%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP407-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:56:57 EDT 2022
% Result : Unsatisfiable 1.88s 2.08s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 82 ( 82 unt; 0 nHn; 5 RR)
% Number of literals : 82 ( 81 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 321 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP407-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP407-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C,
file('GRP407-1.p',unknown),
[] ).
cnf(5,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))))))) = C,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.1.1.1.1.1,3.1.1')] ).
cnf(7,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(B),multiply(inverse(B),B))))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4])]),
[iquote('para_into,3.1.1.2.1.1.1,3.1.1,flip.1')] ).
cnf(22,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(B),multiply(inverse(B),B)))))) = C,
inference(para_from,[status(thm),theory(equality)],[7,4]),
[iquote('para_from,7.1.1,3.1.1.2')] ).
cnf(36,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(inverse(D),multiply(inverse(E),multiply(inverse(E),E))))))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),D),
inference(para_into,[status(thm),theory(equality)],[22,7]),
[iquote('para_into,21.1.1.2.2,7.1.1')] ).
cnf(63,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(C,multiply(D,inverse(multiply(inverse(E),multiply(inverse(F),multiply(inverse(F),F)))))))),G)),multiply(inverse(multiply(C,multiply(D,inverse(multiply(inverse(E),multiply(inverse(F),multiply(inverse(F),F))))))),multiply(inverse(E),E)))) = multiply(A,inverse(multiply(inverse(G),multiply(inverse(B),multiply(inverse(B),B))))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[36,7]),22]),
[iquote('para_from,36.1.1,7.1.1.1.2.2,demod,22')] ).
cnf(105,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),B)),multiply(inverse(D),C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[5,36]),4]),
[iquote('para_from,5.1.1,36.1.1.2.2,demod,4')] ).
cnf(110,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[105])]),
[iquote('copy,105,flip.1')] ).
cnf(151,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(para_into,[status(thm),theory(equality)],[110,110]),
[iquote('para_into,110.1.1,110.1.1')] ).
cnf(158,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)),
inference(para_into,[status(thm),theory(equality)],[151,151]),
[iquote('para_into,151.1.1.1.1,151.1.1')] ).
cnf(161,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))),
inference(para_into,[status(thm),theory(equality)],[151,151]),
[iquote('para_into,151.1.1.2,151.1.1')] ).
cnf(164,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(C,D))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),multiply(inverse(multiply(F,E)),multiply(F,D))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[161])]),
[iquote('copy,161,flip.1')] ).
cnf(168,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,multiply(inverse(B),B)))))) = multiply(inverse(B),D),
inference(para_from,[status(thm),theory(equality)],[151,22]),
[iquote('para_from,151.1.1,21.1.1.2.2.1')] ).
cnf(171,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(B),multiply(inverse(B),B)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[151,7]),4]),
[iquote('para_from,151.1.1,7.1.1.1.1.1,demod,4')] ).
cnf(173,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(B,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D,
inference(para_from,[status(thm),theory(equality)],[151,22]),
[iquote('para_from,151.1.1,21.1.1.2.2.1.2.2')] ).
cnf(195,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,multiply(inverse(C),multiply(inverse(C),C)))),multiply(E,D)),
inference(para_from,[status(thm),theory(equality)],[171,151]),
[iquote('para_from,171.1.1,151.1.1.1')] ).
cnf(203,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(multiply(D,E)),multiply(inverse(B),B)))))) = multiply(inverse(B),multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),multiply(inverse(E),E)))))),
inference(para_into,[status(thm),theory(equality)],[168,22]),
[iquote('para_into,168.1.1.2.2.1.1.1,21.1.1')] ).
cnf(206,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(C,multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,C))),multiply(inverse(B),B)))))) = multiply(inverse(B),multiply(inverse(E),multiply(inverse(E),E))),
inference(para_into,[status(thm),theory(equality)],[168,171]),
[iquote('para_into,168.1.1.2.2.1.1,171.1.1')] ).
cnf(209,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(multiply(D,E)),multiply(D,multiply(inverse(multiply(F,C)),multiply(F,C))))))) = multiply(inverse(multiply(B,C)),E),
inference(para_into,[status(thm),theory(equality)],[168,151]),
[iquote('para_into,168.1.1.2.2.1.2.2,151.1.1')] ).
cnf(213,plain,
inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),multiply(inverse(A),A)))) = inverse(multiply(inverse(multiply(C,B)),multiply(C,multiply(inverse(A),A)))),
inference(para_from,[status(thm),theory(equality)],[168,171]),
[iquote('para_from,168.1.1,171.1.1.1.1.1')] ).
cnf(246,plain,
multiply(inverse(multiply(A,B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,E))) = multiply(inverse(multiply(F,B)),multiply(F,multiply(inverse(multiply(inverse(multiply(G,D)),multiply(G,A))),E))),
inference(para_into,[status(thm),theory(equality)],[161,171]),
[iquote('para_into,161.1.1.1.1.1,171.1.1')] ).
cnf(256,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))),
inference(para_into,[status(thm),theory(equality)],[161,158]),
[iquote('para_into,161.1.1,158.1.1')] ).
cnf(257,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,E))),F))) = multiply(inverse(multiply(E,B)),multiply(inverse(multiply(G,multiply(inverse(D),multiply(inverse(D),D)))),multiply(G,F))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[246])]),
[iquote('copy,246,flip.1')] ).
cnf(271,plain,
multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),C))),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(E,C)),multiply(E,multiply(B,C))))))) = D,
inference(para_from,[status(thm),theory(equality)],[161,22]),
[iquote('para_from,161.1.1,21.1.1.2.2.1.2')] ).
cnf(275,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(C,D)))),multiply(inverse(multiply(inverse(multiply(C,E)),B)),F)) = multiply(inverse(multiply(G,multiply(inverse(multiply(H,E)),multiply(H,D)))),multiply(G,F)),
inference(para_from,[status(thm),theory(equality)],[161,151]),
[iquote('para_from,161.1.1,151.1.1.1.1')] ).
cnf(278,plain,
multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D)))),multiply(A,E)) = multiply(inverse(multiply(inverse(multiply(F,G)),multiply(F,multiply(H,D)))),multiply(inverse(multiply(inverse(multiply(H,C)),G)),E)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[275])]),
[iquote('copy,275,flip.1')] ).
cnf(316,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),multiply(inverse(C),D))) = multiply(inverse(multiply(E,multiply(F,multiply(inverse(C),C)))),multiply(E,multiply(F,D))),
inference(para_into,[status(thm),theory(equality)],[256,171]),
[iquote('para_into,256.1.1.1,171.1.1')] ).
cnf(319,plain,
multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),D))),multiply(A,E)) = multiply(inverse(multiply(F,multiply(G,D))),multiply(F,multiply(G,multiply(B,inverse(multiply(inverse(E),multiply(inverse(C),multiply(inverse(C),C)))))))),
inference(para_into,[status(thm),theory(equality)],[256,22]),
[iquote('para_into,256.1.1.2.2,21.1.1')] ).
cnf(325,plain,
multiply(inverse(multiply(A,multiply(B,multiply(inverse(C),C)))),multiply(A,multiply(B,D))) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),multiply(inverse(C),D))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[316])]),
[iquote('copy,316,flip.1')] ).
cnf(327,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,multiply(D,inverse(multiply(inverse(E),multiply(inverse(F),multiply(inverse(F),F)))))))) = multiply(inverse(multiply(G,multiply(inverse(multiply(D,F)),C))),multiply(G,E)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[319])]),
[iquote('copy,319,flip.1')] ).
cnf(337,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(inverse(multiply(D,multiply(E,F))),multiply(D,multiply(E,G))))))) = multiply(inverse(multiply(inverse(multiply(C,G)),B)),multiply(inverse(G),multiply(inverse(G),F))),
inference(para_from,[status(thm),theory(equality)],[256,36]),
[iquote('para_from,256.1.1,36.1.1.2.2.2.1')] ).
cnf(350,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),D))) = multiply(inverse(multiply(E,C)),multiply(E,multiply(A,inverse(multiply(inverse(multiply(F,multiply(G,D))),multiply(F,multiply(G,B))))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[337])]),
[iquote('copy,337,flip.1')] ).
cnf(390,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(C),C)))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(C),C)))),
inference(para_into,[status(thm),theory(equality)],[213,151]),
[iquote('para_into,213.1.1.1,151.1.1')] ).
cnf(437,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(B),B))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[195,173]),209]),
[iquote('para_from,195.1.1,173.1.1.2.2.1,demod,209')] ).
cnf(442,plain,
multiply(inverse(A),A) = multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),
inference(para_from,[status(thm),theory(equality)],[437,195]),
[iquote('para_from,436.1.1,195.1.1.2')] ).
cnf(444,plain,
multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[442])]),
[iquote('copy,442,flip.1')] ).
cnf(446,plain,
multiply(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[442,1]),
[iquote('para_from,442.1.1,1.1.1.1')] ).
cnf(447,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[446,437]),437]),
[iquote('para_into,446.1.1.1.1.1,436.1.1,demod,437')] ).
cnf(454,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[444,437]),437]),
[iquote('para_into,444.1.1.1.1,436.1.1,demod,437')] ).
cnf(470,plain,
multiply(A,multiply(inverse(B),B)) = multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(multiply(E,D)),multiply(E,A)))),
inference(para_from,[status(thm),theory(equality)],[454,195]),
[iquote('para_from,454.1.1,195.1.1.2')] ).
cnf(495,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(B),B)))) = B,
inference(para_from,[status(thm),theory(equality)],[454,171]),
[iquote('para_from,454.1.1,171.1.1.1.1.1')] ).
cnf(540,plain,
multiply(inverse(multiply(A,multiply(inverse(B),B))),multiply(A,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(D),D)),multiply(inverse(multiply(E,B)),multiply(E,B))))))) = C,
inference(para_from,[status(thm),theory(equality)],[454,173]),
[iquote('para_from,454.1.1,173.1.1.2.2.1.2.1.1')] ).
cnf(545,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(D),multiply(inverse(B),B)))))) = multiply(inverse(B),D),
inference(para_from,[status(thm),theory(equality)],[454,168]),
[iquote('para_from,454.1.1,168.1.1.2.2.1.1.1')] ).
cnf(547,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)),
inference(para_from,[status(thm),theory(equality)],[454,151]),
[iquote('para_from,454.1.1,151.1.1.2')] ).
cnf(561,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(D),D))) = C,
inference(para_from,[status(thm),theory(equality)],[454,437]),
[iquote('para_from,454.1.1,436.1.1.2.2')] ).
cnf(571,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(C),C)))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(C),C)))),
inference(para_from,[status(thm),theory(equality)],[454,390]),
[iquote('para_from,454.1.1,390.1.1.1.1.1')] ).
cnf(574,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(C,D))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),multiply(inverse(multiply(F,E)),multiply(F,D))),
inference(para_from,[status(thm),theory(equality)],[454,164]),
[iquote('para_from,454.1.1,164.1.1.1.1')] ).
cnf(575,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(para_from,[status(thm),theory(equality)],[454,151]),
[iquote('para_from,454.1.1,151.1.1.1.1')] ).
cnf(590,plain,
multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(multiply(C,B)),multiply(C,D)))) = multiply(D,multiply(inverse(E),E)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[470])]),
[iquote('copy,470,flip.1')] ).
cnf(608,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),multiply(inverse(D),D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[547])]),
[iquote('copy,547,flip.1')] ).
cnf(615,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(C),C)))) = inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(B),multiply(inverse(C),C)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[571])]),
[iquote('copy,571,flip.1')] ).
cnf(616,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(inverse(F),F)),multiply(inverse(C),multiply(A,E))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[574])]),
[iquote('copy,574,flip.1')] ).
cnf(617,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),D)),multiply(inverse(B),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[575])]),
[iquote('copy,575,flip.1')] ).
cnf(625,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(C),C)))) = B,
inference(para_into,[status(thm),theory(equality)],[495,454]),
[iquote('para_into,495.1.1.1.2.2,454.1.1')] ).
cnf(634,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(B),B)))) = B,
inference(para_into,[status(thm),theory(equality)],[495,151]),
[iquote('para_into,495.1.1.1,151.1.1')] ).
cnf(636,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(C),C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[615]),625]),
[iquote('back_demod,615,demod,625')] ).
cnf(639,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[545]),625]),
[iquote('back_demod,545,demod,625')] ).
cnf(643,plain,
inverse(multiply(inverse(A),multiply(inverse(A),A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[634]),639]),
[iquote('back_demod,634,demod,639')] ).
cnf(674,plain,
inverse(multiply(inverse(A),multiply(inverse(B),B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[636]),639]),
[iquote('back_demod,636,demod,639')] ).
cnf(685,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),C)) = multiply(inverse(B),C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[617]),639])]),
[iquote('back_demod,617,demod,639,flip.1')] ).
cnf(687,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),D)) = multiply(inverse(C),multiply(A,D)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[616]),639,685]),
[iquote('back_demod,616,demod,639,685')] ).
cnf(693,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(B),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[608]),639])]),
[iquote('back_demod,608,demod,639,flip.1')] ).
cnf(704,plain,
multiply(A,multiply(inverse(A),B)) = multiply(B,multiply(inverse(C),C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[590]),639,639,643]),
[iquote('back_demod,590,demod,639,639,643')] ).
cnf(709,plain,
multiply(inverse(inverse(A)),multiply(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[561]),639,639]),
[iquote('back_demod,561,demod,639,639')] ).
cnf(713,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[540]),639,685,674,639]),
[iquote('back_demod,540,demod,639,685,674,639')] ).
cnf(761,plain,
multiply(inverse(A),multiply(B,inverse(multiply(inverse(C),D)))) = multiply(inverse(A),multiply(B,multiply(inverse(D),C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[350]),687,639,639,639])]),
[iquote('back_demod,350,demod,687,639,639,639,flip.1')] ).
cnf(771,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),D) = multiply(inverse(C),multiply(A,multiply(B,D))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[327]),639,639,761,643,639])]),
[iquote('back_demod,327,demod,639,639,761,643,639,flip.1')] ).
cnf(775,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[325]),639,639,713,639,639])]),
[iquote('back_demod,325,demod,639,639,713,639,639,flip.1')] ).
cnf(784,plain,
multiply(inverse(multiply(inverse(A),B)),C) = multiply(inverse(B),multiply(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[278]),639,639,639,771,639,639]),
[iquote('back_demod,278,demod,639,639,639,771,639,639')] ).
cnf(792,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[271]),639,761,784,639,639]),
[iquote('back_demod,271,demod,639,761,784,639,639')] ).
cnf(801,plain,
multiply(inverse(multiply(A,B)),multiply(C,D)) = multiply(inverse(B),multiply(inverse(A),multiply(C,D))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[257]),639,784,639,639,643])]),
[iquote('back_demod,257,demod,639,784,639,639,643,flip.1')] ).
cnf(812,plain,
multiply(inverse(A),multiply(inverse(B),multiply(inverse(B),B))) = multiply(inverse(A),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[206]),639,801,709,775,639])]),
[iquote('back_demod,206,demod,639,801,709,775,639,flip.1')] ).
cnf(815,plain,
multiply(inverse(A),multiply(B,multiply(inverse(inverse(C)),D))) = multiply(inverse(A),multiply(B,multiply(C,D))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[203]),801,761,784,674,639,812,761])]),
[iquote('back_demod,203,demod,801,761,784,674,639,812,761,flip.1')] ).
cnf(870,plain,
inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(inverse(D),D))))) = multiply(C,inverse(multiply(inverse(A),inverse(B)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),812,801,784,801,801,815,801,812,801,801,639,639,639,801,801,812]),
[iquote('back_demod,63,demod,812,801,784,801,801,815,801,812,801,801,639,639,639,801,801,812')] ).
cnf(882,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[704])]),775]),
[iquote('copy,704,flip.1,demod,775')] ).
cnf(922,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[693]),882]),
[iquote('back_demod,693,demod,882')] ).
cnf(948,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[674]),882]),
[iquote('back_demod,673,demod,882')] ).
cnf(950,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[870]),882,922,922,948,922,948]),
[iquote('back_demod,870,demod,882,922,922,948,922,948')] ).
cnf(953,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[447]),950,792]),
[iquote('back_demod,447,demod,950,792')] ).
cnf(954,plain,
$false,
inference(binary,[status(thm)],[953,2]),
[iquote('binary,953.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP407-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:13:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.88/2.08 ----- Otter 3.3f, August 2004 -----
% 1.88/2.08 The process was started by sandbox2 on n018.cluster.edu,
% 1.88/2.08 Wed Jul 27 05:13:31 2022
% 1.88/2.08 The command was "./otter". The process ID is 5141.
% 1.88/2.08
% 1.88/2.08 set(prolog_style_variables).
% 1.88/2.08 set(auto).
% 1.88/2.08 dependent: set(auto1).
% 1.88/2.08 dependent: set(process_input).
% 1.88/2.08 dependent: clear(print_kept).
% 1.88/2.08 dependent: clear(print_new_demod).
% 1.88/2.08 dependent: clear(print_back_demod).
% 1.88/2.08 dependent: clear(print_back_sub).
% 1.88/2.08 dependent: set(control_memory).
% 1.88/2.08 dependent: assign(max_mem, 12000).
% 1.88/2.08 dependent: assign(pick_given_ratio, 4).
% 1.88/2.08 dependent: assign(stats_level, 1).
% 1.88/2.08 dependent: assign(max_seconds, 10800).
% 1.88/2.08 clear(print_given).
% 1.88/2.08
% 1.88/2.08 list(usable).
% 1.88/2.08 0 [] A=A.
% 1.88/2.08 0 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 1.88/2.08 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.88/2.08 end_of_list.
% 1.88/2.08
% 1.88/2.08 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.88/2.08
% 1.88/2.08 All clauses are units, and equality is present; the
% 1.88/2.08 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.88/2.08
% 1.88/2.08 dependent: set(knuth_bendix).
% 1.88/2.08 dependent: set(anl_eq).
% 1.88/2.08 dependent: set(para_from).
% 1.88/2.08 dependent: set(para_into).
% 1.88/2.08 dependent: clear(para_from_right).
% 1.88/2.08 dependent: clear(para_into_right).
% 1.88/2.08 dependent: set(para_from_vars).
% 1.88/2.08 dependent: set(eq_units_both_ways).
% 1.88/2.08 dependent: set(dynamic_demod_all).
% 1.88/2.08 dependent: set(dynamic_demod).
% 1.88/2.08 dependent: set(order_eq).
% 1.88/2.08 dependent: set(back_demod).
% 1.88/2.08 dependent: set(lrpo).
% 1.88/2.08
% 1.88/2.08 ------------> process usable:
% 1.88/2.08 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.88/2.08
% 1.88/2.08 ------------> process sos:
% 1.88/2.08 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.88/2.08 ** KEPT (pick-wt=20): 3 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 1.88/2.08 ---> New Demodulator: 4 [new_demod,3] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 1.88/2.08 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.88/2.08 >>>> Starting back demodulation with 4.
% 1.88/2.08
% 1.88/2.08 ======= end of input processing =======
% 1.88/2.08
% 1.88/2.08 =========== start of search ===========
% 1.88/2.08
% 1.88/2.08
% 1.88/2.08 Resetting weight limit to 40.
% 1.88/2.08
% 1.88/2.08
% 1.88/2.08 Resetting weight limit to 40.
% 1.88/2.08
% 1.88/2.08 sos_size=66
% 1.88/2.08
% 1.88/2.08
% 1.88/2.08 Resetting weight limit to 30.
% 1.88/2.08
% 1.88/2.08
% 1.88/2.08 Resetting weight limit to 30.
% 1.88/2.08
% 1.88/2.08 sos_size=246
% 1.88/2.08
% 1.88/2.08 -------- PROOF --------
% 1.88/2.08
% 1.88/2.08 ----> UNIT CONFLICT at 0.22 sec ----> 954 [binary,953.1,2.1] $F.
% 1.88/2.08
% 1.88/2.08 Length of proof is 78. Level of proof is 26.
% 1.88/2.08
% 1.88/2.08 ---------------- PROOF ----------------
% 1.88/2.08 % SZS status Unsatisfiable
% 1.88/2.08 % SZS output start Refutation
% See solution above
% 1.88/2.09 ------------ end of proof -------------
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Search stopped by max_proofs option.
% 1.88/2.09
% 1.88/2.09
% 1.88/2.09 Search stopped by max_proofs option.
% 1.88/2.09
% 1.88/2.09 ============ end of search ============
% 1.88/2.09
% 1.88/2.09 -------------- statistics -------------
% 1.88/2.09 clauses given 39
% 1.88/2.09 clauses generated 4329
% 1.88/2.09 clauses kept 697
% 1.88/2.09 clauses forward subsumed 1396
% 1.88/2.09 clauses back subsumed 78
% 1.88/2.09 Kbytes malloced 7812
% 1.88/2.09
% 1.88/2.09 ----------- times (seconds) -----------
% 1.88/2.09 user CPU time 0.22 (0 hr, 0 min, 0 sec)
% 1.88/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.88/2.09
% 1.88/2.09 That finishes the proof of the theorem.
% 1.88/2.09
% 1.88/2.09 Process 5141 finished Wed Jul 27 05:13:33 2022
% 1.88/2.09 Otter interrupted
% 1.88/2.09 PROOF FOUND
%------------------------------------------------------------------------------