TSTP Solution File: GRP050-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP050-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:55:58 EDT 2022
% Result : Unsatisfiable 2.09s 2.27s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 82 ( 78 unt; 0 nHn; 5 RR)
% Number of literals : 90 ( 89 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 320 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('GRP050-1.p',unknown),
[] ).
cnf(2,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('GRP050-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C,
file('GRP050-1.p',unknown),
[] ).
cnf(6,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)],[5,5]),
[iquote('para_into,4.1.1.2.1.1.1.1.1,4.1.1')] ).
cnf(8,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)],[5,5])]),
[iquote('para_into,4.1.1.2.1.1.1,4.1.1,flip.1')] ).
cnf(23,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)],[8,5]),
[iquote('para_from,8.1.1,4.1.1.2')] ).
cnf(37,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)],[23,8]),
[iquote('para_into,22.1.1.2.2,8.1.1')] ).
cnf(64,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)],[37,8]),23]),
[iquote('para_from,37.1.1,8.1.1.1.2.2,demod,23')] ).
cnf(106,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)],[6,37]),5]),
[iquote('para_from,6.1.1,37.1.1.2.2,demod,5')] ).
cnf(111,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)],[106])]),
[iquote('copy,106,flip.1')] ).
cnf(152,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(para_into,[status(thm),theory(equality)],[111,111]),
[iquote('para_into,111.1.1,111.1.1')] ).
cnf(159,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)],[152,152]),
[iquote('para_into,152.1.1.1.1,152.1.1')] ).
cnf(162,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)],[152,152]),
[iquote('para_into,152.1.1.2,152.1.1')] ).
cnf(165,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)],[162])]),
[iquote('copy,162,flip.1')] ).
cnf(169,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)],[152,23]),
[iquote('para_from,152.1.1,22.1.1.2.2.1')] ).
cnf(172,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)],[152,8]),5]),
[iquote('para_from,152.1.1,8.1.1.1.1.1,demod,5')] ).
cnf(174,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)],[152,23]),
[iquote('para_from,152.1.1,22.1.1.2.2.1.2.2')] ).
cnf(196,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)],[172,152]),
[iquote('para_from,172.1.1,152.1.1.1')] ).
cnf(204,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)],[169,23]),
[iquote('para_into,169.1.1.2.2.1.1.1,22.1.1')] ).
cnf(207,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)],[169,172]),
[iquote('para_into,169.1.1.2.2.1.1,172.1.1')] ).
cnf(210,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)],[169,152]),
[iquote('para_into,169.1.1.2.2.1.2.2,152.1.1')] ).
cnf(214,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)],[169,172]),
[iquote('para_from,169.1.1,172.1.1.1.1.1')] ).
cnf(247,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)],[162,172]),
[iquote('para_into,162.1.1.1.1.1,172.1.1')] ).
cnf(257,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)],[162,159]),
[iquote('para_into,162.1.1,159.1.1')] ).
cnf(258,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)],[247])]),
[iquote('copy,247,flip.1')] ).
cnf(272,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)],[162,23]),
[iquote('para_from,162.1.1,22.1.1.2.2.1.2')] ).
cnf(276,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)],[162,152]),
[iquote('para_from,162.1.1,152.1.1.1.1')] ).
cnf(279,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)],[276])]),
[iquote('copy,276,flip.1')] ).
cnf(317,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)],[257,172]),
[iquote('para_into,257.1.1.1,172.1.1')] ).
cnf(320,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)],[257,23]),
[iquote('para_into,257.1.1.2.2,22.1.1')] ).
cnf(326,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)],[317])]),
[iquote('copy,317,flip.1')] ).
cnf(328,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)],[320])]),
[iquote('copy,320,flip.1')] ).
cnf(338,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)],[257,37]),
[iquote('para_from,257.1.1,37.1.1.2.2.2.1')] ).
cnf(351,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)],[338])]),
[iquote('copy,338,flip.1')] ).
cnf(391,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)],[214,152]),
[iquote('para_into,214.1.1.1,152.1.1')] ).
cnf(438,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)],[196,174]),210]),
[iquote('para_from,196.1.1,174.1.1.2.2.1,demod,210')] ).
cnf(443,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)],[438,196]),
[iquote('para_from,437.1.1,196.1.1.2')] ).
cnf(445,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)],[443])]),
[iquote('copy,443,flip.1')] ).
cnf(447,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[445,438]),438]),
[iquote('para_into,445.1.1.1.1,437.1.1,demod,438')] ).
cnf(462,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)],[447,196]),
[iquote('para_from,447.1.1,196.1.1.2')] ).
cnf(484,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(B),B)))) = B,
inference(para_from,[status(thm),theory(equality)],[447,172]),
[iquote('para_from,447.1.1,172.1.1.1.1.1')] ).
cnf(526,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)],[447,174]),
[iquote('para_from,447.1.1,174.1.1.2.2.1.2.1.1')] ).
cnf(531,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)],[447,169]),
[iquote('para_from,447.1.1,169.1.1.2.2.1.1.1')] ).
cnf(533,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)],[447,152]),
[iquote('para_from,447.1.1,152.1.1.2')] ).
cnf(545,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)],[447,438]),
[iquote('para_from,447.1.1,437.1.1.2.2')] ).
cnf(555,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)],[447,391]),
[iquote('para_from,447.1.1,391.1.1.1.1.1')] ).
cnf(558,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)],[447,165]),
[iquote('para_from,447.1.1,165.1.1.1.1')] ).
cnf(559,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)],[447,152]),
[iquote('para_from,447.1.1,152.1.1.1.1')] ).
cnf(570,plain,
( multiply(inverse(A),A) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(para_from,[status(thm),theory(equality)],[447,2]),
[iquote('para_from,447.1.1,2.1.1')] ).
cnf(575,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)],[462])]),
[iquote('copy,462,flip.1')] ).
cnf(593,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)],[533])]),
[iquote('copy,533,flip.1')] ).
cnf(600,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)],[555])]),
[iquote('copy,555,flip.1')] ).
cnf(601,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)],[558])]),
[iquote('copy,558,flip.1')] ).
cnf(602,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)],[559])]),
[iquote('copy,559,flip.1')] ).
cnf(610,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(C),C)))) = B,
inference(para_into,[status(thm),theory(equality)],[484,447]),
[iquote('para_into,484.1.1.1.2.2,447.1.1')] ).
cnf(619,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(B),B)))) = B,
inference(para_into,[status(thm),theory(equality)],[484,152]),
[iquote('para_into,484.1.1.1,152.1.1')] ).
cnf(621,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)],[600]),610]),
[iquote('back_demod,600,demod,610')] ).
cnf(624,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[531]),610]),
[iquote('back_demod,531,demod,610')] ).
cnf(628,plain,
inverse(multiply(inverse(A),multiply(inverse(A),A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[619]),624]),
[iquote('back_demod,619,demod,624')] ).
cnf(659,plain,
inverse(multiply(inverse(A),multiply(inverse(B),B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[621]),624]),
[iquote('back_demod,621,demod,624')] ).
cnf(670,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)],[602]),624])]),
[iquote('back_demod,602,demod,624,flip.1')] ).
cnf(672,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)],[601]),624,670]),
[iquote('back_demod,601,demod,624,670')] ).
cnf(678,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)],[593]),624])]),
[iquote('back_demod,593,demod,624,flip.1')] ).
cnf(689,plain,
multiply(A,multiply(inverse(A),B)) = multiply(B,multiply(inverse(C),C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[575]),624,624,628]),
[iquote('back_demod,575,demod,624,624,628')] ).
cnf(694,plain,
multiply(inverse(inverse(A)),multiply(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[545]),624,624]),
[iquote('back_demod,545,demod,624,624')] ).
cnf(697,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[526]),624,670,659,624]),
[iquote('back_demod,526,demod,624,670,659,624')] ).
cnf(745,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)],[351]),672,624,624,624])]),
[iquote('back_demod,351,demod,672,624,624,624,flip.1')] ).
cnf(755,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)],[328]),624,624,745,628,624])]),
[iquote('back_demod,328,demod,624,624,745,628,624,flip.1')] ).
cnf(759,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)],[326]),624,624,697,624,624])]),
[iquote('back_demod,326,demod,624,624,697,624,624,flip.1')] ).
cnf(768,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)],[279]),624,624,624,755,624,624]),
[iquote('back_demod,279,demod,624,624,624,755,624,624')] ).
cnf(776,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[272]),624,745,768,624,624]),
[iquote('back_demod,272,demod,624,745,768,624,624')] ).
cnf(785,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)],[258]),624,768,624,624,628])]),
[iquote('back_demod,258,demod,624,768,624,624,628,flip.1')] ).
cnf(796,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)],[207]),624,785,694,759,624])]),
[iquote('back_demod,207,demod,624,785,694,759,624,flip.1')] ).
cnf(799,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)],[204]),785,745,768,659,624,796,745])]),
[iquote('back_demod,204,demod,785,745,768,659,624,796,745,flip.1')] ).
cnf(853,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)],[64]),796,785,768,785,785,799,785,796,785,785,624,624,624,785,785,796]),
[iquote('back_demod,64,demod,796,785,768,785,785,799,785,796,785,785,624,624,624,785,785,796')] ).
cnf(865,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[689])]),759]),
[iquote('copy,689,flip.1,demod,759')] ).
cnf(905,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[678]),865]),
[iquote('back_demod,678,demod,865')] ).
cnf(931,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[659]),865]),
[iquote('back_demod,658,demod,865')] ).
cnf(933,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[853]),865,905,905,931,905,931]),
[iquote('back_demod,853,demod,865,905,905,931,905,931')] ).
cnf(936,plain,
( multiply(inverse(A),A) != multiply(inverse(a1),a1)
| a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[570]),933,776,933]),
[iquote('back_demod,570,demod,933,776,933')] ).
cnf(958,plain,
$false,
inference(hyper,[status(thm)],[936,447,3,3]),
[iquote('hyper,936,447,3,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP050-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 05:30:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.09/2.26 ----- Otter 3.3f, August 2004 -----
% 2.09/2.26 The process was started by sandbox2 on n015.cluster.edu,
% 2.09/2.26 Wed Jul 27 05:30:11 2022
% 2.09/2.26 The command was "./otter". The process ID is 1680.
% 2.09/2.26
% 2.09/2.26 set(prolog_style_variables).
% 2.09/2.26 set(auto).
% 2.09/2.26 dependent: set(auto1).
% 2.09/2.26 dependent: set(process_input).
% 2.09/2.26 dependent: clear(print_kept).
% 2.09/2.26 dependent: clear(print_new_demod).
% 2.09/2.26 dependent: clear(print_back_demod).
% 2.09/2.26 dependent: clear(print_back_sub).
% 2.09/2.26 dependent: set(control_memory).
% 2.09/2.26 dependent: assign(max_mem, 12000).
% 2.09/2.26 dependent: assign(pick_given_ratio, 4).
% 2.09/2.26 dependent: assign(stats_level, 1).
% 2.09/2.26 dependent: assign(max_seconds, 10800).
% 2.09/2.26 clear(print_given).
% 2.09/2.26
% 2.09/2.26 list(usable).
% 2.09/2.26 0 [] A=A.
% 2.09/2.26 0 [] multiply(Z,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),X)),multiply(inverse(Y),multiply(inverse(Y),Y)))))=X.
% 2.09/2.26 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.09/2.26 end_of_list.
% 2.09/2.26
% 2.09/2.26 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.09/2.26
% 2.09/2.26 This is a Horn set with equality. The strategy will be
% 2.09/2.27 Knuth-Bendix and hyper_res, with positive clauses in
% 2.09/2.27 sos and nonpositive clauses in usable.
% 2.09/2.27
% 2.09/2.27 dependent: set(knuth_bendix).
% 2.09/2.27 dependent: set(anl_eq).
% 2.09/2.27 dependent: set(para_from).
% 2.09/2.27 dependent: set(para_into).
% 2.09/2.27 dependent: clear(para_from_right).
% 2.09/2.27 dependent: clear(para_into_right).
% 2.09/2.27 dependent: set(para_from_vars).
% 2.09/2.27 dependent: set(eq_units_both_ways).
% 2.09/2.27 dependent: set(dynamic_demod_all).
% 2.09/2.27 dependent: set(dynamic_demod).
% 2.09/2.27 dependent: set(order_eq).
% 2.09/2.27 dependent: set(back_demod).
% 2.09/2.27 dependent: set(lrpo).
% 2.09/2.27 dependent: set(hyper_res).
% 2.09/2.27 dependent: clear(order_hyper).
% 2.09/2.27
% 2.09/2.27 ------------> process usable:
% 2.09/2.27 ** KEPT (pick-wt=28): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.09/2.27
% 2.09/2.27 ------------> process sos:
% 2.09/2.27 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.09/2.27 ** KEPT (pick-wt=20): 4 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.09/2.27 ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.09/2.27 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.09/2.27 >>>> Starting back demodulation with 5.
% 2.09/2.27
% 2.09/2.27 ======= end of input processing =======
% 2.09/2.27
% 2.09/2.27 =========== start of search ===========
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Resetting weight limit to 40.
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Resetting weight limit to 40.
% 2.09/2.27
% 2.09/2.27 sos_size=66
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Resetting weight limit to 30.
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Resetting weight limit to 30.
% 2.09/2.27
% 2.09/2.27 sos_size=246
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Resetting weight limit to 23.
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Resetting weight limit to 23.
% 2.09/2.27
% 2.09/2.27 sos_size=1
% 2.09/2.27
% 2.09/2.27 -------- PROOF --------
% 2.09/2.27
% 2.09/2.27 -----> EMPTY CLAUSE at 0.19 sec ----> 958 [hyper,936,447,3,3] $F.
% 2.09/2.27
% 2.09/2.27 Length of proof is 78. Level of proof is 26.
% 2.09/2.27
% 2.09/2.27 ---------------- PROOF ----------------
% 2.09/2.27 % SZS status Unsatisfiable
% 2.09/2.27 % SZS output start Refutation
% See solution above
% 2.09/2.27 ------------ end of proof -------------
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Search stopped by max_proofs option.
% 2.09/2.27
% 2.09/2.27
% 2.09/2.27 Search stopped by max_proofs option.
% 2.09/2.27
% 2.09/2.27 ============ end of search ============
% 2.09/2.27
% 2.09/2.27 -------------- statistics -------------
% 2.09/2.27 clauses given 48
% 2.09/2.27 clauses generated 3617
% 2.09/2.27 clauses kept 692
% 2.09/2.27 clauses forward subsumed 1506
% 2.09/2.27 clauses back subsumed 73
% 2.09/2.27 Kbytes malloced 6835
% 2.09/2.27
% 2.09/2.27 ----------- times (seconds) -----------
% 2.09/2.27 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 2.09/2.27 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.09/2.27 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.09/2.27
% 2.09/2.27 That finishes the proof of the theorem.
% 2.09/2.27
% 2.09/2.27 Process 1680 finished Wed Jul 27 05:30:13 2022
% 2.09/2.27 Otter interrupted
% 2.09/2.27 PROOF FOUND
%------------------------------------------------------------------------------