From aa72b216f5f46a195e9fb3de613f43d93fb85e82 Mon Sep 17 00:00:00 2001 From: josd Date: Fri, 22 Nov 2024 11:42:34 +0100 Subject: [PATCH] experimental (functor; args) compound terms --- RELEASE | 1 + VERSION | 2 +- eye.pl | 20 +- eye.zip | Bin 108014 -> 108115 bytes reasoning/good-cobbler/cobbler-query.n3 | 2 +- reasoning/good-cobbler/cobbler.n3 | 2 +- reasoning/peano/peano-answer.n3 | 2 +- reasoning/peano/peano-proof.n3 | 1222 +++++++++++------------ reasoning/peano/peano-query.n3 | 4 +- reasoning/peano/peano.n3 | 10 +- 10 files changed, 642 insertions(+), 623 deletions(-) diff --git a/RELEASE b/RELEASE index 904b66066..249668a2d 100644 --- a/RELEASE +++ b/RELEASE @@ -1,5 +1,6 @@ EYE release +v10.30.5 (2024-11-22) experimental (functor; args) compound terms v10.30.4 (2024-11-19) simplify negative answer surfaces v10.30.3 (2024-11-13) solving issue https://github.com/eyereasoner/eye/issues/121 v10.30.2 (2024-11-11) adjusting to https://eyereasoner.github.io/eye/#eye-color diff --git a/VERSION b/VERSION index 4a8969ef5..4eb11e88a 100644 --- a/VERSION +++ b/VERSION @@ -1 +1 @@ -10.30.4 +10.30.5 diff --git a/eye.pl b/eye.pl index 7fc41b1e1..059c707af 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 v10.30.4 (2024-11-19)'). +version_info('EYE v10.30.5 (2024-11-22)'). license_info('MIT License @@ -2145,6 +2145,15 @@ { sort(List, Distinct) }, ['$', ')']. +pathitem(compound_term(Functor, Args), Triples) --> + ['('], + expression(Functor, T1), + [';'], + !, + pathlist(Args, T2), + [')'], + { append(T1, T2, Triples) + }. pathitem(List, Triples) --> ['('], !, @@ -4179,6 +4188,13 @@ write(' true') ). +wt2(compound_term(X, Y)) :- + !, + write('('), + wt(X), + write(';'), + wl(Y), + write(')'). wt2((X, Y)) :- !, ( atomic(X), @@ -12703,6 +12719,8 @@ !. raw_type(set(_), '') :- !. +raw_type(compound_term(_, _), '') :- + !. raw_type(A, '') :- functor(A, B, 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(:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). +(:s; (:s; (:s; (:s; (:s; 0))))) :factorial (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). diff --git a/reasoning/peano/peano-proof.n3 b/reasoning/peano/peano-proof.n3 index aac481c5d..c097ba24f 100644 --- a/reasoning/peano/peano-proof.n3 +++ b/reasoning/peano/peano-proof.n3 @@ -7,65 +7,65 @@ skolem:proof a r:Proof, r:Conjunction; r:component skolem:lemma1; r:gives { - (:s (:s (:s (:s (:s 0))))) :factorial (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). + (:s; (:s; (:s; (:s; (:s; 0))))) :factorial (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). }. skolem:lemma1 a r:Inference; r:gives { - (:s (:s (:s (:s (:s 0))))) :factorial (:s (:s (:s (:s (:s (:s (:s 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(:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; r:rule skolem:lemma5. skolem:lemma2 a r:Inference; r:gives { - ((:s 0) (:s (:s 0))) :multiply (:s (:s 0)). + ((:s; 0) (:s; (:s; 0))) :multiply (:s; (:s; 0)). }; r:evidence ( skolem:lemma6 skolem:lemma7 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; 0))]; r:rule skolem:lemma8. skolem:lemma3 a r:Inference; r:gives { - ((:s (:s 0)) (:s (:s (:s 0)))) :add (:s (:s (:s (:s (:s 0))))). + ((:s; (:s; 0)) (:s; (:s; (:s; 0)))) :add (:s; (:s; (:s; (:s; (:s; 0))))). }; r:evidence ( skolem:lemma9 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s 0))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; 0))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; 0))]; r:rule skolem:lemma10. skolem:lemma4 a r:Inference; r:gives { - (:s (:s (:s (:s (:s 0))))) :factorial (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). + (:s; (:s; (:s; (:s; (:s; 0))))) :factorial (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). }; r:evidence ( skolem:lemma11 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; r:rule skolem:lemma12. skolem:lemma5 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2. { - ((:s 0) (:s (:s 0))) :multiply var:x_0. - (var:x_0 (:s (:s (:s 0)))) :add var:x_1. + ((:s; 0) (:s; (:s; 0))) :multiply var:x_0. + (var:x_0 (:s; (:s; (:s; 0)))) :add var:x_1. var:x_1 :factorial var:x_2. } => { var:x_1 :factorial var:x_2. @@ -75,34 +75,34 @@ skolem:lemma5 a r:Extraction; skolem:lemma6 a r:Inference; r:gives { - ((:s 0) (:s 0)) :multiply (:s 0). + ((:s; 0) (:s; 0)) :multiply (:s; 0). }; r:evidence ( skolem:lemma13 skolem:lemma14 ); 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_0"]; r:boundTo (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 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_3"]; r:boundTo (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; 0)]; r:rule skolem:lemma8. skolem:lemma7 a r:Inference; r:gives { - ((:s 0) (:s 0)) :add (:s (:s 0)). + ((:s; 0) (:s; 0)) :add (:s; (:s; 0)). }; r:evidence ( skolem:lemma14 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:rule skolem:lemma10. skolem:lemma8 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2, var:x_3. { - (var:x_0 (:s var:x_1)) :multiply var:x_3. + (var:x_0 (:s; var:x_1)) :multiply var:x_3. } <= { (var:x_0 var:x_1) :multiply var:x_2. (var:x_0 var:x_2) :add var:x_3. @@ -112,20 +112,20 @@ skolem:lemma8 a r:Extraction; skolem:lemma9 a r:Inference; r:gives { - ((:s (:s 0)) (:s (:s 0))) :add (:s (:s (:s (:s 0)))). + ((:s; (:s; 0)) (:s; (:s; 0))) :add (:s; (:s; (:s; (:s; 0)))). }; r:evidence ( skolem:lemma15 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s 0)))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; 0)]; r:rule skolem:lemma10. skolem:lemma10 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2. { - (var:x_0 (:s var:x_1)) :add (:s var:x_2). + (var:x_0 (:s; var:x_1)) :add (:s; var:x_2). } <= { (var:x_0 var:x_1) :add var:x_2. }. @@ -134,16 +134,16 @@ skolem:lemma10 a r:Extraction; skolem:lemma11 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s 0)) :fac (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). + ((:s; (:s; (:s; (:s; (:s; 0))))) (:s; 0)) :fac (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). }; r:evidence ( skolem:lemma16 skolem:lemma17 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s (:s 0))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; (:s; 0))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; r:rule skolem:lemma18. skolem:lemma12 a r:Extraction; @@ -151,77 +151,77 @@ skolem:lemma12 a r:Extraction; @forAll var:x_0, var:x_1. { var:x_0 :factorial var:x_1. } <= { - (var:x_0 (:s 0)) :fac var:x_1. + (var:x_0 (:s; 0)) :fac var:x_1. }. }; r:because [ a r:Parsing; r:source ]. skolem:lemma13 a r:Inference; r:gives { - ((:s 0) 0) :multiply 0 . + ((:s; 0) 0) :multiply 0 . }; 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 (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; r:rule skolem:lemma19. skolem:lemma14 a r:Inference; r:gives { - ((:s 0) 0) :add (:s 0). + ((:s; 0) 0) :add (:s; 0). }; 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 (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; r:rule skolem:lemma20. skolem:lemma15 a r:Inference; r:gives { - ((:s (:s 0)) (:s 0)) :add (:s (:s (:s 0))). + ((:s; (:s; 0)) (:s; 0)) :add (:s; (:s; (:s; 0))). }; r:evidence ( skolem:lemma21 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; 0))]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:rule skolem:lemma10. skolem:lemma16 a r:Inference; r:gives { - ((:s 0) (:s (:s (:s (:s (:s 0)))))) :multiply (:s (:s (:s (:s (:s 0))))). + ((:s; 0) (:s; (:s; (:s; (:s; (:s; 0)))))) :multiply (:s; (:s; (:s; (:s; (:s; 0))))). }; r:evidence ( skolem:lemma22 skolem:lemma23 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s 0))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s (:s 0))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; 0))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; (:s; 0))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; r:rule skolem:lemma8. skolem:lemma17 a r:Inference; r:gives { - ((:s (:s (:s (:s 0)))) (:s (:s (:s (:s (:s 0)))))) :fac (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). + ((:s; (:s; (:s; (:s; 0)))) (:s; (:s; (:s; (:s; (:s; 0)))))) :fac (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). }; r:evidence ( skolem:lemma24 skolem:lemma25 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s 0)))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; r:rule skolem:lemma18. skolem:lemma18 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2, var:x_3. { - ((:s var:x_1) var:x_0) :fac var:x_3. + ((:s; var:x_1) var:x_0) :fac var:x_3. } <= { - (var:x_0 (:s var:x_1)) :multiply var:x_2. + (var:x_0 (:s; var:x_1)) :multiply var:x_2. (var:x_1 var:x_2) :fac var:x_3. }. }; @@ -245,540 +245,540 @@ skolem:lemma20 a r:Extraction; skolem:lemma21 a r:Inference; r:gives { - ((:s (:s 0)) 0) :add (:s (:s 0)). + ((:s; (:s; 0)) 0) :add (:s; (:s; 0)). }; 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 (:s (:s 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; 0))]; r:rule skolem:lemma20. skolem:lemma22 a r:Inference; r:gives { - ((:s 0) (:s (:s (:s (:s 0))))) :multiply (:s (:s (:s (:s 0)))). + ((:s; 0) (:s; (:s; (:s; (:s; 0))))) :multiply (:s; (:s; (:s; (:s; 0)))). }; r:evidence ( skolem:lemma26 skolem:lemma27 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s 0)))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s 0)))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s 0))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; 0))))]; r:rule skolem:lemma8. skolem:lemma23 a r:Inference; r:gives { - ((:s 0) (:s (:s (:s (:s 0))))) :add (:s (:s (:s (:s (:s 0))))). + ((:s; 0) (:s; (:s; (:s; (:s; 0))))) :add (:s; (:s; (:s; (:s; (:s; 0))))). }; r:evidence ( skolem:lemma27 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s 0))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; 0))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; 0)))]; r:rule skolem:lemma10. skolem:lemma24 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s (:s (:s 0))))) :multiply (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))). + ((:s; (:s; (:s; (:s; (:s; 0))))) (:s; (:s; (:s; (:s; 0))))) :multiply (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))). }; r:evidence ( skolem:lemma28 skolem:lemma29 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s 0)))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))]; r:rule skolem:lemma8. skolem:lemma25 a r:Inference; r:gives { - ((:s (:s (:s 0))) (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))) :fac (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). + ((:s; (:s; (:s; 0))) (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))) :fac (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). }; r:evidence ( skolem:lemma30 skolem:lemma31 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; r:rule skolem:lemma18. skolem:lemma26 a r:Inference; r:gives { - ((:s 0) (:s (:s (:s 0)))) :multiply (:s (:s (:s 0))). + ((:s; 0) (:s; (:s; (:s; 0)))) :multiply (:s; (:s; (:s; 0))). }; r:evidence ( skolem:lemma2 skolem:lemma32 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; 0)))]; r:rule skolem:lemma8. skolem:lemma27 a r:Inference; r:gives { - ((:s 0) (:s (:s (:s 0)))) :add (:s (:s (:s (:s 0)))). + ((:s; 0) (:s; (:s; (:s; 0)))) :add (:s; (:s; (:s; (:s; 0)))). }; r:evidence ( skolem:lemma32 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s 0)))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; 0))]; r:rule skolem:lemma10. skolem:lemma28 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s (:s 0)))) :multiply (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))). + ((:s; (:s; (:s; (:s; (:s; 0))))) (:s; (:s; (:s; 0)))) :multiply (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))). }; r:evidence ( skolem:lemma33 skolem:lemma34 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))]; r:rule skolem:lemma8. skolem:lemma29 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))) :add (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))). + ((:s; 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r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))]; r:rule skolem:lemma10. skolem:lemma30 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))) (:s (:s (:s 0)))) :multiply (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). + ((:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))) (:s; (:s; (:s; 0)))) :multiply (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 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r:evidence ( skolem:lemma38 skolem:lemma39 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; 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+ r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))]; r:rule skolem:lemma18. skolem:lemma32 a r:Inference; r:gives { - ((:s 0) (:s (:s 0))) :add (:s (:s (:s 0))). + ((:s; 0) (:s; (:s; 0))) :add (:s; (:s; (:s; 0))). }; r:evidence ( skolem:lemma7 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s 0))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; 0))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; 0)]; r:rule skolem:lemma10. skolem:lemma33 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s 0))) :multiply (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))). + ((:s; (:s; (:s; (:s; (:s; 0))))) (:s; (:s; 0))) :multiply (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))). }; r:evidence ( skolem:lemma40 skolem:lemma41 ); 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(:s; (:s; (:s; (:s; 0))))). }; r:evidence ( skolem:lemma51 skolem:lemma52 ); 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_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 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_3"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; r:rule skolem:lemma8. skolem:lemma41 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s (:s (:s (:s 0)))))) :add (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))). + ((:s; (:s; (:s; (:s; (:s; 0))))) (:s; (:s; (:s; (:s; (:s; 0)))))) :add (:s; (:s; (:s; (:s; 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(:s; (:s; (:s; (:s; 0))))))))). }; r:evidence ( skolem:lemma66 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s 0)))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; 0)))]; r:rule skolem:lemma10. skolem:lemma54 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))) :add (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))). + ((:s; 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r:rule skolem:lemma10. skolem:lemma55 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s 0))))) (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))) :add (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))). + ((:s; (:s; (:s; (:s; (:s; 0))))) (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))) :add (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))). }; r:evidence ( skolem:lemma68 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s (:s (:s (:s (:s 0)))))]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; 0)))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))]; r:rule skolem:lemma10. skolem:lemma56 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))) 0) :multiply 0 . + ((:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))) 0) :multiply 0 . }; 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 (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0))))))))))))))))))))]; r:rule skolem:lemma19. skolem:lemma57 a r:Inference; r:gives { - ((:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))) 0) :add (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0)))))))))))))))))))). + ((:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))) 0) :add (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; (:s; 0)))))))))))))))))))). }; 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 (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s (:s 0))))))))))))))))))))]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo (:s; (:s; 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?B)) :add (:s; ?C)} <= { (?A ?B) :add ?C. }. # multiply {(?A 0) :multiply 0} <= true. -{(?A (:s ?B)) :multiply ?C} <= { +{(?A (:s; ?B)) :multiply ?C} <= { (?A ?B) :multiply ?D. (?A ?D) :add ?C. }. # factorial {?A :factorial ?B} <= { - (?A (:s 0)) :fac ?B. + (?A (:s; 0)) :fac ?B. }. {(0 ?A) :fac ?A} <= true. -{((:s ?A) ?B) :fac ?C} <= { - (?B (:s ?A)) :multiply ?D. +{((:s; ?A) ?B) :fac ?C} <= { + (?B (:s; ?A)) :multiply ?D. (?A ?D) :fac ?C. }.