TSTP Solution File: GRP437-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:57:01 EDT 2022
% Result : Unsatisfiable 1.89s 2.10s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 3 RR)
% Number of literals : 90 ( 89 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 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 : 316 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP437-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP437-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D,
file('GRP437-1.p',unknown),
[] ).
cnf(5,plain,
multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E)))),multiply(F,multiply(multiply(inverse(F),inverse(D)),A))))) = E,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.1.2.2.1.2.1,3.1.1')] ).
cnf(7,plain,
multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,D))),inverse(E))),multiply(E,multiply(C,A))))) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.1.2.2.1,3.1.1')] ).
cnf(15,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(D))),multiply(D,multiply(E,A))))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(C,E))),inverse(B))),
inference(para_into,[status(thm),theory(equality)],[7,4]),
[iquote('para_into,7.1.1.2.1.1.2.1,3.1.1')] ).
cnf(17,plain,
multiply(A,inverse(multiply(multiply(B,C),multiply(multiply(multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),inverse(F))),multiply(F,multiply(E,multiply(inverse(B),inverse(multiply(G,H)))))),multiply(G,A))))) = H,
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1.2.1.1.2,7.1.1')] ).
cnf(36,plain,
multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),inverse(multiply(multiply(E,multiply(F,inverse(G))),multiply(G,C)))) = multiply(H,multiply(multiply(inverse(H),inverse(multiply(F,D))),inverse(E))),
inference(para_into,[status(thm),theory(equality)],[15,4]),
[iquote('para_into,15.1.1.2.1.2.2,3.1.1')] ).
cnf(39,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B))) = D,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,7])]),
[iquote('para_into,15.1.1,7.1.1,flip.1')] ).
cnf(40,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(C),inverse(multiply(D,multiply(E,multiply(B,inverse(C))))))))),inverse(E))) = D,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,4])]),
[iquote('para_into,15.1.1,3.1.1,flip.1')] ).
cnf(61,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,E))),inverse(F))))),G))),inverse(B))) = inverse(multiply(multiply(F,multiply(D,inverse(H))),multiply(H,multiply(E,G)))),
inference(para_into,[status(thm),theory(equality)],[39,15]),
[iquote('para_into,38.1.1.2.1.2.1.1.2.1,15.1.1')] ).
cnf(69,plain,
inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(G),inverse(multiply(H,multiply(multiply(inverse(H),inverse(multiply(B,D))),inverse(A))))),E))),inverse(G))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[61])]),
[iquote('copy,61,flip.1')] ).
cnf(138,plain,
multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(B)),inverse(C))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[5,39]),4]),
[iquote('para_from,5.1.1,38.1.1.2.1.2.1.1,demod,4')] ).
cnf(169,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(E))))),F))),inverse(B))) = multiply(multiply(inverse(F),inverse(D)),inverse(E)),
inference(para_from,[status(thm),theory(equality)],[138,39]),
[iquote('para_from,138.1.1,38.1.1.2.1.2.1.1.2.1')] ).
cnf(185,plain,
inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(multiply(inverse(E),inverse(multiply(B,D))),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[69]),169]),
[iquote('back_demod,69,demod,169')] ).
cnf(250,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,multiply(D,inverse(B)))))),C))) = D,
inference(para_from,[status(thm),theory(equality)],[40,4]),
[iquote('para_from,40.1.1,3.1.1.2.1.2')] ).
cnf(258,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))) = multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(E,D))),E))),
inference(para_into,[status(thm),theory(equality)],[250,39]),
[iquote('para_into,250.1.1.2.1.1.2.1.2,38.1.1')] ).
cnf(261,plain,
multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(inverse(E),inverse(multiply(B,multiply(C,multiply(D,inverse(E)))))),
inference(para_from,[status(thm),theory(equality)],[250,4]),
[iquote('para_from,250.1.1,3.1.1.2.1.2.2.1')] ).
cnf(262,plain,
multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(D,inverse(A)))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[261])]),
[iquote('copy,261,flip.1')] ).
cnf(268,plain,
multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))),
inference(para_into,[status(thm),theory(equality)],[262,262]),
[iquote('para_into,262.1.1,262.1.1')] ).
cnf(270,plain,
multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(C,multiply(A,multiply(D,B))))),C))) = D,
inference(para_from,[status(thm),theory(equality)],[268,250]),
[iquote('para_from,268.1.1,250.1.1.2.1.1')] ).
cnf(272,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))),inverse(E))) = D,
inference(para_from,[status(thm),theory(equality)],[268,40]),
[iquote('para_from,268.1.1,40.1.1.2.1.2.1.2')] ).
cnf(290,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(multiply(inverse(A),inverse(multiply(D,C))),D)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[258,17]),17]),
[iquote('para_from,258.1.1,16.1.1.2.1.2.1.2.2.2.2.1,demod,17')] ).
cnf(293,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(A)))))),B)) = inverse(D),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[290,5]),4])]),
[iquote('para_into,290.1.1.1.1,5.1.1,demod,4,flip.1')] ).
cnf(304,plain,
inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C))))) = inverse(D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[293,270]),185]),
[iquote('para_into,293.1.1.1.1,270.1.1,demod,185')] ).
cnf(306,plain,
inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B)) = inverse(D),
inference(para_into,[status(thm),theory(equality)],[293,268]),
[iquote('para_into,293.1.1.1.1,268.1.1')] ).
cnf(313,plain,
multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))),inverse(B)) = inverse(D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[306,185]),185]),
[iquote('para_into,306.1.1.1.1.2,184.1.1,demod,185')] ).
cnf(323,plain,
multiply(multiply(inverse(inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(inverse(A),inverse(D)),multiply(E,multiply(B,C)))))))),inverse(E)) = inverse(D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[304,268]),185]),
[iquote('para_into,304.1.1.1.2.2.1,268.1.1,demod,185')] ).
cnf(332,plain,
inverse(multiply(multiply(inverse(A),inverse(B)),multiply(C,multiply(inverse(C),inverse(D))))) = multiply(multiply(inverse(inverse(D)),inverse(inverse(B))),inverse(inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[323,313])]),
[iquote('para_from,323.1.1,313.1.1.1.2.1,flip.1')] ).
cnf(342,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),multiply(multiply(inverse(inverse(B)),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C))))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[332,270]),
[iquote('para_from,332.1.1,270.1.1.2.1.1.2')] ).
cnf(347,plain,
multiply(inverse(A),inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C))))) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[342,138]),
[iquote('para_into,342.1.1.2.1.1,138.1.1')] ).
cnf(350,plain,
multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(inverse(C),inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[347,138]),347]),
[iquote('para_from,346.1.1,138.1.1.2.1,demod,347')] ).
cnf(352,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[350,347]),347]),
[iquote('para_into,350.1.1.2,346.1.1,demod,347')] ).
cnf(426,plain,
inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(D,inverse(D)),A))))),B)) = inverse(inverse(C)),
inference(para_from,[status(thm),theory(equality)],[352,306]),
[iquote('para_from,352.1.1,306.1.1.1.1.2.1.2.2.1')] ).
cnf(429,plain,
multiply(A,multiply(B,inverse(B))) = multiply(C,multiply(inverse(C),inverse(inverse(A)))),
inference(para_from,[status(thm),theory(equality)],[352,350]),
[iquote('para_from,352.1.1,350.1.1.2')] ).
cnf(442,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),D))),inverse(B))) = inverse(D),
inference(para_from,[status(thm),theory(equality)],[352,39]),
[iquote('para_from,352.1.1,38.1.1.2.1.2.1.1.2.1')] ).
cnf(449,plain,
multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(A,multiply(D,inverse(D)))))),C))) = B,
inference(para_from,[status(thm),theory(equality)],[352,270]),
[iquote('para_from,352.1.1,270.1.1.2.1.1.2.1.2.2')] ).
cnf(454,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,multiply(C,inverse(C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[429])]),
[iquote('copy,429,flip.1')] ).
cnf(510,plain,
multiply(A,multiply(B,inverse(B))) = multiply(A,multiply(C,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[454,352]),
[iquote('para_into,454.1.1.2,352.1.1')] ).
cnf(621,plain,
multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(D,inverse(D)),A))))),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[449,426]),449])]),
[iquote('para_into,448.1.1.2.1.1.1,426.1.1,demod,449,flip.1')] ).
cnf(626,plain,
multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B) = D,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[449,306]),449])]),
[iquote('para_into,448.1.1.2.1.1.1,306.1.1,demod,449,flip.1')] ).
cnf(632,plain,
multiply(multiply(inverse(A),inverse(multiply(B,C))),B) = multiply(multiply(inverse(A),inverse(multiply(D,C))),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[449,290]),449]),
[iquote('para_into,448.1.1.2.1.1.1,290.1.1,demod,449')] ).
cnf(641,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(C,inverse(C)),A))),D))) = D,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[449,36]),185,39])]),
[iquote('para_into,448.1.1.2.1.1,36.1.1,demod,185,39,flip.1')] ).
cnf(645,plain,
multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),inverse(inverse(multiply(inverse(C),inverse(multiply(multiply(D,inverse(D)),multiply(A,multiply(E,inverse(E)))))))))))) = C,
inference(para_into,[status(thm),theory(equality)],[449,429]),
[iquote('para_into,448.1.1.2.1,429.1.1')] ).
cnf(697,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),multiply(E,inverse(E))))))),B) = D,
inference(para_into,[status(thm),theory(equality)],[626,510]),
[iquote('para_into,626.1.1.1.2.1.2.2,510.1.1')] ).
cnf(744,plain,
multiply(A,multiply(B,multiply(C,inverse(C)))) = inverse(multiply(inverse(B),inverse(multiply(multiply(D,inverse(D)),A)))),
inference(para_into,[status(thm),theory(equality)],[641,352]),
[iquote('para_into,641.1.1.2.2,352.1.1')] ).
cnf(748,plain,
inverse(multiply(inverse(A),inverse(multiply(multiply(B,inverse(B)),C)))) = multiply(C,multiply(A,multiply(D,inverse(D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[744])]),
[iquote('copy,744,flip.1')] ).
cnf(751,plain,
multiply(multiply(A,inverse(A)),B) = multiply(multiply(C,inverse(C)),B),
inference(para_from,[status(thm),theory(equality)],[641,626]),
[iquote('para_from,641.1.1,626.1.1.1.2.1')] ).
cnf(755,plain,
multiply(A,multiply(B,inverse(B))) = multiply(multiply(C,inverse(C)),multiply(inverse(multiply(D,inverse(D))),inverse(inverse(A)))),
inference(para_into,[status(thm),theory(equality)],[751,454]),
[iquote('para_into,751.1.1,454.1.1')] ).
cnf(786,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),C) = multiply(multiply(inverse(A),inverse(multiply(D,inverse(C)))),D),
inference(para_into,[status(thm),theory(equality)],[632,352]),
[iquote('para_into,632.1.1.1.2.1,352.1.1')] ).
cnf(787,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B) = multiply(multiply(inverse(A),inverse(multiply(D,inverse(D)))),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[786])]),
[iquote('copy,786,flip.1')] ).
cnf(788,plain,
multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),C))) = multiply(D,inverse(D)),
inference(para_from,[status(thm),theory(equality)],[632,641]),
[iquote('para_from,632.1.1,641.1.1.2.2')] ).
cnf(794,plain,
multiply(inverse(A),multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),A))) = multiply(D,inverse(D)),
inference(para_into,[status(thm),theory(equality)],[788,352]),
[iquote('para_into,788.1.1.2.2.1.2.1,352.1.1')] ).
cnf(806,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[788,268]),4]),
[iquote('para_from,788.1.1,268.1.1.2.1,demod,4')] ).
cnf(815,plain,
multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = inverse(C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[442]),806]),
[iquote('back_demod,442,demod,806')] ).
cnf(817,plain,
multiply(inverse(A),multiply(B,multiply(inverse(B),A))) = multiply(C,inverse(C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[794]),806]),
[iquote('back_demod,794,demod,806')] ).
cnf(819,plain,
multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B) = multiply(inverse(A),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[787]),806]),
[iquote('back_demod,787,demod,806')] ).
cnf(855,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),inverse(multiply(B,multiply(C,multiply(inverse(C),inverse(D)))))),B) = D,
inference(para_from,[status(thm),theory(equality)],[806,626]),
[iquote('para_from,805.1.1,626.1.1.1.2.1.2.2')] ).
cnf(923,plain,
multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(inverse(C),D))))),B) = multiply(inverse(A),inverse(D)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[817,632]),806])]),
[iquote('para_from,817.1.1,632.1.1.1.2.1,demod,806,flip.1')] ).
cnf(936,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[855]),923]),
[iquote('back_demod,855,demod,923')] ).
cnf(941,plain,
multiply(A,multiply(B,inverse(B))) = multiply(multiply(C,inverse(C)),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[755]),936]),
[iquote('back_demod,755,demod,936')] ).
cnf(954,plain,
multiply(A,multiply(inverse(A),B)) = inverse(inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[936,39]),806,819]),
[iquote('para_from,935.1.1,38.1.1.2.1.2.1.1.2.1,demod,806,819')] ).
cnf(970,plain,
multiply(multiply(A,inverse(A)),B) = inverse(inverse(inverse(inverse(B)))),
inference(para_into,[status(thm),theory(equality)],[954,936]),
[iquote('para_into,954.1.1.2,935.1.1')] ).
cnf(973,plain,
multiply(A,inverse(A)) = inverse(inverse(inverse(multiply(B,inverse(B))))),
inference(para_into,[status(thm),theory(equality)],[954,806]),
[iquote('para_into,954.1.1.2,805.1.1')] ).
cnf(982,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(inverse(inverse(A)))),
inference(para_into,[status(thm),theory(equality)],[954,352]),
[iquote('para_into,954.1.1.2,352.1.1')] ).
cnf(992,plain,
inverse(inverse(inverse(inverse(A)))) = multiply(multiply(B,inverse(B)),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[970])]),
[iquote('copy,970,flip.1')] ).
cnf(995,plain,
inverse(inverse(inverse(multiply(A,inverse(A))))) = multiply(B,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[973])]),
[iquote('copy,973,flip.1')] ).
cnf(1000,plain,
inverse(inverse(inverse(inverse(A)))) = multiply(A,multiply(B,inverse(B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[982])]),
[iquote('copy,982,flip.1')] ).
cnf(1004,plain,
multiply(A,multiply(B,inverse(inverse(C)))) = multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(D,inverse(D)),A)))),C),
inference(para_from,[status(thm),theory(equality)],[954,641]),
[iquote('para_from,954.1.1,641.1.1.2.2')] ).
cnf(1020,plain,
inverse(multiply(A,inverse(multiply(B,inverse(inverse(A)))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[954,272]),815]),
[iquote('para_from,954.1.1,272.1.1.2.1.2.1.2.2.1.2,demod,815')] ).
cnf(1045,plain,
multiply(inverse(multiply(inverse(A),inverse(multiply(multiply(B,inverse(B)),C)))),D) = multiply(C,multiply(A,inverse(inverse(D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1004])]),
[iquote('copy,1004,flip.1')] ).
cnf(1090,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(inverse(multiply(B,inverse(B))))))))))) = A,
inference(para_from,[status(thm),theory(equality)],[970,1020]),
[iquote('para_from,970.1.1,1020.1.1.1')] ).
cnf(1113,plain,
multiply(A,inverse(inverse(inverse(inverse(multiply(B,inverse(B))))))) = A,
inference(para_from,[status(thm),theory(equality)],[973,806]),
[iquote('para_from,973.1.1,805.1.1.2.1')] ).
cnf(1121,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),B) = inverse(C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[982,621]),1113]),
[iquote('para_from,982.1.1,621.1.1.1.2.1.2.2,demod,1113')] ).
cnf(1127,plain,
inverse(multiply(A,multiply(multiply(inverse(A),inverse(B)),multiply(C,inverse(C))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[697]),1121]),
[iquote('back_demod,697,demod,1121')] ).
cnf(1152,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),inverse(multiply(B,multiply(C,inverse(C)))))) = B,
inference(para_from,[status(thm),theory(equality)],[995,1020]),
[iquote('para_from,995.1.1,1020.1.1.1.2.1.2')] ).
cnf(1154,plain,
inverse(inverse(multiply(A,inverse(A)))) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[995,992]),806]),
[iquote('para_from,995.1.1,992.1.1.1.1,demod,806')] ).
cnf(1184,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1154,1020]),806]),
[iquote('para_from,1154.1.1,1020.1.1.1.2.1.2.1,demod,806')] ).
cnf(1187,plain,
multiply(A,inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C))))) = A,
inference(para_from,[status(thm),theory(equality)],[1154,806]),
[iquote('para_from,1154.1.1,805.1.1.2.1.2')] ).
cnf(1197,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1152]),1184]),
[iquote('back_demod,1152,demod,1184')] ).
cnf(1202,plain,
multiply(A,inverse(inverse(multiply(B,inverse(B))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1187]),1197]),
[iquote('back_demod,1187,demod,1197')] ).
cnf(1210,plain,
inverse(multiply(A,multiply(inverse(A),inverse(B)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1127]),1197]),
[iquote('back_demod,1127,demod,1197')] ).
cnf(1220,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1000]),1197]),
[iquote('back_demod,1000,demod,1197')] ).
cnf(1230,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[941]),1197])]),
[iquote('back_demod,941,demod,1197,flip.1')] ).
cnf(1256,plain,
inverse(multiply(inverse(A),inverse(B))) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[748]),1230,1197]),
[iquote('back_demod,748,demod,1230,1197')] ).
cnf(1266,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[645]),1197,1230,1256,1210]),
[iquote('back_demod,645,demod,1197,1230,1256,1210')] ).
cnf(1286,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1090]),1202,1220]),
[iquote('back_demod,1090,demod,1202,1220')] ).
cnf(1308,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1045]),1230,1256,1286]),
[iquote('back_demod,1045,demod,1230,1256,1286')] ).
cnf(1322,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),1308,1266]),
[iquote('back_demod,1,demod,1308,1266')] ).
cnf(1323,plain,
$false,
inference(binary,[status(thm)],[1322,2]),
[iquote('binary,1322.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 04:37:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.10 ----- Otter 3.3f, August 2004 -----
% 1.89/2.10 The process was started by sandbox2 on n017.cluster.edu,
% 1.89/2.10 Wed Jul 27 04:37:48 2022
% 1.89/2.10 The command was "./otter". The process ID is 24504.
% 1.89/2.10
% 1.89/2.10 set(prolog_style_variables).
% 1.89/2.10 set(auto).
% 1.89/2.10 dependent: set(auto1).
% 1.89/2.10 dependent: set(process_input).
% 1.89/2.10 dependent: clear(print_kept).
% 1.89/2.10 dependent: clear(print_new_demod).
% 1.89/2.10 dependent: clear(print_back_demod).
% 1.89/2.10 dependent: clear(print_back_sub).
% 1.89/2.10 dependent: set(control_memory).
% 1.89/2.10 dependent: assign(max_mem, 12000).
% 1.89/2.10 dependent: assign(pick_given_ratio, 4).
% 1.89/2.10 dependent: assign(stats_level, 1).
% 1.89/2.10 dependent: assign(max_seconds, 10800).
% 1.89/2.10 clear(print_given).
% 1.89/2.10
% 1.89/2.10 list(usable).
% 1.89/2.10 0 [] A=A.
% 1.89/2.10 0 [] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.89/2.10 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.89/2.10 end_of_list.
% 1.89/2.10
% 1.89/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.89/2.10
% 1.89/2.10 All clauses are units, and equality is present; the
% 1.89/2.10 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.89/2.10
% 1.89/2.10 dependent: set(knuth_bendix).
% 1.89/2.10 dependent: set(anl_eq).
% 1.89/2.10 dependent: set(para_from).
% 1.89/2.10 dependent: set(para_into).
% 1.89/2.10 dependent: clear(para_from_right).
% 1.89/2.10 dependent: clear(para_into_right).
% 1.89/2.10 dependent: set(para_from_vars).
% 1.89/2.10 dependent: set(eq_units_both_ways).
% 1.89/2.10 dependent: set(dynamic_demod_all).
% 1.89/2.10 dependent: set(dynamic_demod).
% 1.89/2.10 dependent: set(order_eq).
% 1.89/2.10 dependent: set(back_demod).
% 1.89/2.10 dependent: set(lrpo).
% 1.89/2.10
% 1.89/2.10 ------------> process usable:
% 1.89/2.10 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.89/2.10
% 1.89/2.10 ------------> process sos:
% 1.89/2.10 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.89/2.10 ** KEPT (pick-wt=18): 3 [] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.89/2.10 ---> New Demodulator: 4 [new_demod,3] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.89/2.10 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.89/2.10 >>>> Starting back demodulation with 4.
% 1.89/2.10
% 1.89/2.10 ======= end of input processing =======
% 1.89/2.10
% 1.89/2.10 =========== start of search ===========
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 31.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 31.
% 1.89/2.10
% 1.89/2.10 sos_size=100
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 29.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 29.
% 1.89/2.10
% 1.89/2.10 sos_size=124
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 22.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 22.
% 1.89/2.10
% 1.89/2.10 sos_size=342
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 16.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 16.
% 1.89/2.10
% 1.89/2.10 sos_size=526
% 1.89/2.10
% 1.89/2.10 -------- PROOF --------
% 1.89/2.10
% 1.89/2.10 ----> UNIT CONFLICT at 0.21 sec ----> 1323 [binary,1322.1,2.1] $F.
% 1.89/2.10
% 1.89/2.10 Length of proof is 86. Level of proof is 32.
% 1.89/2.10
% 1.89/2.10 ---------------- PROOF ----------------
% 1.89/2.10 % SZS status Unsatisfiable
% 1.89/2.10 % SZS output start Refutation
% See solution above
% 1.89/2.10 ------------ end of proof -------------
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Search stopped by max_proofs option.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Search stopped by max_proofs option.
% 1.89/2.10
% 1.89/2.10 ============ end of search ============
% 1.89/2.10
% 1.89/2.10 -------------- statistics -------------
% 1.89/2.10 clauses given 77
% 1.89/2.10 clauses generated 8918
% 1.89/2.10 clauses kept 931
% 1.89/2.10 clauses forward subsumed 2319
% 1.89/2.10 clauses back subsumed 11
% 1.89/2.10 Kbytes malloced 10742
% 1.89/2.10
% 1.89/2.10 ----------- times (seconds) -----------
% 1.89/2.10 user CPU time 0.21 (0 hr, 0 min, 0 sec)
% 1.89/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.89/2.10
% 1.89/2.10 That finishes the proof of the theorem.
% 1.89/2.10
% 1.89/2.10 Process 24504 finished Wed Jul 27 04:37:50 2022
% 1.89/2.10 Otter interrupted
% 1.89/2.10 PROOF FOUND
%------------------------------------------------------------------------------