - r:gives { - (7 6 3) :sort (3 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 3) list:firstRest (7 (6 3))}] - skolem:lemma6356 - skolem:lemma4565 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 6) (7)) list:append (3 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5557 a r:Inference; - r:gives { - (2 (7 6 4)) :split (() (7 6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 4) list:firstRest (7 (6 4))}] - [ a r:Fact; r:gives {(7 6 4) list:firstRest (7 (6 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5558 a r:Inference; - r:gives { - (7 6 4) :sort (4 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 4) list:firstRest (7 (6 4))}] - skolem:lemma6357 - skolem:lemma4739 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 6) (7)) list:append (4 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5559 a r:Inference; - r:gives { - (2 (7 6 5)) :split (() (7 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 5) list:firstRest (7 (6 5))}] - [ a r:Fact; r:gives {(7 6 5) list:firstRest (7 (6 5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5560 a r:Inference; - r:gives { - (7 6 5) :sort (5 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 5) list:firstRest (7 (6 5))}] - skolem:lemma6358 - skolem:lemma4567 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((5 6) (7)) list:append (5 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5561 a r:Inference; - r:gives { - (2 (7 6 6)) :split (() (7 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 6) list:firstRest (7 (6 6))}] - [ a r:Fact; r:gives {(7 6 6) list:firstRest (7 (6 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5562 a r:Inference; - r:gives { - (7 6 6) :sort (6 6 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 6) list:firstRest (7 (6 6))}] - skolem:lemma6359 - skolem:lemma4569 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((6 6) (7)) list:append (6 6 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5563 a r:Inference; - r:gives { - (2 (7 6 7)) :split (() (7 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 7) list:firstRest (7 (6 7))}] - [ a r:Fact; r:gives {(7 6 7) list:firstRest (7 (6 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5564 a r:Inference; - r:gives { - (7 6 7) :sort (6 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 7) list:firstRest (7 (6 7))}] - skolem:lemma6360 - skolem:lemma4575 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((6 7) (7)) list:append (6 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5565 a r:Inference; - r:gives { - (2 (7 6 8)) :split (() (7 6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 8) list:firstRest (7 (6 8))}] - [ a r:Fact; r:gives {(7 6 8) list:firstRest (7 (6 8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5566 a r:Inference; - r:gives { - (7 6 8) :sort (6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 8) list:firstRest (7 (6 8))}] - skolem:lemma6361 - skolem:lemma4458 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((6) (7 8)) list:append (6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5567 a r:Inference; - r:gives { - (2 (7 6 9)) :split (() (7 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 9) list:firstRest (7 (6 9))}] - [ a r:Fact; r:gives {(7 6 9) list:firstRest (7 (6 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5568 a r:Inference; - r:gives { - (7 6 9) :sort (6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6 9) list:firstRest (7 (6 9))}] - skolem:lemma6362 - skolem:lemma4458 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((6) (7 9)) list:append (6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5569 a r:Inference; - r:gives { - (2 (7 7 0)) :split ((0) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 0) list:firstRest (7 (7 0))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5570 a r:Inference; - r:gives { - (2 (7 7 1)) :split ((1) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 1) list:firstRest (7 (7 1))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5571 a r:Inference; - r:gives { - (2 (7 7 2)) :split ((2) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 2) list:firstRest (7 (7 2))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5572 a r:Inference; - r:gives { - (2 (7 7 3)) :split (() (7 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 3) list:firstRest (7 (7 3))}] - [ a r:Fact; r:gives {(7 7 3) list:firstRest (7 (7 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5573 a r:Inference; - r:gives { - (7 7 3) :sort (3 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 3) list:firstRest (7 (7 3))}] - skolem:lemma6363 - skolem:lemma4592 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((3 7) (7)) list:append (3 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5574 a r:Inference; - r:gives { - (2 (7 7 4)) :split (() (7 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 4) list:firstRest (7 (7 4))}] - [ a r:Fact; r:gives {(7 7 4) list:firstRest (7 (7 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5575 a r:Inference; - r:gives { - (7 7 4) :sort (4 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 4) list:firstRest (7 (7 4))}] - skolem:lemma6364 - skolem:lemma4594 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((4 7) (7)) list:append (4 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5576 a r:Inference; - r:gives { - (2 (7 7 5)) :split (() (7 7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 5) list:firstRest (7 (7 5))}] - [ a r:Fact; r:gives {(7 7 5) list:firstRest (7 (7 5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5577 a r:Inference; - r:gives { - (7 7 5) :sort (5 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 5) list:firstRest (7 (7 5))}] - skolem:lemma6365 - skolem:lemma4596 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((5 7) (7)) list:append (5 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5578 a r:Inference; - r:gives { - (2 (7 7 6)) :split (() (7 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 6) list:firstRest (7 (7 6))}] - [ a r:Fact; r:gives {(7 7 6) list:firstRest (7 (7 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5579 a r:Inference; - r:gives { - (7 7 6) :sort (6 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 6) list:firstRest (7 (7 6))}] - skolem:lemma6366 - skolem:lemma4598 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((6 7) (7)) list:append (6 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5580 a r:Inference; - r:gives { - (2 (7 7 7)) :split (() (7 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 7) list:firstRest (7 (7 7))}] - [ a r:Fact; r:gives {(7 7 7) list:firstRest (7 (7 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5581 a r:Inference; - r:gives { - (7 7 7) :sort (7 7 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 7) list:firstRest (7 (7 7))}] - skolem:lemma6367 - skolem:lemma4600 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((7 7) (7)) list:append (7 7 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5582 a r:Inference; - r:gives { - (2 (7 7 8)) :split (() (7 7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 8) list:firstRest (7 (7 8))}] - [ a r:Fact; r:gives {(7 7 8) list:firstRest (7 (7 8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5583 a r:Inference; - r:gives { - (7 7 8) :sort (7 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 8) list:firstRest (7 (7 8))}] - skolem:lemma6368 - skolem:lemma4422 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((7) (7 8)) list:append (7 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5584 a r:Inference; - r:gives { - (2 (7 7 9)) :split (() (7 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 9) list:firstRest (7 (7 9))}] - [ a r:Fact; r:gives {(7 7 9) list:firstRest (7 (7 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5585 a r:Inference; - r:gives { - (7 7 9) :sort (7 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7 9) list:firstRest (7 (7 9))}] - skolem:lemma6369 - skolem:lemma4422 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((7) (7 9)) list:append (7 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5586 a r:Inference; - r:gives { - (2 (7 8 0)) :split ((0) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 0) list:firstRest (7 (8 0))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5587 a r:Inference; - r:gives { - (2 (7 8 1)) :split ((1) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 1) list:firstRest (7 (8 1))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5588 a r:Inference; - r:gives { - (2 (7 8 2)) :split ((2) (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 2) list:firstRest (7 (8 2))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5589 a r:Inference; - r:gives { - (2 (7 8 3)) :split (() (7 8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 3) list:firstRest (7 (8 3))}] - [ a r:Fact; r:gives {(7 8 3) list:firstRest (7 (8 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5590 a r:Inference; - r:gives { - (7 8 3) :sort (3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 3) list:firstRest (7 (8 3))}] - skolem:lemma6370 - skolem:lemma4408 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((3) (7 8)) list:append (3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5591 a r:Inference; - r:gives { - (2 (7 8 4)) :split (() (7 8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 4) list:firstRest (7 (8 4))}] - [ a r:Fact; r:gives {(7 8 4) list:firstRest (7 (8 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5592 a r:Inference; - r:gives { - (7 8 4) :sort (4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 4) list:firstRest (7 (8 4))}] - skolem:lemma6371 - skolem:lemma4414 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((4) (7 8)) list:append (4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5593 a r:Inference; - r:gives { - (2 (7 8 6)) :split (() (7 8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 6) list:firstRest (7 (8 6))}] - [ a r:Fact; r:gives {(7 8 6) list:firstRest (7 (8 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5594 a r:Inference; - r:gives { - (7 8 6) :sort (6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 6) list:firstRest (7 (8 6))}] - skolem:lemma6372 - skolem:lemma4458 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((6) (7 8)) list:append (6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5595 a r:Inference; - r:gives { - (2 (7 8 7)) :split (() (7 8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 7) list:firstRest (7 (8 7))}] - [ a r:Fact; r:gives {(7 8 7) list:firstRest (7 (8 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5596 a r:Inference; - r:gives { - (7 8 7) :sort (7 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 7) list:firstRest (7 (8 7))}] - skolem:lemma6373 - skolem:lemma4422 - skolem:lemma4426 - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {((7) (7 8)) list:append (7 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5597 a r:Inference; - r:gives { - (2 (7 8 8)) :split (() (7 8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 8) list:firstRest (7 (8 8))}] - [ a r:Fact; r:gives {(7 8 8) list:firstRest (7 (8 8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5598 a r:Inference; - r:gives { - (7 8 8) :sort (7 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 8) list:firstRest (7 (8 8))}] - skolem:lemma6374 - skolem:lemma4395 - skolem:lemma4629 - [ a r:Fact; r:gives {(7 8 8) list:firstRest (7 (8 8))}] - [ a r:Fact; r:gives {(() (7 8 8)) list:append (7 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5599 a r:Inference; - r:gives { - (2 (7 8 9)) :split (() (7 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 9) list:firstRest (7 (8 9))}] - [ a r:Fact; r:gives {(7 8 9) list:firstRest (7 (8 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5600 a r:Inference; - r:gives { - (7 8 9) :sort (7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8 9) list:firstRest (7 (8 9))}] - skolem:lemma6375 - skolem:lemma4395 - skolem:lemma4631 - [ a r:Fact; r:gives {(7 8 9) list:firstRest (7 (8 9))}] - [ a r:Fact; r:gives {(() (7 8 9)) list:append (7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5601 a r:Inference; - r:gives { - (2 (7 9 0)) :split ((0) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 0) list:firstRest (7 (9 0))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5602 a r:Inference; - r:gives { - (2 (7 9 1)) :split ((1) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 1) list:firstRest (7 (9 1))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5603 a r:Inference; - r:gives { - (2 (7 9 2)) :split ((2) (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 2) list:firstRest (7 (9 2))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5604 a r:Inference; - r:gives { - (2 (7 9 3)) :split (() (7 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 3) list:firstRest (7 (9 3))}] - [ a r:Fact; r:gives {(7 9 3) list:firstRest (7 (9 3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5605 a r:Inference; - r:gives { - (7 9 3) :sort (3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 3) list:firstRest (7 (9 3))}] - skolem:lemma6376 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((3) (7 9)) list:append (3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5606 a r:Inference; - r:gives { - (2 (7 9 4)) :split (() (7 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 4) list:firstRest (7 (9 4))}] - [ a r:Fact; r:gives {(7 9 4) list:firstRest (7 (9 4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5607 a r:Inference; - r:gives { - (7 9 4) :sort (4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 4) list:firstRest (7 (9 4))}] - skolem:lemma6377 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((4) (7 9)) list:append (4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5608 a r:Inference; - r:gives { - (2 (7 9 5)) :split (() (7 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 5) list:firstRest (7 (9 5))}] - [ a r:Fact; r:gives {(7 9 5) list:firstRest (7 (9 5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5609 a r:Inference; - r:gives { - (7 9 5) :sort (5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 5) list:firstRest (7 (9 5))}] - skolem:lemma6378 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((5) (7 9)) list:append (5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5610 a r:Inference; - r:gives { - (2 (7 9 6)) :split (() (7 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 6) list:firstRest (7 (9 6))}] - [ a r:Fact; r:gives {(7 9 6) list:firstRest (7 (9 6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5611 a r:Inference; - r:gives { - (7 9 6) :sort (6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 6) list:firstRest (7 (9 6))}] - skolem:lemma6379 - skolem:lemma4458 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((6) (7 9)) list:append (6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5612 a r:Inference; - r:gives { - (2 (7 9 7)) :split (() (7 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 7) list:firstRest (7 (9 7))}] - [ a r:Fact; r:gives {(7 9 7) list:firstRest (7 (9 7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5613 a r:Inference; - r:gives { - (7 9 7) :sort (7 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 7) list:firstRest (7 (9 7))}] - skolem:lemma6380 - skolem:lemma4422 - skolem:lemma4430 - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {((7) (7 9)) list:append (7 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5614 a r:Inference; - r:gives { - (2 (7 9 8)) :split (() (7 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 8) list:firstRest (7 (9 8))}] - [ a r:Fact; r:gives {(7 9 8) list:firstRest (7 (9 8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5615 a r:Inference; - r:gives { - (7 9 8) :sort (7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 8) list:firstRest (7 (9 8))}] - skolem:lemma6381 - skolem:lemma4395 - skolem:lemma4648 - [ a r:Fact; r:gives {(7 8 9) list:firstRest (7 (8 9))}] - [ a r:Fact; r:gives {(() (7 8 9)) list:append (7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5616 a r:Inference; - r:gives { - (2 (7 9 9)) :split (() (7 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 9) list:firstRest (7 (9 9))}] - [ a r:Fact; r:gives {(7 9 9) list:firstRest (7 (9 9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5617 a r:Inference; - r:gives { - (7 9 9) :sort (7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9 9) list:firstRest (7 (9 9))}] - skolem:lemma6382 - skolem:lemma4395 - skolem:lemma4650 - [ a r:Fact; r:gives {(7 9 9) list:firstRest (7 (9 9))}] - [ a r:Fact; r:gives {(() (7 9 9)) list:append (7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5618 a r:Inference; - r:gives { - (2 (8 0 0)) :split ((0 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 0) list:firstRest (8 (0 0))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5619 a r:Inference; - r:gives { - (2 (8 0 1)) :split ((0 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 1) list:firstRest (8 (0 1))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5620 a r:Inference; - r:gives { - (2 (8 0 2)) :split ((0 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 2) list:firstRest (8 (0 2))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5621 a r:Inference; - r:gives { - (2 (8 0 3)) :split ((0) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 3) list:firstRest (8 (0 3))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5622 a r:Inference; - r:gives { - (2 (8 0 4)) :split ((0) (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 4) list:firstRest (8 (0 4))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5623 a r:Inference; - r:gives { - (2 (8 0 5)) :split ((0) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 5) list:firstRest (8 (0 5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5624 a r:Inference; - r:gives { - (2 (8 0 6)) :split ((0) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 6) list:firstRest (8 (0 6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5625 a r:Inference; - r:gives { - (2 (8 0 7)) :split ((0) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 7) list:firstRest (8 (0 7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5626 a r:Inference; - r:gives { - (2 (8 0 8)) :split ((0) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 8) list:firstRest (8 (0 8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5627 a r:Inference; - r:gives { - (2 (8 0 9)) :split ((0) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0 9) list:firstRest (8 (0 9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5628 a r:Inference; - r:gives { - (2 (8 1 0)) :split ((1 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 0) list:firstRest (8 (1 0))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5629 a r:Inference; - r:gives { - (2 (8 1 1)) :split ((1 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 1) list:firstRest (8 (1 1))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5630 a r:Inference; - r:gives { - (2 (8 1 2)) :split ((1 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 2) list:firstRest (8 (1 2))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5631 a r:Inference; - r:gives { - (2 (8 1 3)) :split ((1) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 3) list:firstRest (8 (1 3))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5632 a r:Inference; - r:gives { - (2 (8 1 4)) :split ((1) (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 4) list:firstRest (8 (1 4))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5633 a r:Inference; - r:gives { - (2 (8 1 5)) :split ((1) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 5) list:firstRest (8 (1 5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5634 a r:Inference; - r:gives { - (2 (8 1 6)) :split ((1) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 6) list:firstRest (8 (1 6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5635 a r:Inference; - r:gives { - (2 (8 1 7)) :split ((1) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 7) list:firstRest (8 (1 7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5636 a r:Inference; - r:gives { - (2 (8 1 8)) :split ((1) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 8) list:firstRest (8 (1 8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5637 a r:Inference; - r:gives { - (2 (8 1 9)) :split ((1) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1 9) list:firstRest (8 (1 9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5638 a r:Inference; - r:gives { - (2 (8 2 0)) :split ((2 0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 0) list:firstRest (8 (2 0))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5639 a r:Inference; - r:gives { - (2 (8 2 1)) :split ((2 1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 1) list:firstRest (8 (2 1))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5640 a r:Inference; - r:gives { - (2 (8 2 2)) :split ((2 2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 2) list:firstRest (8 (2 2))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5641 a r:Inference; - r:gives { - (2 (8 2 3)) :split ((2) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 3) list:firstRest (8 (2 3))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5642 a r:Inference; - r:gives { - (2 (8 2 5)) :split ((2) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 5) list:firstRest (8 (2 5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5643 a r:Inference; - r:gives { - (2 (8 2 6)) :split ((2) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 6) list:firstRest (8 (2 6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5644 a r:Inference; - r:gives { - (2 (8 2 7)) :split ((2) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 7) list:firstRest (8 (2 7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5645 a r:Inference; - r:gives { - (2 (8 2 8)) :split ((2) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 8) list:firstRest (8 (2 8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5646 a r:Inference; - r:gives { - (2 (8 2 9)) :split ((2) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2 9) list:firstRest (8 (2 9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5647 a r:Inference; - r:gives { - (2 (8 3 0)) :split ((0) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 0) list:firstRest (8 (3 0))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5648 a r:Inference; - r:gives { - (2 (8 3 1)) :split ((1) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 1) list:firstRest (8 (3 1))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5649 a r:Inference; - r:gives { - (2 (8 3 2)) :split ((2) (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 2) list:firstRest (8 (3 2))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5650 a r:Inference; - r:gives { - (2 (8 3 3)) :split (() (8 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 3) list:firstRest (8 (3 3))}] - [ a r:Fact; r:gives {(8 3 3) list:firstRest (8 (3 3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5651 a r:Inference; - r:gives { - (8 3 3) :sort (3 3 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 3) list:firstRest (8 (3 3))}] - skolem:lemma6383 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 3) (8)) list:append (3 3 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5652 a r:Inference; - r:gives { - (2 (8 3 4)) :split (() (8 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 4) list:firstRest (8 (3 4))}] - [ a r:Fact; r:gives {(8 3 4) list:firstRest (8 (3 4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5653 a r:Inference; - r:gives { - (8 3 4) :sort (3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 4) list:firstRest (8 (3 4))}] - skolem:lemma6384 - skolem:lemma4509 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 4) (8)) list:append (3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5654 a r:Inference; - r:gives { - (2 (8 3 6)) :split (() (8 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 6) list:firstRest (8 (3 6))}] - [ a r:Fact; r:gives {(8 3 6) list:firstRest (8 (3 6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5655 a r:Inference; - r:gives { - (8 3 6) :sort (3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 6) list:firstRest (8 (3 6))}] - skolem:lemma6385 - skolem:lemma4513 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 6) (8)) list:append (3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5656 a r:Inference; - r:gives { - (2 (8 3 7)) :split (() (8 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 7) list:firstRest (8 (3 7))}] - [ a r:Fact; r:gives {(8 3 7) list:firstRest (8 (3 7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5657 a r:Inference; - r:gives { - (8 3 7) :sort (3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 7) list:firstRest (8 (3 7))}] - skolem:lemma6386 - skolem:lemma4515 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 7) (8)) list:append (3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5658 a r:Inference; - r:gives { - (2 (8 3 8)) :split (() (8 3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 8) list:firstRest (8 (3 8))}] - [ a r:Fact; r:gives {(8 3 8) list:firstRest (8 (3 8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5659 a r:Inference; - r:gives { - (8 3 8) :sort (3 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 8) list:firstRest (8 (3 8))}] - skolem:lemma6387 - skolem:lemma4517 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 8) (8)) list:append (3 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5660 a r:Inference; - r:gives { - (2 (8 3 9)) :split (() (8 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 9) list:firstRest (8 (3 9))}] - [ a r:Fact; r:gives {(8 3 9) list:firstRest (8 (3 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5661 a r:Inference; - r:gives { - (8 3 9) :sort (3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3 9) list:firstRest (8 (3 9))}] - skolem:lemma6388 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((3) (8 9)) list:append (3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5662 a r:Inference; - r:gives { - (2 (8 4 0)) :split ((0) (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 0) list:firstRest (8 (4 0))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5663 a r:Inference; - r:gives { - (2 (8 4 1)) :split ((1) (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 1) list:firstRest (8 (4 1))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5664 a r:Inference; - r:gives { - (2 (8 4 3)) :split (() (8 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 3) list:firstRest (8 (4 3))}] - [ a r:Fact; r:gives {(8 4 3) list:firstRest (8 (4 3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5665 a r:Inference; - r:gives { - (8 4 3) :sort (3 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 3) list:firstRest (8 (4 3))}] - skolem:lemma6389 - skolem:lemma4524 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 4) (8)) list:append (3 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5666 a r:Inference; - r:gives { - (2 (8 4 4)) :split (() (8 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 4) list:firstRest (8 (4 4))}] - [ a r:Fact; r:gives {(8 4 4) list:firstRest (8 (4 4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5667 a r:Inference; - r:gives { - (8 4 4) :sort (4 4 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 4) list:firstRest (8 (4 4))}] - skolem:lemma6390 - skolem:lemma4526 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 4) (8)) list:append (4 4 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5668 a r:Inference; - r:gives { - (2 (8 4 5)) :split (() (8 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 5) list:firstRest (8 (4 5))}] - [ a r:Fact; r:gives {(8 4 5) list:firstRest (8 (4 5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5669 a r:Inference; - r:gives { - (8 4 5) :sort (4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 5) list:firstRest (8 (4 5))}] - skolem:lemma6391 - skolem:lemma4528 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 5) (8)) list:append (4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5670 a r:Inference; - r:gives { - (2 (8 4 7)) :split (() (8 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 7) list:firstRest (8 (4 7))}] - [ a r:Fact; r:gives {(8 4 7) list:firstRest (8 (4 7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5671 a r:Inference; - r:gives { - (8 4 7) :sort (4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 7) list:firstRest (8 (4 7))}] - skolem:lemma6392 - skolem:lemma4530 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 7) (8)) list:append (4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5672 a r:Inference; - r:gives { - (2 (8 4 8)) :split (() (8 4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 8) list:firstRest (8 (4 8))}] - [ a r:Fact; r:gives {(8 4 8) list:firstRest (8 (4 8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5673 a r:Inference; - r:gives { - (8 4 8) :sort (4 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 8) list:firstRest (8 (4 8))}] - skolem:lemma6393 - skolem:lemma4532 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 8) (8)) list:append (4 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5674 a r:Inference; - r:gives { - (2 (8 4 9)) :split (() (8 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 9) list:firstRest (8 (4 9))}] - [ a r:Fact; r:gives {(8 4 9) list:firstRest (8 (4 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5675 a r:Inference; - r:gives { - (8 4 9) :sort (4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4 9) list:firstRest (8 (4 9))}] - skolem:lemma6394 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((4) (8 9)) list:append (4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5676 a r:Inference; - r:gives { - (2 (8 5 0)) :split ((0) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 0) list:firstRest (8 (5 0))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5677 a r:Inference; - r:gives { - (2 (8 5 1)) :split ((1) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 1) list:firstRest (8 (5 1))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5678 a r:Inference; - r:gives { - (2 (8 5 2)) :split ((2) (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 2) list:firstRest (8 (5 2))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5679 a r:Inference; - r:gives { - (2 (8 5 4)) :split (() (8 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 4) list:firstRest (8 (5 4))}] - [ a r:Fact; r:gives {(8 5 4) list:firstRest (8 (5 4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5680 a r:Inference; - r:gives { - (8 5 4) :sort (4 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 4) list:firstRest (8 (5 4))}] - skolem:lemma6395 - skolem:lemma4541 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 5) (8)) list:append (4 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5681 a r:Inference; - r:gives { - (2 (8 5 5)) :split (() (8 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 5) list:firstRest (8 (5 5))}] - [ a r:Fact; r:gives {(8 5 5) list:firstRest (8 (5 5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5682 a r:Inference; - r:gives { - (8 5 5) :sort (5 5 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 5) list:firstRest (8 (5 5))}] - skolem:lemma6396 - skolem:lemma4543 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((5 5) (8)) list:append (5 5 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5683 a r:Inference; - r:gives { - (2 (8 5 6)) :split (() (8 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 6) list:firstRest (8 (5 6))}] - [ a r:Fact; r:gives {(8 5 6) list:firstRest (8 (5 6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5684 a r:Inference; - r:gives { - (8 5 6) :sort (5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 6) list:firstRest (8 (5 6))}] - skolem:lemma6397 - skolem:lemma4547 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((5 6) (8)) list:append (5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5685 a r:Inference; - r:gives { - (2 (8 5 8)) :split (() (8 5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 8) list:firstRest (8 (5 8))}] - [ a r:Fact; r:gives {(8 5 8) list:firstRest (8 (5 8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5686 a r:Inference; - r:gives { - (8 5 8) :sort (5 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 8) list:firstRest (8 (5 8))}] - skolem:lemma6398 - skolem:lemma4555 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((5 8) (8)) list:append (5 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5687 a r:Inference; - r:gives { - (2 (8 5 9)) :split (() (8 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 9) list:firstRest (8 (5 9))}] - [ a r:Fact; r:gives {(8 5 9) list:firstRest (8 (5 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5688 a r:Inference; - r:gives { - (8 5 9) :sort (5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5 9) list:firstRest (8 (5 9))}] - skolem:lemma6399 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((5) (8 9)) list:append (5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5689 a r:Inference; - r:gives { - (2 (8 6 0)) :split ((0) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 0) list:firstRest (8 (6 0))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5690 a r:Inference; - r:gives { - (2 (8 6 1)) :split ((1) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 1) list:firstRest (8 (6 1))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5691 a r:Inference; - r:gives { - (2 (8 6 2)) :split ((2) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 2) list:firstRest (8 (6 2))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5692 a r:Inference; - r:gives { - (2 (8 6 3)) :split (() (8 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 3) list:firstRest (8 (6 3))}] - [ a r:Fact; r:gives {(8 6 3) list:firstRest (8 (6 3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5693 a r:Inference; - r:gives { - (8 6 3) :sort (3 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 3) list:firstRest (8 (6 3))}] - skolem:lemma6400 - skolem:lemma4565 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 6) (8)) list:append (3 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5694 a r:Inference; - r:gives { - (2 (8 6 5)) :split (() (8 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 5) list:firstRest (8 (6 5))}] - [ a r:Fact; r:gives {(8 6 5) list:firstRest (8 (6 5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5695 a r:Inference; - r:gives { - (8 6 5) :sort (5 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 5) list:firstRest (8 (6 5))}] - skolem:lemma6401 - skolem:lemma4567 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((5 6) (8)) list:append (5 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5696 a r:Inference; - r:gives { - (2 (8 6 6)) :split (() (8 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 6) list:firstRest (8 (6 6))}] - [ a r:Fact; r:gives {(8 6 6) list:firstRest (8 (6 6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5697 a r:Inference; - r:gives { - (8 6 6) :sort (6 6 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 6) list:firstRest (8 (6 6))}] - skolem:lemma6402 - skolem:lemma4569 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((6 6) (8)) list:append (6 6 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5698 a r:Inference; - r:gives { - (2 (8 6 7)) :split (() (8 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 7) list:firstRest (8 (6 7))}] - [ a r:Fact; r:gives {(8 6 7) list:firstRest (8 (6 7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5699 a r:Inference; - r:gives { - (8 6 7) :sort (6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 7) list:firstRest (8 (6 7))}] - skolem:lemma6403 - skolem:lemma4575 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((6 7) (8)) list:append (6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5700 a r:Inference; - r:gives { - (2 (8 6 9)) :split (() (8 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 9) list:firstRest (8 (6 9))}] - [ a r:Fact; r:gives {(8 6 9) list:firstRest (8 (6 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5701 a r:Inference; - r:gives { - (8 6 9) :sort (6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6 9) list:firstRest (8 (6 9))}] - skolem:lemma6404 - skolem:lemma4458 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((6) (8 9)) list:append (6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5702 a r:Inference; - r:gives { - (2 (8 7 0)) :split ((0) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 0) list:firstRest (8 (7 0))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5703 a r:Inference; - r:gives { - (2 (8 7 1)) :split ((1) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 1) list:firstRest (8 (7 1))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5704 a r:Inference; - r:gives { - (2 (8 7 2)) :split ((2) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 2) list:firstRest (8 (7 2))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5705 a r:Inference; - r:gives { - (2 (8 7 3)) :split (() (8 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 3) list:firstRest (8 (7 3))}] - [ a r:Fact; r:gives {(8 7 3) list:firstRest (8 (7 3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5706 a r:Inference; - r:gives { - (8 7 3) :sort (3 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 3) list:firstRest (8 (7 3))}] - skolem:lemma6405 - skolem:lemma4592 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 7) (8)) list:append (3 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5707 a r:Inference; - r:gives { - (2 (8 7 4)) :split (() (8 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 4) list:firstRest (8 (7 4))}] - [ a r:Fact; r:gives {(8 7 4) list:firstRest (8 (7 4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5708 a r:Inference; - r:gives { - (8 7 4) :sort (4 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 4) list:firstRest (8 (7 4))}] - skolem:lemma6406 - skolem:lemma4594 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 7) (8)) list:append (4 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5709 a r:Inference; - r:gives { - (2 (8 7 6)) :split (() (8 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 6) list:firstRest (8 (7 6))}] - [ a r:Fact; r:gives {(8 7 6) list:firstRest (8 (7 6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5710 a r:Inference; - r:gives { - (8 7 6) :sort (6 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 6) list:firstRest (8 (7 6))}] - skolem:lemma6407 - skolem:lemma4598 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((6 7) (8)) list:append (6 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5711 a r:Inference; - r:gives { - (2 (8 7 7)) :split (() (8 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 7) list:firstRest (8 (7 7))}] - [ a r:Fact; r:gives {(8 7 7) list:firstRest (8 (7 7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5712 a r:Inference; - r:gives { - (8 7 7) :sort (7 7 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 7) list:firstRest (8 (7 7))}] - skolem:lemma6408 - skolem:lemma4600 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((7 7) (8)) list:append (7 7 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5713 a r:Inference; - r:gives { - (2 (8 7 8)) :split (() (8 7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 8) list:firstRest (8 (7 8))}] - [ a r:Fact; r:gives {(8 7 8) list:firstRest (8 (7 8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5714 a r:Inference; - r:gives { - (8 7 8) :sort (7 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 8) list:firstRest (8 (7 8))}] - skolem:lemma6409 - skolem:lemma4606 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((7 8) (8)) list:append (7 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5715 a r:Inference; - r:gives { - (2 (8 7 9)) :split (() (8 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 9) list:firstRest (8 (7 9))}] - [ a r:Fact; r:gives {(8 7 9) list:firstRest (8 (7 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5716 a r:Inference; - r:gives { - (8 7 9) :sort (7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7 9) list:firstRest (8 (7 9))}] - skolem:lemma6410 - skolem:lemma4422 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((7) (8 9)) list:append (7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5717 a r:Inference; - r:gives { - (2 (8 8 0)) :split ((0) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 0) list:firstRest (8 (8 0))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5718 a r:Inference; - r:gives { - (2 (8 8 1)) :split ((1) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 1) list:firstRest (8 (8 1))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5719 a r:Inference; - r:gives { - (2 (8 8 2)) :split ((2) (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 2) list:firstRest (8 (8 2))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5720 a r:Inference; - r:gives { - (2 (8 8 3)) :split (() (8 8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 3) list:firstRest (8 (8 3))}] - [ a r:Fact; r:gives {(8 8 3) list:firstRest (8 (8 3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5721 a r:Inference; - r:gives { - (8 8 3) :sort (3 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 3) list:firstRest (8 (8 3))}] - skolem:lemma6411 - skolem:lemma4619 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((3 8) (8)) list:append (3 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5722 a r:Inference; - r:gives { - (2 (8 8 4)) :split (() (8 8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 4) list:firstRest (8 (8 4))}] - [ a r:Fact; r:gives {(8 8 4) list:firstRest (8 (8 4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5723 a r:Inference; - r:gives { - (8 8 4) :sort (4 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 4) list:firstRest (8 (8 4))}] - skolem:lemma6412 - skolem:lemma4621 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((4 8) (8)) list:append (4 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5724 a r:Inference; - r:gives { - (2 (8 8 5)) :split (() (8 8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 5) list:firstRest (8 (8 5))}] - [ a r:Fact; r:gives {(8 8 5) list:firstRest (8 (8 5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5725 a r:Inference; - r:gives { - (8 8 5) :sort (5 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 5) list:firstRest (8 (8 5))}] - skolem:lemma6413 - skolem:lemma4623 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((5 8) (8)) list:append (5 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5726 a r:Inference; - r:gives { - (2 (8 8 7)) :split (() (8 8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 7) list:firstRest (8 (8 7))}] - [ a r:Fact; r:gives {(8 8 7) list:firstRest (8 (8 7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5727 a r:Inference; - r:gives { - (8 8 7) :sort (7 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 7) list:firstRest (8 (8 7))}] - skolem:lemma6414 - skolem:lemma4627 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((7 8) (8)) list:append (7 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5728 a r:Inference; - r:gives { - (2 (8 8 8)) :split (() (8 8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 8) list:firstRest (8 (8 8))}] - [ a r:Fact; r:gives {(8 8 8) list:firstRest (8 (8 8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5729 a r:Inference; - r:gives { - (8 8 8) :sort (8 8 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 8) list:firstRest (8 (8 8))}] - skolem:lemma6415 - skolem:lemma4629 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((8 8) (8)) list:append (8 8 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 8 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5730 a r:Inference; - r:gives { - (2 (8 8 9)) :split (() (8 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 9) list:firstRest (8 (8 9))}] - [ a r:Fact; r:gives {(8 8 9) list:firstRest (8 (8 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5731 a r:Inference; - r:gives { - (8 8 9) :sort (8 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8 9) list:firstRest (8 (8 9))}] - skolem:lemma6416 - skolem:lemma4426 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((8) (8 9)) list:append (8 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5732 a r:Inference; - r:gives { - (2 (8 9 0)) :split ((0) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 0) list:firstRest (8 (9 0))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5733 a r:Inference; - r:gives { - (2 (8 9 1)) :split ((1) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 1) list:firstRest (8 (9 1))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5734 a r:Inference; - r:gives { - (2 (8 9 2)) :split ((2) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 2) list:firstRest (8 (9 2))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5735 a r:Inference; - r:gives { - (2 (8 9 3)) :split (() (8 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 3) list:firstRest (8 (9 3))}] - [ a r:Fact; r:gives {(8 9 3) list:firstRest (8 (9 3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5736 a r:Inference; - r:gives { - (8 9 3) :sort (3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 3) list:firstRest (8 (9 3))}] - skolem:lemma6417 - skolem:lemma4408 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((3) (8 9)) list:append (3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5737 a r:Inference; - r:gives { - (2 (8 9 4)) :split (() (8 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 4) list:firstRest (8 (9 4))}] - [ a r:Fact; r:gives {(8 9 4) list:firstRest (8 (9 4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5738 a r:Inference; - r:gives { - (8 9 4) :sort (4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 4) list:firstRest (8 (9 4))}] - skolem:lemma6418 - skolem:lemma4414 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((4) (8 9)) list:append (4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5739 a r:Inference; - r:gives { - (2 (8 9 5)) :split (() (8 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 5) list:firstRest (8 (9 5))}] - [ a r:Fact; r:gives {(8 9 5) list:firstRest (8 (9 5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5740 a r:Inference; - r:gives { - (8 9 5) :sort (5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 5) list:firstRest (8 (9 5))}] - skolem:lemma6419 - skolem:lemma4416 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((5) (8 9)) list:append (5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5741 a r:Inference; - r:gives { - (2 (8 9 6)) :split (() (8 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 6) list:firstRest (8 (9 6))}] - [ a r:Fact; r:gives {(8 9 6) list:firstRest (8 (9 6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5742 a r:Inference; - r:gives { - (8 9 6) :sort (6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 6) list:firstRest (8 (9 6))}] - skolem:lemma6420 - skolem:lemma4458 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((6) (8 9)) list:append (6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5743 a r:Inference; - r:gives { - (2 (8 9 7)) :split (() (8 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 7) list:firstRest (8 (9 7))}] - [ a r:Fact; r:gives {(8 9 7) list:firstRest (8 (9 7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5744 a r:Inference; - r:gives { - (8 9 7) :sort (7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 7) list:firstRest (8 (9 7))}] - skolem:lemma6421 - skolem:lemma4422 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((7) (8 9)) list:append (7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5745 a r:Inference; - r:gives { - (2 (8 9 8)) :split (() (8 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 8) list:firstRest (8 (9 8))}] - [ a r:Fact; r:gives {(8 9 8) list:firstRest (8 (9 8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5746 a r:Inference; - r:gives { - (8 9 8) :sort (8 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 8) list:firstRest (8 (9 8))}] - skolem:lemma6422 - skolem:lemma4426 - skolem:lemma4430 - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {((8) (8 9)) list:append (8 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5747 a r:Inference; - r:gives { - (2 (8 9 9)) :split (() (8 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 9) list:firstRest (8 (9 9))}] - [ a r:Fact; r:gives {(8 9 9) list:firstRest (8 (9 9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5748 a r:Inference; - r:gives { - (8 9 9) :sort (8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9 9) list:firstRest (8 (9 9))}] - skolem:lemma6423 - skolem:lemma4395 - skolem:lemma4650 - [ a r:Fact; r:gives {(8 9 9) list:firstRest (8 (9 9))}] - [ a r:Fact; r:gives {(() (8 9 9)) list:append (8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5749 a r:Inference; - r:gives { - (2 (9 0 0)) :split ((0 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 0) list:firstRest (9 (0 0))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5898 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5750 a r:Inference; - r:gives { - (2 (9 0 1)) :split ((0 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 1) list:firstRest (9 (0 1))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5902 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5751 a r:Inference; - r:gives { - (2 (9 0 2)) :split ((0 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 2) list:firstRest (9 (0 2))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5904 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5752 a r:Inference; - r:gives { - (2 (9 0 3)) :split ((0) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 3) list:firstRest (9 (0 3))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5906 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5753 a r:Inference; - r:gives { - (2 (9 0 4)) :split ((0) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 4) list:firstRest (9 (0 4))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5910 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5754 a r:Inference; - r:gives { - (2 (9 0 5)) :split ((0) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 5) list:firstRest (9 (0 5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5912 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5755 a r:Inference; - r:gives { - (2 (9 0 6)) :split ((0) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 6) list:firstRest (9 (0 6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6117 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5756 a r:Inference; - r:gives { - (2 (9 0 7)) :split ((0) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 7) list:firstRest (9 (0 7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5916 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5757 a r:Inference; - r:gives { - (2 (9 0 8)) :split ((0) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 8) list:firstRest (9 (0 8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5920 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5758 a r:Inference; - r:gives { - (2 (9 0 9)) :split ((0) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0 9) list:firstRest (9 (0 9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5924 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5759 a r:Inference; - r:gives { - (2 (9 1 0)) :split ((1 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 0) list:firstRest (9 (1 0))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5928 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5760 a r:Inference; - r:gives { - (2 (9 1 1)) :split ((1 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 1) list:firstRest (9 (1 1))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5930 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5761 a r:Inference; - r:gives { - (2 (9 1 2)) :split ((1 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 2) list:firstRest (9 (1 2))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5932 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5762 a r:Inference; - r:gives { - (2 (9 1 3)) :split ((1) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 3) list:firstRest (9 (1 3))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5934 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5763 a r:Inference; - r:gives { - (2 (9 1 4)) :split ((1) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 4) list:firstRest (9 (1 4))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5937 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5764 a r:Inference; - r:gives { - (2 (9 1 5)) :split ((1) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 5) list:firstRest (9 (1 5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5939 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5765 a r:Inference; - r:gives { - (2 (9 1 6)) :split ((1) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 6) list:firstRest (9 (1 6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5942 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5766 a r:Inference; - r:gives { - (2 (9 1 7)) :split ((1) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 7) list:firstRest (9 (1 7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5946 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5767 a r:Inference; - r:gives { - (2 (9 1 8)) :split ((1) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 8) list:firstRest (9 (1 8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5949 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5768 a r:Inference; - r:gives { - (2 (9 1 9)) :split ((1) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1 9) list:firstRest (9 (1 9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5952 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5769 a r:Inference; - r:gives { - (2 (9 2 0)) :split ((2 0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 0) list:firstRest (9 (2 0))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5955 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 0)]; - 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 ()]; - 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 0)]; - r:rule skolem:lemma6150. - -skolem:lemma5770 a r:Inference; - r:gives { - (2 (9 2 1)) :split ((2 1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 1) list:firstRest (9 (2 1))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5957 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - 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 ()]; - 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 1)]; - r:rule skolem:lemma6150. - -skolem:lemma5771 a r:Inference; - r:gives { - (2 (9 2 2)) :split ((2 2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 2) list:firstRest (9 (2 2))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5959 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - 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 ()]; - 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 2)]; - r:rule skolem:lemma6150. - -skolem:lemma5772 a r:Inference; - r:gives { - (2 (9 2 3)) :split ((2) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 3) list:firstRest (9 (2 3))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5961 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5773 a r:Inference; - r:gives { - (2 (9 2 4)) :split ((2) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 4) list:firstRest (9 (2 4))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5963 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5774 a r:Inference; - r:gives { - (2 (9 2 5)) :split ((2) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 5) list:firstRest (9 (2 5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5965 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5775 a r:Inference; - r:gives { - (2 (9 2 6)) :split ((2) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 6) list:firstRest (9 (2 6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5967 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5776 a r:Inference; - r:gives { - (2 (9 2 7)) :split ((2) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 7) list:firstRest (9 (2 7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5969 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5777 a r:Inference; - r:gives { - (2 (9 2 8)) :split ((2) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 8) list:firstRest (9 (2 8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5971 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5778 a r:Inference; - r:gives { - (2 (9 2 9)) :split ((2) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2 9) list:firstRest (9 (2 9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5973 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5779 a r:Inference; - r:gives { - (2 (9 3 0)) :split ((0) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 0) list:firstRest (9 (3 0))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5975 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5780 a r:Inference; - r:gives { - (2 (9 3 1)) :split ((1) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 1) list:firstRest (9 (3 1))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5976 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5781 a r:Inference; - r:gives { - (2 (9 3 2)) :split ((2) (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 2) list:firstRest (9 (3 2))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5977 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5782 a r:Inference; - r:gives { - (2 (9 3 3)) :split (() (9 3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 3) list:firstRest (9 (3 3))}] - [ a r:Fact; r:gives {(9 3 3) list:firstRest (9 (3 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5978 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5783 a r:Inference; - r:gives { - (9 3 3) :sort (3 3 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 3) list:firstRest (9 (3 3))}] - skolem:lemma6424 - skolem:lemma4507 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 3) (9)) list:append (3 3 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 3 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5784 a r:Inference; - r:gives { - (2 (9 3 4)) :split (() (9 3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 4) list:firstRest (9 (3 4))}] - [ a r:Fact; r:gives {(9 3 4) list:firstRest (9 (3 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5981 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5785 a r:Inference; - r:gives { - (9 3 4) :sort (3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 4) list:firstRest (9 (3 4))}] - skolem:lemma6425 - skolem:lemma4509 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 4) (9)) list:append (3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5786 a r:Inference; - r:gives { - (2 (9 3 5)) :split (() (9 3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 5) list:firstRest (9 (3 5))}] - [ a r:Fact; r:gives {(9 3 5) list:firstRest (9 (3 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5983 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5787 a r:Inference; - r:gives { - (9 3 5) :sort (3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 5) list:firstRest (9 (3 5))}] - skolem:lemma6426 - skolem:lemma4511 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 5) (9)) list:append (3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5788 a r:Inference; - r:gives { - (2 (9 3 6)) :split (() (9 3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 6) list:firstRest (9 (3 6))}] - [ a r:Fact; r:gives {(9 3 6) list:firstRest (9 (3 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5985 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5789 a r:Inference; - r:gives { - (9 3 6) :sort (3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 6) list:firstRest (9 (3 6))}] - skolem:lemma6427 - skolem:lemma4513 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 6) (9)) list:append (3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5790 a r:Inference; - r:gives { - (2 (9 3 7)) :split (() (9 3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 7) list:firstRest (9 (3 7))}] - [ a r:Fact; r:gives {(9 3 7) list:firstRest (9 (3 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5987 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5791 a r:Inference; - r:gives { - (9 3 7) :sort (3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 7) list:firstRest (9 (3 7))}] - skolem:lemma6428 - skolem:lemma4515 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 7) (9)) list:append (3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5792 a r:Inference; - r:gives { - (2 (9 3 8)) :split (() (9 3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 8) list:firstRest (9 (3 8))}] - [ a r:Fact; r:gives {(9 3 8) list:firstRest (9 (3 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5989 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5793 a r:Inference; - r:gives { - (9 3 8) :sort (3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 8) list:firstRest (9 (3 8))}] - skolem:lemma6429 - skolem:lemma4517 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 8) (9)) list:append (3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5794 a r:Inference; - r:gives { - (2 (9 3 9)) :split (() (9 3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 9) list:firstRest (9 (3 9))}] - [ a r:Fact; r:gives {(9 3 9) list:firstRest (9 (3 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5991 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5795 a r:Inference; - r:gives { - (9 3 9) :sort (3 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3 9) list:firstRest (9 (3 9))}] - skolem:lemma6430 - skolem:lemma4519 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 9) (9)) list:append (3 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5796 a r:Inference; - r:gives { - (2 (9 4 0)) :split ((0) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 0) list:firstRest (9 (4 0))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5993 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5797 a r:Inference; - r:gives { - (2 (9 4 1)) :split ((1) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 1) list:firstRest (9 (4 1))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5994 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5798 a r:Inference; - r:gives { - (2 (9 4 2)) :split ((2) (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 2) list:firstRest (9 (4 2))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5995 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5799 a r:Inference; - r:gives { - (2 (9 4 3)) :split (() (9 4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 3) list:firstRest (9 (4 3))}] - [ a r:Fact; r:gives {(9 4 3) list:firstRest (9 (4 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5996 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5800 a r:Inference; - r:gives { - (9 4 3) :sort (3 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 3) list:firstRest (9 (4 3))}] - skolem:lemma6431 - skolem:lemma4524 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 4) (9)) list:append (3 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5801 a r:Inference; - r:gives { - (2 (9 4 4)) :split (() (9 4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 4) list:firstRest (9 (4 4))}] - [ a r:Fact; r:gives {(9 4 4) list:firstRest (9 (4 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma5998 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5802 a r:Inference; - r:gives { - (9 4 4) :sort (4 4 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 4) list:firstRest (9 (4 4))}] - skolem:lemma6432 - skolem:lemma4526 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 4) (9)) list:append (4 4 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 4 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5803 a r:Inference; - r:gives { - (2 (9 4 5)) :split (() (9 4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 5) list:firstRest (9 (4 5))}] - [ a r:Fact; r:gives {(9 4 5) list:firstRest (9 (4 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6000 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5804 a r:Inference; - r:gives { - (9 4 5) :sort (4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 5) list:firstRest (9 (4 5))}] - skolem:lemma6433 - skolem:lemma4528 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 5) (9)) list:append (4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5805 a r:Inference; - r:gives { - (2 (9 4 6)) :split (() (9 4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 6) list:firstRest (9 (4 6))}] - [ a r:Fact; r:gives {(9 4 6) list:firstRest (9 (4 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6129 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5806 a r:Inference; - r:gives { - (9 4 6) :sort (4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 6) list:firstRest (9 (4 6))}] - skolem:lemma6434 - skolem:lemma4719 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 6) (9)) list:append (4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5807 a r:Inference; - r:gives { - (2 (9 4 7)) :split (() (9 4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 7) list:firstRest (9 (4 7))}] - [ a r:Fact; r:gives {(9 4 7) list:firstRest (9 (4 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6002 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5808 a r:Inference; - r:gives { - (9 4 7) :sort (4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 7) list:firstRest (9 (4 7))}] - skolem:lemma6435 - skolem:lemma4530 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 7) (9)) list:append (4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5809 a r:Inference; - r:gives { - (2 (9 4 8)) :split (() (9 4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 8) list:firstRest (9 (4 8))}] - [ a r:Fact; r:gives {(9 4 8) list:firstRest (9 (4 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6004 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5810 a r:Inference; - r:gives { - (9 4 8) :sort (4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 8) list:firstRest (9 (4 8))}] - skolem:lemma6436 - skolem:lemma4532 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 8) (9)) list:append (4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5811 a r:Inference; - r:gives { - (2 (9 4 9)) :split (() (9 4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 9) list:firstRest (9 (4 9))}] - [ a r:Fact; r:gives {(9 4 9) list:firstRest (9 (4 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6006 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5812 a r:Inference; - r:gives { - (9 4 9) :sort (4 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4 9) list:firstRest (9 (4 9))}] - skolem:lemma6437 - skolem:lemma4534 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 9) (9)) list:append (4 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5813 a r:Inference; - r:gives { - (2 (9 5 0)) :split ((0) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 0) list:firstRest (9 (5 0))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6008 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5814 a r:Inference; - r:gives { - (2 (9 5 1)) :split ((1) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 1) list:firstRest (9 (5 1))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6009 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5815 a r:Inference; - r:gives { - (2 (9 5 2)) :split ((2) (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 2) list:firstRest (9 (5 2))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6010 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5816 a r:Inference; - r:gives { - (2 (9 5 3)) :split (() (9 5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 3) list:firstRest (9 (5 3))}] - [ a r:Fact; r:gives {(9 5 3) list:firstRest (9 (5 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6011 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5817 a r:Inference; - r:gives { - (9 5 3) :sort (3 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 3) list:firstRest (9 (5 3))}] - skolem:lemma6438 - skolem:lemma4539 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 5) (9)) list:append (3 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5818 a r:Inference; - r:gives { - (2 (9 5 4)) :split (() (9 5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 4) list:firstRest (9 (5 4))}] - [ a r:Fact; r:gives {(9 5 4) list:firstRest (9 (5 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6013 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5819 a r:Inference; - r:gives { - (9 5 4) :sort (4 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 4) list:firstRest (9 (5 4))}] - skolem:lemma6439 - skolem:lemma4541 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 5) (9)) list:append (4 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5820 a r:Inference; - r:gives { - (2 (9 5 5)) :split (() (9 5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 5) list:firstRest (9 (5 5))}] - [ a r:Fact; r:gives {(9 5 5) list:firstRest (9 (5 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6015 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5821 a r:Inference; - r:gives { - (9 5 5) :sort (5 5 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 5) list:firstRest (9 (5 5))}] - skolem:lemma6440 - skolem:lemma4543 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 5) (9)) list:append (5 5 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 5 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5822 a r:Inference; - r:gives { - (2 (9 5 6)) :split (() (9 5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 6) list:firstRest (9 (5 6))}] - [ a r:Fact; r:gives {(9 5 6) list:firstRest (9 (5 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6019 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5823 a r:Inference; - r:gives { - (9 5 6) :sort (5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 6) list:firstRest (9 (5 6))}] - skolem:lemma6441 - skolem:lemma4547 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 6) (9)) list:append (5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5824 a r:Inference; - r:gives { - (2 (9 5 7)) :split (() (9 5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 7) list:firstRest (9 (5 7))}] - [ a r:Fact; r:gives {(9 5 7) list:firstRest (9 (5 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6023 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5825 a r:Inference; - r:gives { - (9 5 7) :sort (5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 7) list:firstRest (9 (5 7))}] - skolem:lemma6442 - skolem:lemma4551 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 7) (9)) list:append (5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5826 a r:Inference; - r:gives { - (2 (9 5 8)) :split (() (9 5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 8) list:firstRest (9 (5 8))}] - [ a r:Fact; r:gives {(9 5 8) list:firstRest (9 (5 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6027 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5827 a r:Inference; - r:gives { - (9 5 8) :sort (5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 8) list:firstRest (9 (5 8))}] - skolem:lemma6443 - skolem:lemma4555 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 8) (9)) list:append (5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5828 a r:Inference; - r:gives { - (2 (9 5 9)) :split (() (9 5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 9) list:firstRest (9 (5 9))}] - [ a r:Fact; r:gives {(9 5 9) list:firstRest (9 (5 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6031 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5829 a r:Inference; - r:gives { - (9 5 9) :sort (5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5 9) list:firstRest (9 (5 9))}] - skolem:lemma6444 - skolem:lemma4559 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 9) (9)) list:append (5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5830 a r:Inference; - r:gives { - (2 (9 6 0)) :split ((0) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 0) list:firstRest (9 (6 0))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6132 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5831 a r:Inference; - r:gives { - (2 (9 6 1)) :split ((1) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 1) list:firstRest (9 (6 1))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6035 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5832 a r:Inference; - r:gives { - (2 (9 6 2)) :split ((2) (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 2) list:firstRest (9 (6 2))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6036 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5833 a r:Inference; - r:gives { - (2 (9 6 3)) :split (() (9 6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 3) list:firstRest (9 (6 3))}] - [ a r:Fact; r:gives {(9 6 3) list:firstRest (9 (6 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6037 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5834 a r:Inference; - r:gives { - (9 6 3) :sort (3 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 3) list:firstRest (9 (6 3))}] - skolem:lemma6445 - skolem:lemma4565 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 6) (9)) list:append (3 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5835 a r:Inference; - r:gives { - (2 (9 6 4)) :split (() (9 6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 4) list:firstRest (9 (6 4))}] - [ a r:Fact; r:gives {(9 6 4) list:firstRest (9 (6 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6133 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5836 a r:Inference; - r:gives { - (9 6 4) :sort (4 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 4) list:firstRest (9 (6 4))}] - skolem:lemma6446 - skolem:lemma4739 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 6) (9)) list:append (4 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5837 a r:Inference; - r:gives { - (2 (9 6 5)) :split (() (9 6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 5) list:firstRest (9 (6 5))}] - [ a r:Fact; r:gives {(9 6 5) list:firstRest (9 (6 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6039 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5838 a r:Inference; - r:gives { - (9 6 5) :sort (5 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 5) list:firstRest (9 (6 5))}] - skolem:lemma6447 - skolem:lemma4567 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 6) (9)) list:append (5 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5839 a r:Inference; - r:gives { - (2 (9 6 6)) :split (() (9 6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 6) list:firstRest (9 (6 6))}] - [ a r:Fact; r:gives {(9 6 6) list:firstRest (9 (6 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6041 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5840 a r:Inference; - r:gives { - (9 6 6) :sort (6 6 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 6) list:firstRest (9 (6 6))}] - skolem:lemma6448 - skolem:lemma4569 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 6) (9)) list:append (6 6 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 6 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5841 a r:Inference; - r:gives { - (2 (9 6 7)) :split (() (9 6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 7) list:firstRest (9 (6 7))}] - [ a r:Fact; r:gives {(9 6 7) list:firstRest (9 (6 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6044 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5842 a r:Inference; - r:gives { - (9 6 7) :sort (6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 7) list:firstRest (9 (6 7))}] - skolem:lemma6449 - skolem:lemma4575 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 7) (9)) list:append (6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5843 a r:Inference; - r:gives { - (2 (9 6 8)) :split (() (9 6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 8) list:firstRest (9 (6 8))}] - [ a r:Fact; r:gives {(9 6 8) list:firstRest (9 (6 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6047 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5844 a r:Inference; - r:gives { - (9 6 8) :sort (6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 8) list:firstRest (9 (6 8))}] - skolem:lemma6450 - skolem:lemma4581 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 8) (9)) list:append (6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5845 a r:Inference; - r:gives { - (2 (9 6 9)) :split (() (9 6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 9) list:firstRest (9 (6 9))}] - [ a r:Fact; r:gives {(9 6 9) list:firstRest (9 (6 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6049 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5846 a r:Inference; - r:gives { - (9 6 9) :sort (6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6 9) list:firstRest (9 (6 9))}] - skolem:lemma6451 - skolem:lemma4583 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 9) (9)) list:append (6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5847 a r:Inference; - r:gives { - (2 (9 7 0)) :split ((0) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 0) list:firstRest (9 (7 0))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6053 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5848 a r:Inference; - r:gives { - (2 (9 7 1)) :split ((1) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 1) list:firstRest (9 (7 1))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6054 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5849 a r:Inference; - r:gives { - (2 (9 7 2)) :split ((2) (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 2) list:firstRest (9 (7 2))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6055 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5850 a r:Inference; - r:gives { - (2 (9 7 3)) :split (() (9 7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 3) list:firstRest (9 (7 3))}] - [ a r:Fact; r:gives {(9 7 3) list:firstRest (9 (7 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6056 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5851 a r:Inference; - r:gives { - (9 7 3) :sort (3 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 3) list:firstRest (9 (7 3))}] - skolem:lemma6452 - skolem:lemma4592 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 7) (9)) list:append (3 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5852 a r:Inference; - r:gives { - (2 (9 7 4)) :split (() (9 7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 4) list:firstRest (9 (7 4))}] - [ a r:Fact; r:gives {(9 7 4) list:firstRest (9 (7 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6058 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5853 a r:Inference; - r:gives { - (9 7 4) :sort (4 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 4) list:firstRest (9 (7 4))}] - skolem:lemma6453 - skolem:lemma4594 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 7) (9)) list:append (4 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5854 a r:Inference; - r:gives { - (2 (9 7 5)) :split (() (9 7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 5) list:firstRest (9 (7 5))}] - [ a r:Fact; r:gives {(9 7 5) list:firstRest (9 (7 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6060 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5855 a r:Inference; - r:gives { - (9 7 5) :sort (5 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 5) list:firstRest (9 (7 5))}] - skolem:lemma6454 - skolem:lemma4596 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 7) (9)) list:append (5 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5856 a r:Inference; - r:gives { - (2 (9 7 6)) :split (() (9 7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 6) list:firstRest (9 (7 6))}] - [ a r:Fact; r:gives {(9 7 6) list:firstRest (9 (7 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6062 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5857 a r:Inference; - r:gives { - (9 7 6) :sort (6 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 6) list:firstRest (9 (7 6))}] - skolem:lemma6455 - skolem:lemma4598 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 7) (9)) list:append (6 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5858 a r:Inference; - r:gives { - (2 (9 7 7)) :split (() (9 7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 7) list:firstRest (9 (7 7))}] - [ a r:Fact; r:gives {(9 7 7) list:firstRest (9 (7 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6064 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5859 a r:Inference; - r:gives { - (9 7 7) :sort (7 7 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 7) list:firstRest (9 (7 7))}] - skolem:lemma6456 - skolem:lemma4600 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((7 7) (9)) list:append (7 7 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 7 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5860 a r:Inference; - r:gives { - (2 (9 7 8)) :split (() (9 7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 8) list:firstRest (9 (7 8))}] - [ a r:Fact; r:gives {(9 7 8) list:firstRest (9 (7 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6067 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5861 a r:Inference; - r:gives { - (9 7 8) :sort (7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 8) list:firstRest (9 (7 8))}] - skolem:lemma6457 - skolem:lemma4606 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((7 8) (9)) list:append (7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5862 a r:Inference; - r:gives { - (2 (9 7 9)) :split (() (9 7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 9) list:firstRest (9 (7 9))}] - [ a r:Fact; r:gives {(9 7 9) list:firstRest (9 (7 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6071 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5863 a r:Inference; - r:gives { - (9 7 9) :sort (7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7 9) list:firstRest (9 (7 9))}] - skolem:lemma6458 - skolem:lemma4610 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((7 9) (9)) list:append (7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5864 a r:Inference; - r:gives { - (2 (9 8 0)) :split ((0) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 0) list:firstRest (9 (8 0))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6075 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5865 a r:Inference; - r:gives { - (2 (9 8 1)) :split ((1) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 1) list:firstRest (9 (8 1))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6076 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5866 a r:Inference; - r:gives { - (2 (9 8 2)) :split ((2) (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 2) list:firstRest (9 (8 2))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6077 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5867 a r:Inference; - r:gives { - (2 (9 8 3)) :split (() (9 8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 3) list:firstRest (9 (8 3))}] - [ a r:Fact; r:gives {(9 8 3) list:firstRest (9 (8 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6078 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5868 a r:Inference; - r:gives { - (9 8 3) :sort (3 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 3) list:firstRest (9 (8 3))}] - skolem:lemma6459 - skolem:lemma4619 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 8) (9)) list:append (3 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5869 a r:Inference; - r:gives { - (2 (9 8 4)) :split (() (9 8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 4) list:firstRest (9 (8 4))}] - [ a r:Fact; r:gives {(9 8 4) list:firstRest (9 (8 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6080 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5870 a r:Inference; - r:gives { - (9 8 4) :sort (4 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 4) list:firstRest (9 (8 4))}] - skolem:lemma6460 - skolem:lemma4621 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 8) (9)) list:append (4 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5871 a r:Inference; - r:gives { - (2 (9 8 5)) :split (() (9 8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 5) list:firstRest (9 (8 5))}] - [ a r:Fact; r:gives {(9 8 5) list:firstRest (9 (8 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6082 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5872 a r:Inference; - r:gives { - (9 8 5) :sort (5 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 5) list:firstRest (9 (8 5))}] - skolem:lemma6461 - skolem:lemma4623 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 8) (9)) list:append (5 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5873 a r:Inference; - r:gives { - (2 (9 8 6)) :split (() (9 8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 6) list:firstRest (9 (8 6))}] - [ a r:Fact; r:gives {(9 8 6) list:firstRest (9 (8 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6084 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5874 a r:Inference; - r:gives { - (9 8 6) :sort (6 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 6) list:firstRest (9 (8 6))}] - skolem:lemma6462 - skolem:lemma4625 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 8) (9)) list:append (6 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5875 a r:Inference; - r:gives { - (2 (9 8 7)) :split (() (9 8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 7) list:firstRest (9 (8 7))}] - [ a r:Fact; r:gives {(9 8 7) list:firstRest (9 (8 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6086 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5876 a r:Inference; - r:gives { - (9 8 7) :sort (7 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 7) list:firstRest (9 (8 7))}] - skolem:lemma6463 - skolem:lemma4627 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((7 8) (9)) list:append (7 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5877 a r:Inference; - r:gives { - (2 (9 8 8)) :split (() (9 8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 8) list:firstRest (9 (8 8))}] - [ a r:Fact; r:gives {(9 8 8) list:firstRest (9 (8 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6088 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5878 a r:Inference; - r:gives { - (9 8 8) :sort (8 8 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 8) list:firstRest (9 (8 8))}] - skolem:lemma6464 - skolem:lemma4629 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((8 8) (9)) list:append (8 8 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 8 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5879 a r:Inference; - r:gives { - (2 (9 8 9)) :split (() (9 8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 9) list:firstRest (9 (8 9))}] - [ a r:Fact; r:gives {(9 8 9) list:firstRest (9 (8 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6090 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5880 a r:Inference; - r:gives { - (9 8 9) :sort (8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8 9) list:firstRest (9 (8 9))}] - skolem:lemma6465 - skolem:lemma4631 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((8 9) (9)) list:append (8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5881 a r:Inference; - r:gives { - (2 (9 9 0)) :split ((0) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 0) list:firstRest (9 (9 0))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6094 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (0)]; - r:rule skolem:lemma6150. - -skolem:lemma5882 a r:Inference; - r:gives { - (2 (9 9 1)) :split ((1) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 1) list:firstRest (9 (9 1))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6095 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5883 a r:Inference; - r:gives { - (2 (9 9 2)) :split ((2) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 2) list:firstRest (9 (9 2))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6096 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5884 a r:Inference; - r:gives { - (2 (9 9 3)) :split (() (9 9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 3) list:firstRest (9 (9 3))}] - [ a r:Fact; r:gives {(9 9 3) list:firstRest (9 (9 3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6097 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 3)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5885 a r:Inference; - r:gives { - (9 9 3) :sort (3 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 3) list:firstRest (9 (9 3))}] - skolem:lemma6466 - skolem:lemma4638 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((3 9) (9)) list:append (3 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (3 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5886 a r:Inference; - r:gives { - (2 (9 9 4)) :split (() (9 9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 4) list:firstRest (9 (9 4))}] - [ a r:Fact; r:gives {(9 9 4) list:firstRest (9 (9 4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6099 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 4)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5887 a r:Inference; - r:gives { - (9 9 4) :sort (4 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 4) list:firstRest (9 (9 4))}] - skolem:lemma6467 - skolem:lemma4640 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((4 9) (9)) list:append (4 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (4 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5888 a r:Inference; - r:gives { - (2 (9 9 5)) :split (() (9 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 5) list:firstRest (9 (9 5))}] - [ a r:Fact; r:gives {(9 9 5) list:firstRest (9 (9 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6101 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5889 a r:Inference; - r:gives { - (9 9 5) :sort (5 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 5) list:firstRest (9 (9 5))}] - skolem:lemma6468 - skolem:lemma4642 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((5 9) (9)) list:append (5 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (5 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5890 a r:Inference; - r:gives { - (2 (9 9 6)) :split (() (9 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 6) list:firstRest (9 (9 6))}] - [ a r:Fact; r:gives {(9 9 6) list:firstRest (9 (9 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6103 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5891 a r:Inference; - r:gives { - (9 9 6) :sort (6 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 6) list:firstRest (9 (9 6))}] - skolem:lemma6469 - skolem:lemma4644 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((6 9) (9)) list:append (6 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (6 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5892 a r:Inference; - r:gives { - (2 (9 9 7)) :split (() (9 9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 7) list:firstRest (9 (9 7))}] - [ a r:Fact; r:gives {(9 9 7) list:firstRest (9 (9 7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6105 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 7)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5893 a r:Inference; - r:gives { - (9 9 7) :sort (7 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 7) list:firstRest (9 (9 7))}] - skolem:lemma6470 - skolem:lemma4646 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((7 9) (9)) list:append (7 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (7 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5894 a r:Inference; - r:gives { - (2 (9 9 8)) :split (() (9 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 8) list:firstRest (9 (9 8))}] - [ a r:Fact; r:gives {(9 9 8) list:firstRest (9 (9 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6107 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5895 a r:Inference; - r:gives { - (9 9 8) :sort (8 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 8) list:firstRest (9 (9 8))}] - skolem:lemma6471 - skolem:lemma4648 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((8 9) (9)) list:append (8 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (8 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5896 a r:Inference; - r:gives { - (2 (9 9 9)) :split (() (9 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 9) list:firstRest (9 (9 9))}] - [ a r:Fact; r:gives {(9 9 9) list:firstRest (9 (9 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6109 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 9)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5897 a r:Inference; - r:gives { - (9 9 9) :sort (9 9 9). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 9) list:firstRest (9 (9 9))}] - skolem:lemma6472 - skolem:lemma4650 - skolem:lemma4395 - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {((9 9) (9)) list:append (9 9 9)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (9 9 9)]; - r:rule skolem:lemma4396. - -skolem:lemma5898 a r:Inference; - r:gives { - (2 (0 0)) :split ((0 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0)]; - 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_2"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5899 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_5 var:x_0) :split (var:x_3 var:x_6). - } <= { - var:x_0 list:firstRest (var:x_1 var:x_2). - var:x_3 list:firstRest (var:x_1 var:x_4). - var:x_1 math:notGreaterThan var:x_5. - (var:x_5 var:x_2) :split (var:x_4 var:x_6). - }. - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma5900 a r:Inference; - r:gives { - (0 (0 0)) :split ((0 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 0}] - skolem:lemma5907 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0)]; - 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_2"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5901 a r:Inference; - r:gives { - (1 (9 9 8)) :split (() (9 9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 8) list:firstRest (9 (9 8))}] - [ a r:Fact; r:gives {(9 9 8) list:firstRest (9 (9 8))}] - [ a r:Fact; r:gives {9 math:greaterThan 1}] - skolem:lemma6473 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 8)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5902 a r:Inference; - r:gives { - (2 (0 1)) :split ((0 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1)]; - 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5903 a r:Inference; - r:gives { - (0 (0 1)) :split ((0) (1)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 0}] - skolem:lemma5935 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma5904 a r:Inference; - r:gives { - (2 (0 2)) :split ((0 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5905 a r:Inference; - r:gives { - (0 (0 2)) :split ((0) (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 0}] - skolem:lemma5962 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 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_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 ()]; - 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:lemma5899. - -skolem:lemma5906 a r:Inference; - r:gives { - (2 (0 3)) :split ((0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3) list:firstRest (0 (3))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 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_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 ()]; - 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:lemma5899. - -skolem:lemma5907 a r:Inference; - r:gives { - (0 (0)) :split ((0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 0}] - skolem:lemma5979 - ); - 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5908 a r:Inference; - r:gives { - (3 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:rule skolem:lemma6475. - -skolem:lemma5909 a r:Inference; - r:gives { - (3 (1 7 7)) :split ((1) (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 7) list:firstRest (1 (7 7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 3}] - skolem:lemma6182 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma5910 a r:Inference; - r:gives { - (2 (0 4)) :split ((0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4) list:firstRest (0 (4))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma5911 a r:Inference; - r:gives { - (4 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:rule skolem:lemma6475. - -skolem:lemma5912 a r:Inference; - r:gives { - (2 (0 5)) :split ((0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5) list:firstRest (0 (5))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma5913 a r:Inference; - r:gives { - (5 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:rule skolem:lemma6475. - -skolem:lemma5914 a r:Inference; - r:gives { - (5 (1 7 5)) :split ((1 5) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 5) list:firstRest (1 (7 5))}] - [ a r:Fact; r:gives {(1 5) list:firstRest (1 (5))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 5}] - skolem:lemma6274 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:rule skolem:lemma5899. - -skolem:lemma5915 a r:Inference; - r:gives { - (1 5) :sort (1 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5) list:firstRest (1 (5))}] - skolem:lemma6478 - skolem:lemma4395 - skolem:lemma4416 - [ a r:Fact; r:gives {(1 5) list:firstRest (1 (5))}] - [ a r:Fact; r:gives {(() (1 5)) list:append (1 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5916 a r:Inference; - r:gives { - (2 (0 7)) :split ((0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 7) list:firstRest (0 (7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 7)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma5917 a r:Inference; - r:gives { - (7 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:rule skolem:lemma6475. - -skolem:lemma5918 a r:Inference; - r:gives { - (7 (1 7 3)) :split ((1 7 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 3) list:firstRest (1 (7 3))}] - [ a r:Fact; r:gives {(1 7 3) list:firstRest (1 (7 3))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 7}] - skolem:lemma6363 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5919 a r:Inference; - r:gives { - (1 7 3) :sort (1 3 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 3) list:firstRest (1 (7 3))}] - skolem:lemma6480 - skolem:lemma4395 - skolem:lemma4592 - [ a r:Fact; r:gives {(1 3 7) list:firstRest (1 (3 7))}] - [ a r:Fact; r:gives {(() (1 3 7)) list:append (1 3 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5920 a r:Inference; - r:gives { - (2 (0 8)) :split ((0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8) list:firstRest (0 (8))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma5921 a r:Inference; - r:gives { - (8 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:rule skolem:lemma6475. - -skolem:lemma5922 a r:Inference; - r:gives { - (8 (1 7 2)) :split ((1 7 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 2) list:firstRest (1 (7 2))}] - [ a r:Fact; r:gives {(1 7 2) list:firstRest (1 (7 2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 8}] - skolem:lemma6482 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5923 a r:Inference; - r:gives { - (1 7 2) :sort (1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 2) list:firstRest (1 (7 2))}] - skolem:lemma6483 - skolem:lemma4395 - skolem:lemma6484 - [ a r:Fact; r:gives {(1 2 7) list:firstRest (1 (2 7))}] - [ a r:Fact; r:gives {(() (1 2 7)) list:append (1 2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5924 a r:Inference; - r:gives { - (2 (0 9)) :split ((0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 9) list:firstRest (0 (9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 9)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma5925 a r:Inference; - r:gives { - (9 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:rule skolem:lemma6475. - -skolem:lemma5926 a r:Inference; - r:gives { - (9 (1 7 1)) :split ((1 7 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 1) list:firstRest (1 (7 1))}] - [ a r:Fact; r:gives {(1 7 1) list:firstRest (1 (7 1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 9}] - skolem:lemma6486 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (7 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5927 a r:Inference; - r:gives { - (1 7 1) :sort (1 1 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7 1) list:firstRest (1 (7 1))}] - skolem:lemma6487 - skolem:lemma4705 - skolem:lemma4422 - [ a r:Fact; r:gives {(1 7) list:firstRest (1 (7))}] - [ a r:Fact; r:gives {((1) (1 7)) list:append (1 1 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 1)]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 1 7)]; - r:rule skolem:lemma4396. - -skolem:lemma5928 a r:Inference; - r:gives { - (2 (1 0)) :split ((1 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5929 a r:Inference; - r:gives { - (0 (1 0)) :split ((0) (1)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:greaterThan 0}] - skolem:lemma5907 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma5930 a r:Inference; - r:gives { - (2 (1 1)) :split ((1 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5931 a r:Inference; - r:gives { - (0 (1 1)) :split (() (1 1)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:greaterThan 0}] - skolem:lemma5935 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5932 a r:Inference; - r:gives { - (2 (1 2)) :split ((1 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (1 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5933 a r:Inference; - r:gives { - (0 (1 2)) :split (() (1 2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {1 math:greaterThan 0}] - skolem:lemma5962 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (1 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5934 a r:Inference; - r:gives { - (2 (1 3)) :split ((1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 3) list:firstRest (1 (3))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5935 a r:Inference; - r:gives { - (0 (1)) :split (() (1)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:greaterThan 0}] - skolem:lemma5979 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5936 a r:Inference; - r:gives { - (3 (0 8 7)) :split ((0) (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 7) list:firstRest (0 (8 7))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 3}] - skolem:lemma6188 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 7)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma5937 a r:Inference; - r:gives { - (2 (1 4)) :split ((1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 4) list:firstRest (1 (4))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5938 a r:Inference; - r:gives { - (4 (0 8 6)) :split ((0) (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 6) list:firstRest (0 (8 6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 4}] - skolem:lemma6488 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 6)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma5939 a r:Inference; - r:gives { - (2 (1 5)) :split ((1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 5) list:firstRest (1 (5))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5940 a r:Inference; - r:gives { - (5 (0 8 5)) :split ((0 5) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 5) list:firstRest (0 (8 5))}] - [ a r:Fact; r:gives {(0 5) list:firstRest (0 (5))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 5}] - skolem:lemma6279 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 5)]; - 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_2"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma5941 a r:Inference; - r:gives { - (0 5) :sort (0 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 5) list:firstRest (0 (5))}] - skolem:lemma6489 - skolem:lemma4395 - skolem:lemma4416 - [ a r:Fact; r:gives {(0 5) list:firstRest (0 (5))}] - [ a r:Fact; r:gives {(() (0 5)) list:append (0 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 5)]; - 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 5)]; - r:rule skolem:lemma4396. - -skolem:lemma5942 a r:Inference; - r:gives { - (2 (1 6)) :split ((1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 6) list:firstRest (1 (6))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5943 a r:Inference; - r:gives { - (6 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:rule skolem:lemma6475. - -skolem:lemma5944 a r:Inference; - r:gives { - (6 (0 8 4)) :split ((0 4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 4) list:firstRest (0 (8 4))}] - [ a r:Fact; r:gives {(0 4) list:firstRest (0 (4))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 6}] - skolem:lemma6491 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 4)]; - 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_2"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma5945 a r:Inference; - r:gives { - (0 4) :sort (0 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 4) list:firstRest (0 (4))}] - skolem:lemma6492 - skolem:lemma4395 - skolem:lemma4414 - [ a r:Fact; r:gives {(0 4) list:firstRest (0 (4))}] - [ a r:Fact; r:gives {(() (0 4)) list:append (0 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 4)]; - 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_2"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 4)]; - r:rule skolem:lemma4396. - -skolem:lemma5946 a r:Inference; - r:gives { - (2 (1 7)) :split ((1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 7) list:firstRest (1 (7))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5947 a r:Inference; - r:gives { - (7 (0 8 3)) :split ((0 3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 3) list:firstRest (0 (8 3))}] - [ a r:Fact; r:gives {(0 3) list:firstRest (0 (3))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 7}] - skolem:lemma6370 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 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_2"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8)]; - r:rule skolem:lemma5899. - -skolem:lemma5948 a r:Inference; - r:gives { - (0 3) :sort (0 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 3) list:firstRest (0 (3))}] - skolem:lemma6493 - skolem:lemma4395 - skolem:lemma4408 - [ a r:Fact; r:gives {(0 3) list:firstRest (0 (3))}] - [ a r:Fact; r:gives {(() (0 3)) list:append (0 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 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_2"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 3)]; - r:rule skolem:lemma4396. - -skolem:lemma5949 a r:Inference; - r:gives { - (2 (1 8)) :split ((1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 8) list:firstRest (1 (8))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5950 a r:Inference; - r:gives { - (8 (0 8 2)) :split ((0 8 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 2) list:firstRest (0 (8 2))}] - [ a r:Fact; r:gives {(0 8 2) list:firstRest (0 (8 2))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 8}] - skolem:lemma6494 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 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_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5951 a r:Inference; - r:gives { - (0 8 2) :sort (0 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 2) list:firstRest (0 (8 2))}] - skolem:lemma6495 - skolem:lemma4395 - skolem:lemma6496 - [ a r:Fact; r:gives {(0 2 8) list:firstRest (0 (2 8))}] - [ a r:Fact; r:gives {(() (0 2 8)) list:append (0 2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 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_2"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 2 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5952 a r:Inference; - r:gives { - (2 (1 9)) :split ((1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 9) list:firstRest (1 (9))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma5953 a r:Inference; - r:gives { - (9 (0 8 1)) :split ((0 8 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 1) list:firstRest (0 (8 1))}] - [ a r:Fact; r:gives {(0 8 1) list:firstRest (0 (8 1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 9}] - skolem:lemma6497 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 1)]; - 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_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5954 a r:Inference; - r:gives { - (0 8 1) :sort (0 1 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 1) list:firstRest (0 (8 1))}] - skolem:lemma6498 - skolem:lemma4395 - skolem:lemma6499 - [ a r:Fact; r:gives {(0 1 8) list:firstRest (0 (1 8))}] - [ a r:Fact; r:gives {(() (0 1 8)) list:append (0 1 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 1)]; - 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_2"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (0 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (0 1 8)]; - r:rule skolem:lemma4396. - -skolem:lemma5955 a r:Inference; - r:gives { - (2 (2 0)) :split ((2 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5956 a r:Inference; - r:gives { - (0 (2 0)) :split ((0) (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:greaterThan 0}] - skolem:lemma5907 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (0)]; - 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 ()]; - 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:lemma6150. - -skolem:lemma5957 a r:Inference; - r:gives { - (2 (2 1)) :split ((2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5958 a r:Inference; - r:gives { - (0 (2 1)) :split (() (2 1)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:greaterThan 0}] - skolem:lemma5935 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5959 a r:Inference; - r:gives { - (2 (2 2)) :split ((2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma5960 a r:Inference; - r:gives { - (0 (2 2)) :split (() (2 2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:greaterThan 0}] - skolem:lemma5962 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5961 a r:Inference; - r:gives { - (2 (2 3)) :split ((2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (3)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5962 a r:Inference; - r:gives { - (0 (2)) :split (() (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:greaterThan 0}] - skolem:lemma5979 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5963 a r:Inference; - r:gives { - (2 (2 4)) :split ((2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 4) list:firstRest (2 (4))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (4)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5964 a r:Inference; - r:gives { - (3 (9 9 6)) :split (() (9 9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 6) list:firstRest (9 (9 6))}] - [ a r:Fact; r:gives {(9 9 6) list:firstRest (9 (9 6))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma6194 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 6)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5965 a r:Inference; - r:gives { - (2 (2 5)) :split ((2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (5)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5966 a r:Inference; - r:gives { - (4 (9 9 5)) :split (() (9 9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 5) list:firstRest (9 (9 5))}] - [ a r:Fact; r:gives {(9 9 5) list:firstRest (9 (9 5))}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma6240 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 5)]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5967 a r:Inference; - r:gives { - (2 (2 6)) :split ((2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (6)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5968 a r:Inference; - r:gives { - (5 (9 9 4)) :split ((4) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 4) list:firstRest (9 (9 4))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6284 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4)]; - r:rule skolem:lemma6150. - -skolem:lemma5969 a r:Inference; - r:gives { - (2 (2 7)) :split ((2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 7) list:firstRest (2 (7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (7)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5970 a r:Inference; - r:gives { - (6 (9 9 3)) :split ((3) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 3) list:firstRest (9 (9 3))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6329 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:rule skolem:lemma6150. - -skolem:lemma5971 a r:Inference; - r:gives { - (2 (2 8)) :split ((2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 8) list:firstRest (2 (8))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (8)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5972 a r:Inference; - r:gives { - (7 (9 9 2)) :split ((2) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 2) list:firstRest (9 (9 2))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6500 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2)]; - r:rule skolem:lemma6150. - -skolem:lemma5973 a r:Inference; - r:gives { - (2 (2 9)) :split ((2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 9) list:firstRest (2 (9))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (9)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma5974 a r:Inference; - r:gives { - (8 (9 9 1)) :split ((1) (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 1) list:firstRest (9 (9 1))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6501 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1)]; - r:rule skolem:lemma6150. - -skolem:lemma5975 a r:Inference; - r:gives { - (2 (3 0)) :split ((0) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 0) list:firstRest (3 (0))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma5976 a r:Inference; - r:gives { - (2 (3 1)) :split ((1) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1) list:firstRest (3 (1))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma5977 a r:Inference; - r:gives { - (2 (3 2)) :split ((2) (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 2) list:firstRest (3 (2))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (2)]; - 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 ()]; - 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:lemma6150. - -skolem:lemma5978 a r:Inference; - r:gives { - (2 (3 3)) :split (() (3 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5979 a r:Inference; - r:gives { - (0 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:rule skolem:lemma6475. - -skolem:lemma5980 a r:Inference; - r:gives { - (3 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5908 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5981 a r:Inference; - r:gives { - (2 (3 4)) :split (() (3 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5982 a r:Inference; - r:gives { - (3 (4)) :split (() (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5908 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5983 a r:Inference; - r:gives { - (2 (3 5)) :split (() (3 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5984 a r:Inference; - r:gives { - (3 (5)) :split (() (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5908 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5985 a r:Inference; - r:gives { - (2 (3 6)) :split (() (3 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5986 a r:Inference; - r:gives { - (3 (6)) :split (() (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5908 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5987 a r:Inference; - r:gives { - (2 (3 7)) :split (() (3 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5988 a r:Inference; - r:gives { - (3 (7)) :split (() (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5908 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5989 a r:Inference; - r:gives { - (2 (3 8)) :split (() (3 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5990 a r:Inference; - r:gives { - (3 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5908 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5991 a r:Inference; - r:gives { - (2 (3 9)) :split (() (3 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5992 a r:Inference; - r:gives { - (3 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5908 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma5993 a r:Inference; - r:gives { - (2 (4 0)) :split ((0) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 0) list:firstRest (4 (0))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma5994 a r:Inference; - r:gives { - (2 (4 1)) :split ((1) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1) list:firstRest (4 (1))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma5995 a r:Inference; - r:gives { - (2 (4 2)) :split ((2) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2) list:firstRest (4 (2))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma5996 a r:Inference; - r:gives { - (2 (4 3)) :split (() (4 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5997 a r:Inference; - r:gives { - (4 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma5911 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma5998 a r:Inference; - r:gives { - (2 (4 4)) :split (() (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma5999 a r:Inference; - r:gives { - (4 (4)) :split ((4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma5911 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6000 a r:Inference; - r:gives { - (2 (4 5)) :split (() (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6001 a r:Inference; - r:gives { - (4 (5)) :split (() (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma5911 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6002 a r:Inference; - r:gives { - (2 (4 7)) :split (() (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6003 a r:Inference; - r:gives { - (4 (7)) :split (() (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma5911 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6004 a r:Inference; - r:gives { - (2 (4 8)) :split (() (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6005 a r:Inference; - r:gives { - (4 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma5911 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6006 a r:Inference; - r:gives { - (2 (4 9)) :split (() (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6007 a r:Inference; - r:gives { - (4 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma5911 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6008 a r:Inference; - r:gives { - (2 (5 0)) :split ((0) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 0) list:firstRest (5 (0))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6009 a r:Inference; - r:gives { - (2 (5 1)) :split ((1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1) list:firstRest (5 (1))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6010 a r:Inference; - r:gives { - (2 (5 2)) :split ((2) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 2) list:firstRest (5 (2))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6011 a r:Inference; - r:gives { - (2 (5 3)) :split (() (5 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6012 a r:Inference; - r:gives { - (5 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma5913 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6013 a r:Inference; - r:gives { - (2 (5 4)) :split (() (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6014 a r:Inference; - r:gives { - (5 (4)) :split ((4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma5913 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6015 a r:Inference; - r:gives { - (2 (5 5)) :split (() (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6016 a r:Inference; - r:gives { - (5 (5)) :split ((5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma5913 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6017 a r:Inference; - r:gives { - (5 (2 6 5)) :split ((2 5) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 5) list:firstRest (2 (6 5))}] - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 5}] - skolem:lemma6267 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:rule skolem:lemma5899. - -skolem:lemma6018 a r:Inference; - r:gives { - (2 5) :sort (2 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - skolem:lemma6477 - skolem:lemma4395 - skolem:lemma4416 - [ a r:Fact; r:gives {(2 5) list:firstRest (2 (5))}] - [ a r:Fact; r:gives {(() (2 5)) list:append (2 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 5)]; - r:rule skolem:lemma4396. - -skolem:lemma6019 a r:Inference; - r:gives { - (2 (5 6)) :split (() (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6020 a r:Inference; - r:gives { - (5 (6)) :split (() (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma5913 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6021 a r:Inference; - r:gives { - (6 (2 6 4)) :split ((2 6 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4) list:firstRest (2 (6 4))}] - [ a r:Fact; r:gives {(2 6 4) list:firstRest (2 (6 4))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 6}] - skolem:lemma6311 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6022 a r:Inference; - r:gives { - (2 6 4) :sort (2 4 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 4) list:firstRest (2 (6 4))}] - skolem:lemma6133 - skolem:lemma4395 - skolem:lemma4739 - [ a r:Fact; r:gives {(2 4 6) list:firstRest (2 (4 6))}] - [ a r:Fact; r:gives {(() (2 4 6)) list:append (2 4 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6023 a r:Inference; - r:gives { - (2 (5 7)) :split (() (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6024 a r:Inference; - r:gives { - (5 (7)) :split (() (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma5913 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6025 a r:Inference; - r:gives { - (7 (2 6 3)) :split ((2 6 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3) list:firstRest (2 (6 3))}] - [ a r:Fact; r:gives {(2 6 3) list:firstRest (2 (6 3))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 7}] - skolem:lemma6356 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6026 a r:Inference; - r:gives { - (2 6 3) :sort (2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 3) list:firstRest (2 (6 3))}] - skolem:lemma6037 - skolem:lemma4395 - skolem:lemma4565 - [ a r:Fact; r:gives {(2 3 6) list:firstRest (2 (3 6))}] - [ a r:Fact; r:gives {(() (2 3 6)) list:append (2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6027 a r:Inference; - r:gives { - (2 (5 8)) :split (() (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6028 a r:Inference; - r:gives { - (5 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 5}] - skolem:lemma5913 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6029 a r:Inference; - r:gives { - (8 (2 6 2)) :split ((2 6 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2) list:firstRest (2 (6 2))}] - [ a r:Fact; r:gives {(2 6 2) list:firstRest (2 (6 2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 8}] - skolem:lemma6502 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6030 a r:Inference; - r:gives { - (2 6 2) :sort (2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 2) list:firstRest (2 (6 2))}] - skolem:lemma6036 - skolem:lemma4833 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((2) (2 6)) list:append (2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 2)]; - 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 (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6031 a r:Inference; - r:gives { - (2 (5 9)) :split (() (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6032 a r:Inference; - r:gives { - (5 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma5913 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6033 a r:Inference; - r:gives { - (9 (2 6 1)) :split ((2 6 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1) list:firstRest (2 (6 1))}] - [ a r:Fact; r:gives {(2 6 1) list:firstRest (2 (6 1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 9}] - skolem:lemma6503 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (6 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6034 a r:Inference; - r:gives { - (2 6 1) :sort (1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 1) list:firstRest (2 (6 1))}] - skolem:lemma6035 - skolem:lemma4705 - skolem:lemma4458 - [ a r:Fact; r:gives {(2 6) list:firstRest (2 (6))}] - [ a r:Fact; r:gives {((1) (2 6)) list:append (1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 1)]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6035 a r:Inference; - r:gives { - (2 (6 1)) :split ((1) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1) list:firstRest (6 (1))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6036 a r:Inference; - r:gives { - (2 (6 2)) :split ((2) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2) list:firstRest (6 (2))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6037 a r:Inference; - r:gives { - (2 (6 3)) :split (() (6 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6038 a r:Inference; - r:gives { - (6 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma5943 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6039 a r:Inference; - r:gives { - (2 (6 5)) :split (() (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6040 a r:Inference; - r:gives { - (6 (5)) :split ((5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma5943 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6041 a r:Inference; - r:gives { - (2 (6 6)) :split (() (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6042 a r:Inference; - r:gives { - (6 (6)) :split ((6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma5943 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6043 a r:Inference; - r:gives { - (6 (3 5 4)) :split ((3 5 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 4) list:firstRest (3 (5 4))}] - [ a r:Fact; r:gives {(3 5 4) list:firstRest (3 (5 4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6304 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 4)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6044 a r:Inference; - r:gives { - (2 (6 7)) :split (() (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6045 a r:Inference; - r:gives { - (6 (7)) :split (() (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma5943 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6046 a r:Inference; - r:gives { - (7 (3 5 3)) :split ((3 5 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 3) list:firstRest (3 (5 3))}] - [ a r:Fact; r:gives {(3 5 3) list:firstRest (3 (5 3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6350 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 3)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6047 a r:Inference; - r:gives { - (2 (6 8)) :split (() (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6048 a r:Inference; - r:gives { - (6 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma5943 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6049 a r:Inference; - r:gives { - (2 (6 9)) :split (() (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6050 a r:Inference; - r:gives { - (6 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma5943 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6051 a r:Inference; - r:gives { - (9 (3 5 1)) :split ((3 5 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 1) list:firstRest (3 (5 1))}] - [ a r:Fact; r:gives {(3 5 1) list:firstRest (3 (5 1))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6504 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6052 a r:Inference; - r:gives { - (3 5 1) :sort (1 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 1) list:firstRest (3 (5 1))}] - skolem:lemma6505 - skolem:lemma4705 - skolem:lemma4416 - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {((1) (3 5)) list:append (1 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 1)]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma6053 a r:Inference; - r:gives { - (2 (7 0)) :split ((0) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 0) list:firstRest (7 (0))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6054 a r:Inference; - r:gives { - (2 (7 1)) :split ((1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1) list:firstRest (7 (1))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6055 a r:Inference; - r:gives { - (2 (7 2)) :split ((2) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2) list:firstRest (7 (2))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6056 a r:Inference; - r:gives { - (2 (7 3)) :split (() (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6057 a r:Inference; - r:gives { - (7 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma5917 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6058 a r:Inference; - r:gives { - (2 (7 4)) :split (() (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6059 a r:Inference; - r:gives { - (7 (4)) :split ((4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma5917 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6060 a r:Inference; - r:gives { - (2 (7 5)) :split (() (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6061 a r:Inference; - r:gives { - (7 (5)) :split ((5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma5917 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6062 a r:Inference; - r:gives { - (2 (7 6)) :split (() (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6063 a r:Inference; - r:gives { - (7 (6)) :split ((6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma5917 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6064 a r:Inference; - r:gives { - (2 (7 7)) :split (() (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6065 a r:Inference; - r:gives { - (7 (7)) :split ((7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma5917 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6066 a r:Inference; - r:gives { - (7 (4 4 3)) :split ((4 4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 3) list:firstRest (4 (4 3))}] - [ a r:Fact; r:gives {(4 4 3) list:firstRest (4 (4 3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6343 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 3)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6067 a r:Inference; - r:gives { - (2 (7 8)) :split (() (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6068 a r:Inference; - r:gives { - (7 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma5917 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6069 a r:Inference; - r:gives { - (8 (4 4 2)) :split ((4 4 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 2) list:firstRest (4 (4 2))}] - [ a r:Fact; r:gives {(4 4 2) list:firstRest (4 (4 2))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6506 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6070 a r:Inference; - r:gives { - (4 4 2) :sort (2 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 2) list:firstRest (4 (4 2))}] - skolem:lemma6507 - skolem:lemma6508 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((2 4) (4)) list:append (2 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma6071 a r:Inference; - r:gives { - (2 (7 9)) :split (() (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6072 a r:Inference; - r:gives { - (7 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma5917 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6073 a r:Inference; - r:gives { - (9 (4 4 1)) :split ((4 4 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 1) list:firstRest (4 (4 1))}] - [ a r:Fact; r:gives {(4 4 1) list:firstRest (4 (4 1))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6509 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6074 a r:Inference; - r:gives { - (4 4 1) :sort (1 4 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 1) list:firstRest (4 (4 1))}] - skolem:lemma6510 - skolem:lemma6511 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((1 4) (4)) list:append (1 4 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 4 4)]; - r:rule skolem:lemma4396. - -skolem:lemma6075 a r:Inference; - r:gives { - (2 (8 0)) :split ((0) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 0) list:firstRest (8 (0))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6076 a r:Inference; - r:gives { - (2 (8 1)) :split ((1) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1) list:firstRest (8 (1))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6077 a r:Inference; - r:gives { - (2 (8 2)) :split ((2) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2) list:firstRest (8 (2))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6078 a r:Inference; - r:gives { - (2 (8 3)) :split (() (8 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6079 a r:Inference; - r:gives { - (8 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6080 a r:Inference; - r:gives { - (2 (8 4)) :split (() (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6081 a r:Inference; - r:gives { - (8 (4)) :split ((4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6082 a r:Inference; - r:gives { - (2 (8 5)) :split (() (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6083 a r:Inference; - r:gives { - (8 (5)) :split ((5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6084 a r:Inference; - r:gives { - (2 (8 6)) :split (() (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6085 a r:Inference; - r:gives { - (8 (6)) :split ((6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6086 a r:Inference; - r:gives { - (2 (8 7)) :split (() (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6087 a r:Inference; - r:gives { - (8 (7)) :split ((7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6088 a r:Inference; - r:gives { - (2 (8 8)) :split (() (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6089 a r:Inference; - r:gives { - (8 (8)) :split ((8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6090 a r:Inference; - r:gives { - (2 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6091 a r:Inference; - r:gives { - (8 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma5921 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6092 a r:Inference; - r:gives { - (9 (5 3 1)) :split ((5 3 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 1) list:firstRest (5 (3 1))}] - [ a r:Fact; r:gives {(5 3 1) list:firstRest (5 (3 1))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6512 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6093 a r:Inference; - r:gives { - (5 3 1) :sort (1 3 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 1) list:firstRest (5 (3 1))}] - skolem:lemma6513 - skolem:lemma6514 - skolem:lemma4395 - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {((1 3) (5)) list:append (1 3 5)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 3 5)]; - r:rule skolem:lemma4396. - -skolem:lemma6094 a r:Inference; - r:gives { - (2 (9 0)) :split ((0) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 0) list:firstRest (9 (0))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6095 a r:Inference; - r:gives { - (2 (9 1)) :split ((1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1) list:firstRest (9 (1))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6141 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6096 a r:Inference; - r:gives { - (2 (9 2)) :split ((2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2) list:firstRest (9 (2))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6142 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6097 a r:Inference; - r:gives { - (2 (9 3)) :split (() (9 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6474 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6098 a r:Inference; - r:gives { - (9 (3)) :split ((3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6099 a r:Inference; - r:gives { - (2 (9 4)) :split (() (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6100 a r:Inference; - r:gives { - (9 (4)) :split ((4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6101 a r:Inference; - r:gives { - (2 (9 5)) :split (() (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6477 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6102 a r:Inference; - r:gives { - (9 (5)) :split ((5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6103 a r:Inference; - r:gives { - (2 (9 6)) :split (() (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6104 a r:Inference; - r:gives { - (9 (6)) :split ((6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6105 a r:Inference; - r:gives { - (2 (9 7)) :split (() (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6479 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6106 a r:Inference; - r:gives { - (9 (7)) :split ((7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6107 a r:Inference; - r:gives { - (2 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6481 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6108 a r:Inference; - r:gives { - (9 (8)) :split ((8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6109 a r:Inference; - r:gives { - (2 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6485 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6110 a r:Inference; - r:gives { - (9 (9)) :split ((9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6111 a r:Inference; - r:gives { - (9 (6 2 1)) :split ((6 2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 1) list:firstRest (6 (2 1))}] - [ a r:Fact; r:gives {(6 2 1) list:firstRest (6 (2 1))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6515 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 1)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6112 a r:Inference; - r:gives { - (6 2 1) :sort (1 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 1) list:firstRest (6 (2 1))}] - skolem:lemma6516 - skolem:lemma4807 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((1 2) (6)) list:append (1 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6113 a r:Inference; - r:gives { - (1 (0 0)) :split ((0 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {(0 0) list:firstRest (0 (0))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 1}] - skolem:lemma6116 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 0)]; - 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_2"]; r:boundTo (0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6114 a r:Inference; - r:gives { - (1 (0 1)) :split ((0 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {(0 1) list:firstRest (0 (1))}] - [ a r:Fact; r:gives {0 math:notGreaterThan 1}] - skolem:lemma6123 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 1)]; - 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (0 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6115 a r:Inference; - r:gives { - (1 (0 2)) :split ((0) (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 2) list:firstRest (0 (2))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 1}] - skolem:lemma6127 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 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_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 ()]; - 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:lemma5899. - -skolem:lemma6116 a r:Inference; - r:gives { - (1 (0)) :split ((0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 1}] - skolem:lemma6128 - ); - 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6117 a r:Inference; - r:gives { - (2 (0 6)) :split ((0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 6) list:firstRest (0 (6))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 6)]; - 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_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 ()]; - 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:lemma5899. - -skolem:lemma6118 a r:Inference; - r:gives { - (1 (1 0)) :split ((1 0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {(1 0) list:firstRest (1 (0))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 1}] - skolem:lemma6116 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6119 a r:Inference; - r:gives { - (1 (1 1)) :split ((1 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {(1 1) list:firstRest (1 (1))}] - [ a r:Fact; r:gives {1 math:notGreaterThan 1}] - skolem:lemma6123 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - 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 (1 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6120 a r:Inference; - r:gives { - (0 (9 9 9)) :split (() (9 9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9 9) list:firstRest (9 (9 9))}] - [ a r:Fact; r:gives {(9 9 9) list:firstRest (9 (9 9))}] - [ a r:Fact; r:gives {9 math:greaterThan 0}] - skolem:lemma6517 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (9 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6121 a r:Inference; - r:gives { - (1 (1 2)) :split ((1) (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(1 2) list:firstRest (1 (2))}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 1}] - skolem:lemma6127 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6122 a r:Inference; - r:gives { - (1 (0 8 9)) :split ((0) (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(0 8 9) list:firstRest (0 (8 9))}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 1}] - skolem:lemma6518 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (0 8 9)]; - 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_2"]; r:boundTo (8 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 ()]; - 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 9)]; - r:rule skolem:lemma5899. - -skolem:lemma6123 a r:Inference; - r:gives { - (1 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 1}] - skolem:lemma6128 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6124 a r:Inference; - r:gives { - (1 (2 0)) :split ((0) (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 0) list:firstRest (2 (0))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:greaterThan 1}] - skolem:lemma6116 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (0)]; - 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 ()]; - 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:lemma6150. - -skolem:lemma6125 a r:Inference; - r:gives { - (1 (2 1)) :split ((1) (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:greaterThan 1}] - skolem:lemma6123 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (1)]; - 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 ()]; - 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:lemma6150. - -skolem:lemma6126 a r:Inference; - r:gives { - (1 (2 2)) :split (() (2 2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:greaterThan 1}] - skolem:lemma6127 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6127 a r:Inference; - r:gives { - (1 (2)) :split (() (2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:greaterThan 1}] - skolem:lemma6128 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6128 a r:Inference; - r:gives { - (1 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:rule skolem:lemma6475. - -skolem:lemma6129 a r:Inference; - r:gives { - (2 (4 6)) :split (() (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6490 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6130 a r:Inference; - r:gives { - (4 (6)) :split (() (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma5911 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6131 a r:Inference; - r:gives { - (4 (2 6 6)) :split ((2) (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 6) list:firstRest (2 (6 6))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 4}] - skolem:lemma6222 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma6132 a r:Inference; - r:gives { - (2 (6 0)) :split ((0) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 0) list:firstRest (6 (0))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6140 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6133 a r:Inference; - r:gives { - (2 (6 4)) :split (() (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6476 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6134 a r:Inference; - r:gives { - (6 (4)) :split ((4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma5943 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6135 a r:Inference; - r:gives { - (5 (3 5 5)) :split ((3 5 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 5) list:firstRest (3 (5 5))}] - [ a r:Fact; r:gives {(3 5 5) list:firstRest (3 (5 5))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6260 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 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_2"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (5 5)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6136 a r:Inference; - r:gives { - (6 (4 4 4)) :split ((4 4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 4) list:firstRest (4 (4 4))}] - [ a r:Fact; r:gives {(4 4 4) list:firstRest (4 (4 4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6298 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 4)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6137 a r:Inference; - r:gives { - (7 (5 3 3)) :split ((5 3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 3) list:firstRest (5 (3 3))}] - [ a r:Fact; r:gives {(5 3 3) list:firstRest (5 (3 3))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6336 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 3)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6138 a r:Inference; - r:gives { - (8 (6 2 2)) :split ((6 2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 2) list:firstRest (6 (2 2))}] - [ a r:Fact; r:gives {(6 2 2) list:firstRest (6 (2 2))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6519 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 2)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6139 a r:Inference; - r:gives { - (6 2 2) :sort (2 2 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 2) list:firstRest (6 (2 2))}] - skolem:lemma6520 - skolem:lemma4822 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((2 2) (6)) list:append (2 2 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 2 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6140 a r:Inference; - r:gives { - (2 (0)) :split ((0) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {(0) list:firstRest (0 ())}] - [ a r:Fact; r:gives {0 math:notGreaterThan 2}] - skolem:lemma6143 - ); - 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 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6141 a r:Inference; - r:gives { - (2 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 2}] - skolem:lemma6143 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6142 a r:Inference; - r:gives { - (2 (2)) :split ((2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 2}] - skolem:lemma6143 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6143 a r:Inference; - r:gives { - (2 ()) :split (() ()). - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:rule skolem:lemma6475. - -skolem:lemma6144 a r:Inference; - r:gives { - (3 (2 6 7)) :split ((2) (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 6 7) list:firstRest (2 (6 7))}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 3}] - skolem:lemma6175 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 6 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_2"]; r:boundTo (6 7)]; - 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 ()]; - 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 7)]; - r:rule skolem:lemma5899. - -skolem:lemma6145 a r:Inference; - r:gives { - (4 (3 5 6)) :split ((3) (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5 6) list:firstRest (3 (5 6))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma6215 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 6)]; - 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 ()]; - 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 6)]; - r:rule skolem:lemma5899. - -skolem:lemma6146 a r:Inference; - r:gives { - (5 (4 4 5)) :split ((4 4 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4 5) list:firstRest (4 (4 5))}] - [ a r:Fact; r:gives {(4 4 5) list:firstRest (4 (4 5))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6253 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (4 5)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6147 a r:Inference; - r:gives { - (6 (5 3 4)) :split ((5 3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3 4) list:firstRest (5 (3 4))}] - [ a r:Fact; r:gives {(5 3 4) list:firstRest (5 (3 4))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6291 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (3 4)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6148 a r:Inference; - r:gives { - (7 (6 2 3)) :split ((6 2 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 3) list:firstRest (6 (2 3))}] - [ a r:Fact; r:gives {(6 2 3) list:firstRest (6 (2 3))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6521 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo (2 3)]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6149 a r:Inference; - r:gives { - (6 2 3) :sort (2 3 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2 3) list:firstRest (6 (2 3))}] - skolem:lemma6522 - skolem:lemma6523 - skolem:lemma4395 - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {((2 3) (6)) list:append (2 3 6)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3 6)]; - r:rule skolem:lemma4396. - -skolem:lemma6150 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_5 var:x_0) :split (var:x_6 var:x_3). - } <= { - var:x_0 list:firstRest (var:x_1 var:x_2). - var:x_3 list:firstRest (var:x_1 var:x_4). - var:x_1 math:greaterThan var:x_5. - (var:x_5 var:x_2) :split (var:x_6 var:x_4). - }. - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma6151 a r:Inference; - r:gives { - (3 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6152 a r:Inference; - r:gives { - (3 (3 4)) :split ((3) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6153 a r:Inference; - r:gives { - (3 (3 5)) :split ((3) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5984 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma6154 a r:Inference; - r:gives { - (3 (3 6)) :split ((3) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6155 a r:Inference; - r:gives { - (3 (3 7)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6156 a r:Inference; - r:gives { - (3 (3 8)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5990 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6157 a r:Inference; - r:gives { - (3 (3 9)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6158 a r:Inference; - r:gives { - (3 (4 3)) :split ((3) (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6159 a r:Inference; - r:gives { - (3 (4 4)) :split (() (4 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6160 a r:Inference; - r:gives { - (3 (4 5)) :split (() (4 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5984 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6161 a r:Inference; - r:gives { - (3 (4 6)) :split (() (4 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6162 a r:Inference; - r:gives { - (3 (4 7)) :split (() (4 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6163 a r:Inference; - r:gives { - (3 (4 8)) :split (() (4 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5990 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6164 a r:Inference; - r:gives { - (3 (4 9)) :split (() (4 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:greaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6165 a r:Inference; - r:gives { - (3 (5 3)) :split ((3) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6166 a r:Inference; - r:gives { - (3 (5 4)) :split (() (5 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6167 a r:Inference; - r:gives { - (3 (5 5)) :split (() (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5984 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6168 a r:Inference; - r:gives { - (3 (5 6)) :split (() (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6169 a r:Inference; - r:gives { - (3 (5 7)) :split (() (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6170 a r:Inference; - r:gives { - (3 (5 9)) :split (() (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6171 a r:Inference; - r:gives { - (3 (6 3)) :split ((3) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6172 a r:Inference; - r:gives { - (3 (6 4)) :split (() (6 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6173 a r:Inference; - r:gives { - (3 (6 5)) :split (() (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5984 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6174 a r:Inference; - r:gives { - (3 (6 6)) :split (() (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6175 a r:Inference; - r:gives { - (3 (6 7)) :split (() (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6176 a r:Inference; - r:gives { - (3 (6 8)) :split (() (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5990 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6177 a r:Inference; - r:gives { - (3 (6 9)) :split (() (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6178 a r:Inference; - r:gives { - (3 (7 3)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6179 a r:Inference; - r:gives { - (3 (7 4)) :split (() (7 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6180 a r:Inference; - r:gives { - (3 (7 5)) :split (() (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5984 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6181 a r:Inference; - r:gives { - (3 (7 6)) :split (() (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6182 a r:Inference; - r:gives { - (3 (7 7)) :split (() (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6183 a r:Inference; - r:gives { - (3 (7 8)) :split (() (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5990 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6184 a r:Inference; - r:gives { - (3 (7 9)) :split (() (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6185 a r:Inference; - r:gives { - (3 (8 3)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6186 a r:Inference; - r:gives { - (3 (8 4)) :split (() (8 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6187 a r:Inference; - r:gives { - (3 (8 6)) :split (() (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6188 a r:Inference; - r:gives { - (3 (8 7)) :split (() (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6189 a r:Inference; - r:gives { - (3 (8 8)) :split (() (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5990 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6190 a r:Inference; - r:gives { - (3 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6191 a r:Inference; - r:gives { - (3 (9 3)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5980 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6192 a r:Inference; - r:gives { - (3 (9 4)) :split (() (9 4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5982 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6193 a r:Inference; - r:gives { - (3 (9 5)) :split (() (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5984 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6194 a r:Inference; - r:gives { - (3 (9 6)) :split (() (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5986 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6195 a r:Inference; - r:gives { - (3 (9 7)) :split (() (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5988 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6196 a r:Inference; - r:gives { - (3 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5990 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6197 a r:Inference; - r:gives { - (3 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 3}] - skolem:lemma5992 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6198 a r:Inference; - r:gives { - (4 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6199 a r:Inference; - r:gives { - (4 (3 4)) :split ((3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6200 a r:Inference; - r:gives { - (4 (3 5)) :split ((3) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - 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 ()]; - 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:lemma5899. - -skolem:lemma6201 a r:Inference; - r:gives { - (4 (3 6)) :split ((3) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6202 a r:Inference; - r:gives { - (4 (3 7)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6203 a r:Inference; - r:gives { - (4 (3 8)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma6005 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6204 a r:Inference; - r:gives { - (4 (3 9)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6205 a r:Inference; - r:gives { - (4 (4 3)) :split ((4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6206 a r:Inference; - r:gives { - (4 (4 4)) :split ((4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6207 a r:Inference; - r:gives { - (4 (4 5)) :split ((4) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6208 a r:Inference; - r:gives { - (4 (4 6)) :split ((4) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6209 a r:Inference; - r:gives { - (4 (4 7)) :split ((4) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6210 a r:Inference; - r:gives { - (4 (4 8)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6005 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6211 a r:Inference; - r:gives { - (4 (4 9)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6212 a r:Inference; - r:gives { - (4 (5 3)) :split ((3) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6213 a r:Inference; - r:gives { - (4 (5 4)) :split ((4) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6214 a r:Inference; - r:gives { - (4 (5 5)) :split (() (5 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6215 a r:Inference; - r:gives { - (4 (5 6)) :split (() (5 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6216 a r:Inference; - r:gives { - (4 (5 7)) :split (() (5 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6217 a r:Inference; - r:gives { - (4 (5 8)) :split (() (5 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma6005 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6218 a r:Inference; - r:gives { - (4 (5 9)) :split (() (5 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:greaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6219 a r:Inference; - r:gives { - (4 (6 3)) :split ((3) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6220 a r:Inference; - r:gives { - (4 (6 4)) :split ((4) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6221 a r:Inference; - r:gives { - (4 (6 5)) :split (() (6 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6222 a r:Inference; - r:gives { - (4 (6 6)) :split (() (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6223 a r:Inference; - r:gives { - (4 (6 7)) :split (() (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6224 a r:Inference; - r:gives { - (4 (6 9)) :split (() (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6225 a r:Inference; - r:gives { - (4 (7 3)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6226 a r:Inference; - r:gives { - (4 (7 4)) :split ((4) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6227 a r:Inference; - r:gives { - (4 (7 5)) :split (() (7 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6228 a r:Inference; - r:gives { - (4 (7 6)) :split (() (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6229 a r:Inference; - r:gives { - (4 (7 7)) :split (() (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6230 a r:Inference; - r:gives { - (4 (7 8)) :split (() (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma6005 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6231 a r:Inference; - r:gives { - (4 (7 9)) :split (() (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6232 a r:Inference; - r:gives { - (4 (8 3)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6233 a r:Inference; - r:gives { - (4 (8 4)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6234 a r:Inference; - r:gives { - (4 (8 5)) :split (() (8 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6235 a r:Inference; - r:gives { - (4 (8 7)) :split (() (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6236 a r:Inference; - r:gives { - (4 (8 8)) :split (() (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma6005 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6237 a r:Inference; - r:gives { - (4 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6238 a r:Inference; - r:gives { - (4 (9 3)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma5997 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6239 a r:Inference; - r:gives { - (4 (9 4)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma5999 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6240 a r:Inference; - r:gives { - (4 (9 5)) :split (() (9 5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma6001 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6241 a r:Inference; - r:gives { - (4 (9 6)) :split (() (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6242 a r:Inference; - r:gives { - (4 (9 7)) :split (() (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma6003 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6243 a r:Inference; - r:gives { - (4 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma6005 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6244 a r:Inference; - r:gives { - (4 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 4}] - skolem:lemma6007 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6245 a r:Inference; - r:gives { - (5 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6012 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6246 a r:Inference; - r:gives { - (5 (3 4)) :split ((3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6247 a r:Inference; - r:gives { - (5 (3 5)) :split ((3 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6248 a r:Inference; - r:gives { - (5 (3 6)) :split ((3) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6249 a r:Inference; - r:gives { - (5 (3 7)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6024 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6250 a r:Inference; - r:gives { - (5 (3 9)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6251 a r:Inference; - r:gives { - (5 (4 3)) :split ((4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6012 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6252 a r:Inference; - r:gives { - (5 (4 4)) :split ((4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6253 a r:Inference; - r:gives { - (5 (4 5)) :split ((4 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6254 a r:Inference; - r:gives { - (5 (4 6)) :split ((4) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6255 a r:Inference; - r:gives { - (5 (4 7)) :split ((4) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6024 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6256 a r:Inference; - r:gives { - (5 (4 8)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6028 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6257 a r:Inference; - r:gives { - (5 (4 9)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6258 a r:Inference; - r:gives { - (5 (5 3)) :split ((5 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6012 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6259 a r:Inference; - r:gives { - (5 (5 4)) :split ((5 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6260 a r:Inference; - r:gives { - (5 (5 5)) :split ((5 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6261 a r:Inference; - r:gives { - (5 (5 6)) :split ((5) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6262 a r:Inference; - r:gives { - (5 (5 7)) :split ((5) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6024 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6263 a r:Inference; - r:gives { - (5 (5 8)) :split ((5) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6028 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6264 a r:Inference; - r:gives { - (5 (5 9)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6265 a r:Inference; - r:gives { - (5 (6 3)) :split ((3) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6012 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6266 a r:Inference; - r:gives { - (5 (6 4)) :split ((4) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6267 a r:Inference; - r:gives { - (5 (6 5)) :split ((5) (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6268 a r:Inference; - r:gives { - (5 (6 6)) :split (() (6 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6269 a r:Inference; - r:gives { - (5 (6 7)) :split (() (6 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6024 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6270 a r:Inference; - r:gives { - (5 (6 8)) :split (() (6 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6028 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6271 a r:Inference; - r:gives { - (5 (6 9)) :split (() (6 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:greaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6272 a r:Inference; - r:gives { - (5 (7 3)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma6012 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6273 a r:Inference; - r:gives { - (5 (7 4)) :split ((4) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6274 a r:Inference; - r:gives { - (5 (7 5)) :split ((5) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6275 a r:Inference; - r:gives { - (5 (7 6)) :split (() (7 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6276 a r:Inference; - r:gives { - (5 (7 7)) :split (() (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma6024 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6277 a r:Inference; - r:gives { - (5 (7 9)) :split (() (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6278 a r:Inference; - r:gives { - (5 (8 4)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6279 a r:Inference; - r:gives { - (5 (8 5)) :split ((5) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6280 a r:Inference; - r:gives { - (5 (8 6)) :split (() (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6281 a r:Inference; - r:gives { - (5 (8 8)) :split (() (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 5}] - skolem:lemma6028 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6282 a r:Inference; - r:gives { - (5 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6283 a r:Inference; - r:gives { - (5 (9 3)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6012 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6284 a r:Inference; - r:gives { - (5 (9 4)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6014 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6285 a r:Inference; - r:gives { - (5 (9 5)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6016 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6286 a r:Inference; - r:gives { - (5 (9 6)) :split (() (9 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6020 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6287 a r:Inference; - r:gives { - (5 (9 7)) :split (() (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6024 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6288 a r:Inference; - r:gives { - (5 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6028 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6289 a r:Inference; - r:gives { - (5 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 5}] - skolem:lemma6032 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6290 a r:Inference; - r:gives { - (6 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6291 a r:Inference; - r:gives { - (6 (3 4)) :split ((3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6292 a r:Inference; - r:gives { - (6 (3 5)) :split ((3 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6293 a r:Inference; - r:gives { - (6 (3 6)) :split ((3 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6294 a r:Inference; - r:gives { - (6 (3 7)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6295 a r:Inference; - r:gives { - (6 (3 8)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6048 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6296 a r:Inference; - r:gives { - (6 (3 9)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6297 a r:Inference; - r:gives { - (6 (4 3)) :split ((4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6298 a r:Inference; - r:gives { - (6 (4 4)) :split ((4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6299 a r:Inference; - r:gives { - (6 (4 5)) :split ((4 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6300 a r:Inference; - r:gives { - (6 (4 6)) :split ((4 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6301 a r:Inference; - r:gives { - (6 (4 7)) :split ((4) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6302 a r:Inference; - r:gives { - (6 (4 9)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6303 a r:Inference; - r:gives { - (6 (5 3)) :split ((5 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6304 a r:Inference; - r:gives { - (6 (5 4)) :split ((5 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6305 a r:Inference; - r:gives { - (6 (5 5)) :split ((5 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6306 a r:Inference; - r:gives { - (6 (5 6)) :split ((5 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6307 a r:Inference; - r:gives { - (6 (5 7)) :split ((5) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6308 a r:Inference; - r:gives { - (6 (5 8)) :split ((5) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6048 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6309 a r:Inference; - r:gives { - (6 (5 9)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6310 a r:Inference; - r:gives { - (6 (6 3)) :split ((6 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6311 a r:Inference; - r:gives { - (6 (6 4)) :split ((6 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6312 a r:Inference; - r:gives { - (6 (6 5)) :split ((6 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6313 a r:Inference; - r:gives { - (6 (6 6)) :split ((6 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6314 a r:Inference; - r:gives { - (6 (6 7)) :split ((6) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6315 a r:Inference; - r:gives { - (6 (6 8)) :split ((6) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6048 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6316 a r:Inference; - r:gives { - (6 (6 9)) :split ((6) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6317 a r:Inference; - r:gives { - (6 (7 3)) :split ((3) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6318 a r:Inference; - r:gives { - (6 (7 4)) :split ((4) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6319 a r:Inference; - r:gives { - (6 (7 5)) :split ((5) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6320 a r:Inference; - r:gives { - (6 (7 6)) :split ((6) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6321 a r:Inference; - r:gives { - (6 (7 7)) :split (() (7 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6322 a r:Inference; - r:gives { - (6 (7 8)) :split (() (7 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6048 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6323 a r:Inference; - r:gives { - (6 (7 9)) :split (() (7 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:greaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6324 a r:Inference; - r:gives { - (6 (8 3)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6325 a r:Inference; - r:gives { - (6 (8 5)) :split ((5) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6326 a r:Inference; - r:gives { - (6 (8 6)) :split ((6) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6327 a r:Inference; - r:gives { - (6 (8 7)) :split (() (8 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6328 a r:Inference; - r:gives { - (6 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6329 a r:Inference; - r:gives { - (6 (9 3)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6330 a r:Inference; - r:gives { - (6 (9 4)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6331 a r:Inference; - r:gives { - (6 (9 5)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6040 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6332 a r:Inference; - r:gives { - (6 (9 6)) :split ((6) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6042 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6333 a r:Inference; - r:gives { - (6 (9 7)) :split (() (9 7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6045 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6334 a r:Inference; - r:gives { - (6 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6048 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6335 a r:Inference; - r:gives { - (6 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 6}] - skolem:lemma6050 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6336 a r:Inference; - r:gives { - (7 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6337 a r:Inference; - r:gives { - (7 (3 4)) :split ((3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6338 a r:Inference; - r:gives { - (7 (3 5)) :split ((3 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6061 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6339 a r:Inference; - r:gives { - (7 (3 6)) :split ((3 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6340 a r:Inference; - r:gives { - (7 (3 7)) :split ((3 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6341 a r:Inference; - r:gives { - (7 (3 8)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6068 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6342 a r:Inference; - r:gives { - (7 (3 9)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6343 a r:Inference; - r:gives { - (7 (4 3)) :split ((4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6344 a r:Inference; - r:gives { - (7 (4 4)) :split ((4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6345 a r:Inference; - r:gives { - (7 (4 5)) :split ((4 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6061 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6346 a r:Inference; - r:gives { - (7 (4 6)) :split ((4 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6347 a r:Inference; - r:gives { - (7 (4 7)) :split ((4 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6348 a r:Inference; - r:gives { - (7 (4 8)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6068 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6349 a r:Inference; - r:gives { - (7 (4 9)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6350 a r:Inference; - r:gives { - (7 (5 3)) :split ((5 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6351 a r:Inference; - r:gives { - (7 (5 4)) :split ((5 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6352 a r:Inference; - r:gives { - (7 (5 5)) :split ((5 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6061 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6353 a r:Inference; - r:gives { - (7 (5 6)) :split ((5 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6354 a r:Inference; - r:gives { - (7 (5 7)) :split ((5 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6355 a r:Inference; - r:gives { - (7 (5 9)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6356 a r:Inference; - r:gives { - (7 (6 3)) :split ((6 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6357 a r:Inference; - r:gives { - (7 (6 4)) :split ((6 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6358 a r:Inference; - r:gives { - (7 (6 5)) :split ((6 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6061 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6359 a r:Inference; - r:gives { - (7 (6 6)) :split ((6 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6360 a r:Inference; - r:gives { - (7 (6 7)) :split ((6 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6361 a r:Inference; - r:gives { - (7 (6 8)) :split ((6) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6068 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6362 a r:Inference; - r:gives { - (7 (6 9)) :split ((6) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6363 a r:Inference; - r:gives { - (7 (7 3)) :split ((7 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6364 a r:Inference; - r:gives { - (7 (7 4)) :split ((7 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6365 a r:Inference; - r:gives { - (7 (7 5)) :split ((7 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6061 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6366 a r:Inference; - r:gives { - (7 (7 6)) :split ((7 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6367 a r:Inference; - r:gives { - (7 (7 7)) :split ((7 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6368 a r:Inference; - r:gives { - (7 (7 8)) :split ((7) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6068 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6369 a r:Inference; - r:gives { - (7 (7 9)) :split ((7) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:notGreaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6370 a r:Inference; - r:gives { - (7 (8 3)) :split ((3) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6371 a r:Inference; - r:gives { - (7 (8 4)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6372 a r:Inference; - r:gives { - (7 (8 6)) :split ((6) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6373 a r:Inference; - r:gives { - (7 (8 7)) :split ((7) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6374 a r:Inference; - r:gives { - (7 (8 8)) :split (() (8 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma6068 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6375 a r:Inference; - r:gives { - (7 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6376 a r:Inference; - r:gives { - (7 (9 3)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6377 a r:Inference; - r:gives { - (7 (9 4)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6059 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6378 a r:Inference; - r:gives { - (7 (9 5)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6061 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6379 a r:Inference; - r:gives { - (7 (9 6)) :split ((6) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6063 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6380 a r:Inference; - r:gives { - (7 (9 7)) :split ((7) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6065 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6381 a r:Inference; - r:gives { - (7 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6068 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6382 a r:Inference; - r:gives { - (7 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6072 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6383 a r:Inference; - r:gives { - (8 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma6079 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6384 a r:Inference; - r:gives { - (8 (3 4)) :split ((3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma6081 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6385 a r:Inference; - r:gives { - (8 (3 6)) :split ((3 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma6085 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6386 a r:Inference; - r:gives { - (8 (3 7)) :split ((3 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma6087 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6387 a r:Inference; - r:gives { - (8 (3 8)) :split ((3 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma6089 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6388 a r:Inference; - r:gives { - (8 (3 9)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:notGreaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6389 a r:Inference; - r:gives { - (8 (4 3)) :split ((4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6079 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6390 a r:Inference; - r:gives { - (8 (4 4)) :split ((4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6081 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6391 a r:Inference; - r:gives { - (8 (4 5)) :split ((4 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6083 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6392 a r:Inference; - r:gives { - (8 (4 7)) :split ((4 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6087 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6393 a r:Inference; - r:gives { - (8 (4 8)) :split ((4 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6089 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6394 a r:Inference; - r:gives { - (8 (4 9)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6395 a r:Inference; - r:gives { - (8 (5 4)) :split ((5 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 8}] - skolem:lemma6081 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6396 a r:Inference; - r:gives { - (8 (5 5)) :split ((5 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 8}] - skolem:lemma6083 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6397 a r:Inference; - r:gives { - (8 (5 6)) :split ((5 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 8}] - skolem:lemma6085 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6398 a r:Inference; - r:gives { - (8 (5 8)) :split ((5 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 8}] - skolem:lemma6089 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6399 a r:Inference; - r:gives { - (8 (5 9)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:notGreaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6400 a r:Inference; - r:gives { - (8 (6 3)) :split ((6 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6079 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6401 a r:Inference; - r:gives { - (8 (6 5)) :split ((6 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6083 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6402 a r:Inference; - r:gives { - (8 (6 6)) :split ((6 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6085 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6403 a r:Inference; - r:gives { - (8 (6 7)) :split ((6 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6087 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6404 a r:Inference; - r:gives { - (8 (6 9)) :split ((6) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6405 a r:Inference; - r:gives { - (8 (7 3)) :split ((7 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6079 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6406 a r:Inference; - r:gives { - (8 (7 4)) :split ((7 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6081 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6407 a r:Inference; - r:gives { - (8 (7 6)) :split ((7 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6085 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6408 a r:Inference; - r:gives { - (8 (7 7)) :split ((7 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6087 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6409 a r:Inference; - r:gives { - (8 (7 8)) :split ((7 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6089 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6410 a r:Inference; - r:gives { - (8 (7 9)) :split ((7) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6411 a r:Inference; - r:gives { - (8 (8 3)) :split ((8 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6079 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6412 a r:Inference; - r:gives { - (8 (8 4)) :split ((8 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6081 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6413 a r:Inference; - r:gives { - (8 (8 5)) :split ((8 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6083 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6414 a r:Inference; - r:gives { - (8 (8 7)) :split ((8 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6087 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6415 a r:Inference; - r:gives { - (8 (8 8)) :split ((8 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6089 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6416 a r:Inference; - r:gives { - (8 (8 9)) :split ((8) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma5899. - -skolem:lemma6417 a r:Inference; - r:gives { - (8 (9 3)) :split ((3) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6079 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6418 a r:Inference; - r:gives { - (8 (9 4)) :split ((4) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6081 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6419 a r:Inference; - r:gives { - (8 (9 5)) :split ((5) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6083 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6420 a r:Inference; - r:gives { - (8 (9 6)) :split ((6) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6085 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6421 a r:Inference; - r:gives { - (8 (9 7)) :split ((7) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6087 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6422 a r:Inference; - r:gives { - (8 (9 8)) :split ((8) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6089 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6423 a r:Inference; - r:gives { - (8 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6091 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6424 a r:Inference; - r:gives { - (9 (3 3)) :split ((3 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {(3 3) list:firstRest (3 (3))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6425 a r:Inference; - r:gives { - (9 (3 4)) :split ((3 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {(3 4) list:firstRest (3 (4))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6426 a r:Inference; - r:gives { - (9 (3 5)) :split ((3 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {(3 5) list:firstRest (3 (5))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 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_2"]; r:boundTo (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6427 a r:Inference; - r:gives { - (9 (3 6)) :split ((3 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {(3 6) list:firstRest (3 (6))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6428 a r:Inference; - r:gives { - (9 (3 7)) :split ((3 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {(3 7) list:firstRest (3 (7))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6429 a r:Inference; - r:gives { - (9 (3 8)) :split ((3 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {(3 8) list:firstRest (3 (8))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6430 a r:Inference; - r:gives { - (9 (3 9)) :split ((3 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {(3 9) list:firstRest (3 (9))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6431 a r:Inference; - r:gives { - (9 (4 3)) :split ((4 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {(4 3) list:firstRest (4 (3))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6432 a r:Inference; - r:gives { - (9 (4 4)) :split ((4 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {(4 4) list:firstRest (4 (4))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6433 a r:Inference; - r:gives { - (9 (4 5)) :split ((4 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {(4 5) list:firstRest (4 (5))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6434 a r:Inference; - r:gives { - (9 (4 6)) :split ((4 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {(4 6) list:firstRest (4 (6))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6435 a r:Inference; - r:gives { - (9 (4 7)) :split ((4 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {(4 7) list:firstRest (4 (7))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6436 a r:Inference; - r:gives { - (9 (4 8)) :split ((4 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {(4 8) list:firstRest (4 (8))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6437 a r:Inference; - r:gives { - (9 (4 9)) :split ((4 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {(4 9) list:firstRest (4 (9))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6438 a r:Inference; - r:gives { - (9 (5 3)) :split ((5 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {(5 3) list:firstRest (5 (3))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6439 a r:Inference; - r:gives { - (9 (5 4)) :split ((5 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {(5 4) list:firstRest (5 (4))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6440 a r:Inference; - r:gives { - (9 (5 5)) :split ((5 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {(5 5) list:firstRest (5 (5))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6441 a r:Inference; - r:gives { - (9 (5 6)) :split ((5 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {(5 6) list:firstRest (5 (6))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6442 a r:Inference; - r:gives { - (9 (5 7)) :split ((5 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {(5 7) list:firstRest (5 (7))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6443 a r:Inference; - r:gives { - (9 (5 8)) :split ((5 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {(5 8) list:firstRest (5 (8))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6444 a r:Inference; - r:gives { - (9 (5 9)) :split ((5 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {(5 9) list:firstRest (5 (9))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6445 a r:Inference; - r:gives { - (9 (6 3)) :split ((6 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {(6 3) list:firstRest (6 (3))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6446 a r:Inference; - r:gives { - (9 (6 4)) :split ((6 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {(6 4) list:firstRest (6 (4))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6447 a r:Inference; - r:gives { - (9 (6 5)) :split ((6 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {(6 5) list:firstRest (6 (5))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6448 a r:Inference; - r:gives { - (9 (6 6)) :split ((6 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {(6 6) list:firstRest (6 (6))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6449 a r:Inference; - r:gives { - (9 (6 7)) :split ((6 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {(6 7) list:firstRest (6 (7))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6450 a r:Inference; - r:gives { - (9 (6 8)) :split ((6 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {(6 8) list:firstRest (6 (8))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6451 a r:Inference; - r:gives { - (9 (6 9)) :split ((6 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {(6 9) list:firstRest (6 (9))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6452 a r:Inference; - r:gives { - (9 (7 3)) :split ((7 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6453 a r:Inference; - r:gives { - (9 (7 4)) :split ((7 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {(7 4) list:firstRest (7 (4))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6454 a r:Inference; - r:gives { - (9 (7 5)) :split ((7 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {(7 5) list:firstRest (7 (5))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6455 a r:Inference; - r:gives { - (9 (7 6)) :split ((7 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {(7 6) list:firstRest (7 (6))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6456 a r:Inference; - r:gives { - (9 (7 7)) :split ((7 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {(7 7) list:firstRest (7 (7))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6457 a r:Inference; - r:gives { - (9 (7 8)) :split ((7 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {(7 8) list:firstRest (7 (8))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6458 a r:Inference; - r:gives { - (9 (7 9)) :split ((7 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {(7 9) list:firstRest (7 (9))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6459 a r:Inference; - r:gives { - (9 (8 3)) :split ((8 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {(8 3) list:firstRest (8 (3))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6460 a r:Inference; - r:gives { - (9 (8 4)) :split ((8 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6461 a r:Inference; - r:gives { - (9 (8 5)) :split ((8 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {(8 5) list:firstRest (8 (5))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6462 a r:Inference; - r:gives { - (9 (8 6)) :split ((8 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6463 a r:Inference; - r:gives { - (9 (8 7)) :split ((8 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {(8 7) list:firstRest (8 (7))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6464 a r:Inference; - r:gives { - (9 (8 8)) :split ((8 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {(8 8) list:firstRest (8 (8))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6465 a r:Inference; - r:gives { - (9 (8 9)) :split ((8 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6466 a r:Inference; - r:gives { - (9 (9 3)) :split ((9 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {(9 3) list:firstRest (9 (3))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6098 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6467 a r:Inference; - r:gives { - (9 (9 4)) :split ((9 4) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {(9 4) list:firstRest (9 (4))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6100 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6468 a r:Inference; - r:gives { - (9 (9 5)) :split ((9 5) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {(9 5) list:firstRest (9 (5))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6102 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6469 a r:Inference; - r:gives { - (9 (9 6)) :split ((9 6) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {(9 6) list:firstRest (9 (6))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6104 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6470 a r:Inference; - r:gives { - (9 (9 7)) :split ((9 7) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {(9 7) list:firstRest (9 (7))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6106 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6471 a r:Inference; - r:gives { - (9 (9 8)) :split ((9 8) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6108 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6472 a r:Inference; - r:gives { - (9 (9 9)) :split ((9 9) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:notGreaterThan 9}] - skolem:lemma6110 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6473 a r:Inference; - r:gives { - (1 (9 8)) :split (() (9 8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {(9 8) list:firstRest (9 (8))}] - [ a r:Fact; r:gives {9 math:greaterThan 1}] - skolem:lemma6524 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6474 a r:Inference; - r:gives { - (2 (3)) :split (() (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6475 a r:Extraction; - r:gives { - @forSome var:x_0. { - (var:x_0 ()) :split (() ()). - } <= true. - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma6476 a r:Inference; - r:gives { - (2 (4)) :split (() (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6477 a r:Inference; - r:gives { - (2 (5)) :split (() (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6478 a r:Inference; - r:gives { - (1 (5)) :split (() (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 1}] - skolem:lemma6128 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6479 a r:Inference; - r:gives { - (2 (7)) :split (() (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6480 a r:Inference; - r:gives { - (1 (7 3)) :split (() (7 3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {(7 3) list:firstRest (7 (3))}] - [ a r:Fact; r:gives {7 math:greaterThan 1}] - skolem:lemma6525 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6481 a r:Inference; - r:gives { - (2 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6482 a r:Inference; - r:gives { - (8 (7 2)) :split ((7 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2) list:firstRest (7 (2))}] - [ a r:Fact; r:gives {(7 2) list:firstRest (7 (2))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 8}] - skolem:lemma6526 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (7 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6483 a r:Inference; - r:gives { - (1 (7 2)) :split (() (7 2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2) list:firstRest (7 (2))}] - [ a r:Fact; r:gives {(7 2) list:firstRest (7 (2))}] - [ a r:Fact; r:gives {7 math:greaterThan 1}] - skolem:lemma6127 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (7 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6484 a r:Inference; - r:gives { - (7 2) :sort (2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 2) list:firstRest (7 (2))}] - skolem:lemma6527 - skolem:lemma4833 - skolem:lemma4395 - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {((2) (7)) list:append (2 7)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 7)]; - r:rule skolem:lemma4396. - -skolem:lemma6485 a r:Inference; - r:gives { - (2 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6486 a r:Inference; - r:gives { - (9 (7 1)) :split ((7 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1) list:firstRest (7 (1))}] - [ a r:Fact; r:gives {(7 1) list:firstRest (7 (1))}] - [ a r:Fact; r:gives {7 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6487 a r:Inference; - r:gives { - (1 (7 1)) :split ((1) (7)). - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1) list:firstRest (7 (1))}] - [ a r:Fact; r:gives {(7) list:firstRest (7 ())}] - [ a r:Fact; r:gives {7 math:greaterThan 1}] - skolem:lemma6123 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; - 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 (7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6488 a r:Inference; - r:gives { - (4 (8 6)) :split (() (8 6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {(8 6) list:firstRest (8 (6))}] - [ a r:Fact; r:gives {8 math:greaterThan 4}] - skolem:lemma6130 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6489 a r:Inference; - r:gives { - (0 (5)) :split (() (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 0}] - skolem:lemma5979 - ); - 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6490 a r:Inference; - r:gives { - (2 (6)) :split (() (6)). - }; - r:evidence ( - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {(6) list:firstRest (6 ())}] - [ a r:Fact; r:gives {6 math:greaterThan 2}] - skolem:lemma6143 - ); - 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6491 a r:Inference; - r:gives { - (6 (8 4)) :split ((4) (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 4) list:firstRest (8 (4))}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 6}] - skolem:lemma6134 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6492 a r:Inference; - r:gives { - (0 (4)) :split (() (4)). - }; - r:evidence ( - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {4 math:greaterThan 0}] - skolem:lemma5979 - ); - 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6493 a r:Inference; - r:gives { - (0 (3)) :split (() (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 0}] - skolem:lemma5979 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6494 a r:Inference; - r:gives { - (8 (8 2)) :split ((8 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2) list:firstRest (8 (2))}] - [ a r:Fact; r:gives {(8 2) list:firstRest (8 (2))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 8}] - skolem:lemma6526 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (8 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6495 a r:Inference; - r:gives { - (0 (8 2)) :split (() (8 2)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2) list:firstRest (8 (2))}] - [ a r:Fact; r:gives {(8 2) list:firstRest (8 (2))}] - [ a r:Fact; r:gives {8 math:greaterThan 0}] - skolem:lemma5962 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (8 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6496 a r:Inference; - r:gives { - (8 2) :sort (2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 2) list:firstRest (8 (2))}] - skolem:lemma6526 - skolem:lemma4833 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((2) (8)) list:append (2 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 8)]; - r:rule skolem:lemma4396. - -skolem:lemma6497 a r:Inference; - r:gives { - (9 (8 1)) :split ((8 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1) list:firstRest (8 (1))}] - [ a r:Fact; r:gives {(8 1) list:firstRest (8 (1))}] - [ a r:Fact; r:gives {8 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6498 a r:Inference; - r:gives { - (0 (8 1)) :split (() (8 1)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1) list:firstRest (8 (1))}] - [ a r:Fact; r:gives {(8 1) list:firstRest (8 (1))}] - [ a r:Fact; r:gives {8 math:greaterThan 0}] - skolem:lemma5935 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6499 a r:Inference; - r:gives { - (8 1) :sort (1 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1) list:firstRest (8 (1))}] - skolem:lemma6529 - skolem:lemma4705 - skolem:lemma4395 - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {((1) (8)) list:append (1 8)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 8)]; - r:rule skolem:lemma4396. - -skolem:lemma6500 a r:Inference; - r:gives { - (7 (9 2)) :split ((2) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 2) list:firstRest (9 (2))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 7}] - skolem:lemma6527 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6501 a r:Inference; - r:gives { - (8 (9 1)) :split ((1) (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1) list:firstRest (9 (1))}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 8}] - skolem:lemma6529 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6502 a r:Inference; - r:gives { - (8 (6 2)) :split ((6 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 2) list:firstRest (6 (2))}] - [ a r:Fact; r:gives {(6 2) list:firstRest (6 (2))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 8}] - skolem:lemma6526 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (6 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6503 a r:Inference; - r:gives { - (9 (6 1)) :split ((6 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1) list:firstRest (6 (1))}] - [ a r:Fact; r:gives {(6 1) list:firstRest (6 (1))}] - [ a r:Fact; r:gives {6 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; - 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 (6 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6504 a r:Inference; - r:gives { - (9 (5 1)) :split ((5 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1) list:firstRest (5 (1))}] - [ a r:Fact; r:gives {(5 1) list:firstRest (5 (1))}] - [ a r:Fact; r:gives {5 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6505 a r:Inference; - r:gives { - (3 (5 1)) :split ((1) (5)). - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1) list:firstRest (5 (1))}] - [ a r:Fact; r:gives {(5) list:firstRest (5 ())}] - [ a r:Fact; r:gives {5 math:greaterThan 3}] - skolem:lemma6530 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; - 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 (5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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:lemma6150. - -skolem:lemma6506 a r:Inference; - r:gives { - (8 (4 2)) :split ((4 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2) list:firstRest (4 (2))}] - [ a r:Fact; r:gives {(4 2) list:firstRest (4 (2))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 8}] - skolem:lemma6526 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (4 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6507 a r:Inference; - r:gives { - (4 (4 2)) :split ((4 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2) list:firstRest (4 (2))}] - [ a r:Fact; r:gives {(4 2) list:firstRest (4 (2))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6531 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (4 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6508 a r:Inference; - r:gives { - (4 2) :sort (2 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 2) list:firstRest (4 (2))}] - skolem:lemma6531 - skolem:lemma4833 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((2) (4)) list:append (2 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/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 (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 4)]; - r:rule skolem:lemma4396. - -skolem:lemma6509 a r:Inference; - r:gives { - (9 (4 1)) :split ((4 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1) list:firstRest (4 (1))}] - [ a r:Fact; r:gives {(4 1) list:firstRest (4 (1))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6510 a r:Inference; - r:gives { - (4 (4 1)) :split ((4 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1) list:firstRest (4 (1))}] - [ a r:Fact; r:gives {(4 1) list:firstRest (4 (1))}] - [ a r:Fact; r:gives {4 math:notGreaterThan 4}] - skolem:lemma6532 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (4 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 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6511 a r:Inference; - r:gives { - (4 1) :sort (1 4). - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1) list:firstRest (4 (1))}] - skolem:lemma6532 - skolem:lemma4705 - skolem:lemma4395 - [ a r:Fact; r:gives {(4) list:firstRest (4 ())}] - [ a r:Fact; r:gives {((1) (4)) list:append (1 4)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (1 4)]; - r:rule skolem:lemma4396. - -skolem:lemma6512 a r:Inference; - r:gives { - (9 (3 1)) :split ((3 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1) list:firstRest (3 (1))}] - [ a r:Fact; r:gives {(3 1) list:firstRest (3 (1))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6513 a r:Inference; - r:gives { - (5 (3 1)) :split ((3 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1) list:firstRest (3 (1))}] - [ a r:Fact; r:gives {(3 1) list:firstRest (3 (1))}] - [ a r:Fact; r:gives {3 math:notGreaterThan 5}] - skolem:lemma6533 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (3 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 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6514 a r:Inference; - r:gives { - (3 1) :sort (1 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1) list:firstRest (3 (1))}] - skolem:lemma6530 - skolem:lemma4705 - skolem:lemma4395 - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {((1) (3)) list:append (1 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - 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 (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo ()]; - 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 ()]; - 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_8"]; r:boundTo (1 3)]; - r:rule skolem:lemma4396. - -skolem:lemma6515 a r:Inference; - r:gives { - (9 (2 1)) :split ((2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 9}] - skolem:lemma6528 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6516 a r:Inference; - r:gives { - (6 (2 1)) :split ((2 1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 6}] - skolem:lemma6534 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6517 a r:Inference; - r:gives { - (0 (9 9)) :split (() (9 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {(9 9) list:firstRest (9 (9))}] - [ a r:Fact; r:gives {9 math:greaterThan 0}] - skolem:lemma6535 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; - 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 (9 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6518 a r:Inference; - r:gives { - (1 (8 9)) :split (() (8 9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {(8 9) list:firstRest (8 (9))}] - [ a r:Fact; r:gives {8 math:greaterThan 1}] - skolem:lemma6536 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; - 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 (8 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma6150. - -skolem:lemma6519 a r:Inference; - r:gives { - (8 (2 2)) :split ((2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 8}] - skolem:lemma6526 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6520 a r:Inference; - r:gives { - (6 (2 2)) :split ((2 2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {(2 2) list:firstRest (2 (2))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 6}] - skolem:lemma6537 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6521 a r:Inference; - r:gives { - (7 (2 3)) :split ((2 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 7}] - skolem:lemma6057 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6522 a r:Inference; - r:gives { - (6 (2 3)) :split ((2 3) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {2 math:notGreaterThan 6}] - skolem:lemma6038 - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 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 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo ()]; - r:rule skolem:lemma5899. - -skolem:lemma6523 a r:Inference; - r:gives { - (2 3) :sort (2 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - skolem:lemma6474 - skolem:lemma4395 - skolem:lemma4408 - [ a r:Fact; r:gives {(2 3) list:firstRest (2 (3))}] - [ a r:Fact; r:gives {(() (2 3)) list:append (2 3)}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (2 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_2"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo ()]; - 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 ()]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo (2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo (2 3)]; - r:rule skolem:lemma4396. - -skolem:lemma6524 a r:Inference; - r:gives { - (1 (8)) :split (() (8)). - }; - r:evidence ( - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {(8) list:firstRest (8 ())}] - [ a r:Fact; r:gives {8 math:greaterThan 1}] - skolem:lemma6128 - ); - 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 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6525 a r:Inference; - r:gives { - (1 (3)) :split (() (3)). - }; - r:evidence ( - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {(3) list:firstRest (3 ())}] - [ a r:Fact; r:gives {3 math:greaterThan 1}] - skolem:lemma6128 - ); - 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 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6526 a r:Inference; - r:gives { - (8 (2)) :split ((2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6527 a r:Inference; - r:gives { - (7 (2)) :split ((2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 7}] - skolem:lemma5917 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6528 a r:Inference; - r:gives { - (9 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 9}] - skolem:lemma5925 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6529 a r:Inference; - r:gives { - (8 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 8}] - skolem:lemma5921 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6530 a r:Inference; - r:gives { - (3 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 3}] - skolem:lemma5908 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6531 a r:Inference; - r:gives { - (4 (2)) :split ((2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 4}] - skolem:lemma5911 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6532 a r:Inference; - r:gives { - (4 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 4}] - skolem:lemma5911 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6533 a r:Inference; - r:gives { - (5 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 5}] - skolem:lemma5913 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6534 a r:Inference; - r:gives { - (6 (1)) :split ((1) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {(1) list:firstRest (1 ())}] - [ a r:Fact; r:gives {1 math:notGreaterThan 6}] - skolem:lemma5943 - ); - 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 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - -skolem:lemma6535 a r:Inference; - r:gives { - (0 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 0}] - skolem:lemma5979 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6536 a r:Inference; - r:gives { - (1 (9)) :split (() (9)). - }; - r:evidence ( - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {(9) list:firstRest (9 ())}] - [ a r:Fact; r:gives {9 math:greaterThan 1}] - skolem:lemma6128 - ); - 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 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma6150. - -skolem:lemma6537 a r:Inference; - r:gives { - (6 (2)) :split ((2) ()). - }; - r:evidence ( - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {(2) list:firstRest (2 ())}] - [ a r:Fact; r:gives {2 math:notGreaterThan 6}] - skolem:lemma5943 - ); - 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 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo ()]; - 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 ()]; - 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 ()]; - r:rule skolem:lemma5899. - diff --git a/reasoning/proof-by-recursion/example2-query.n3 b/reasoning/proof-by-recursion/example2-query.n3 index 97d3ee426..01249d7d4 100644 --- a/reasoning/proof-by-recursion/example2-query.n3 +++ b/reasoning/proof-by-recursion/example2-query.n3 @@ -6,8 +6,7 @@ { 1000 log:repeat ?A. (?A 2000) math:sum ?B. - ?B :kaprekar ?C. - { :recursion :count ?D } log:becomes { :recursion :count 0 }. + ?B :kaprekar (0 ?C). } => { - (?B ?C) :recursionsNeeded ?D. + ?B :recursionCount ?C. }. diff --git a/reasoning/proof-by-recursion/example2.n3 b/reasoning/proof-by-recursion/example2.n3 index 8fdd9a404..363c96791 100644 --- a/reasoning/proof-by-recursion/example2.n3 +++ b/reasoning/proof-by-recursion/example2.n3 @@ -6,32 +6,19 @@ @prefix log: . @prefix : . -# recursion counter -:recursion :count 0. - -# skip 0 -{ 0 :kaprekar 0 } <= { - true log:callWithCut true. -}. - # recursive case till 6174 is reached -{ ?A :kaprekar ?B } <= { - :recursion :count ?N. - (?N 1) math:sum ?N1. - { :recursion :count ?N } log:becomes { :recursion :count ?N1 }. - ?A :numberToDigits ?C. - ?C :sort ?D. - ?D list:reverse ?E. - ?D :digitsToNumber ?F. +{ ?A :kaprekar (?B ?C) } <= { + ?A math:notEqualTo 0. + ?A :numberToDigits ?D. + ?D list:quicksort ?E. + ?E list:reverse ?F. ?E :digitsToNumber ?G. - (?G ?F) math:difference ?H. - ?H math:notEqualTo 6174. - ?H :kaprekar ?B. + ?F :digitsToNumber ?H. + (?H ?G) math:difference ?I. + (?B 1) math:sum ?J. + ({ ?I math:equalTo 6174 } { ?C log:equalTo ?J } { ?I :kaprekar (?J ?C) }) log:ifThenElseIn ?SCOPE. }. -# base case -{?A :kaprekar 6174} <= true. - # convert 4 digit number to digits { ?A :numberToDigits (?B ?C ?D ?E) } <= { (?A 1000) math:integerQuotient ?B. @@ -49,32 +36,3 @@ (?C 10) math:product ?H. (?F ?G ?H ?D) math:sum ?E. }. - -# base case: an empty list is already sorted -() :sort (). - -# recursive case: split the list, sort the sublists and append them -{ ?A :sort ?B } <= { - ?A list:firstRest (?C ?D). - (?C ?D) :split (?E ?F). - ?E :sort ?G. - ?F :sort ?H. - ?I list:firstRest (?C ?H). - (?G ?I) list:append ?B. -}. - -# split the list based on a pivot -{ (?A ()) :split (() ()) } <= true. - -{ (?A ?B) :split (?C ?D) } <= { - ?B list:firstRest (?E ?F). - ?C list:firstRest (?E ?G). - ?E math:notGreaterThan ?A. - (?A ?F) :split (?G ?D). -}. -{ (?A ?B) :split (?C ?D) } <= { - ?B list:firstRest (?E ?F). - ?D list:firstRest (?E ?G). - ?E math:greaterThan ?A. - (?A ?F) :split (?C ?G). -}.