TSTP Solution File: GRP438-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP438-1 : 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 1.78s 1.99s
% Output   : Refutation 1.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   78 (  78 unt;   0 nHn;   2 RR)
%            Number of literals    :   78 (  77 equ;   1 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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  282 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('GRP438-1.p',unknown),
    [] ).

cnf(4,axiom,
    multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D,
    file('GRP438-1.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(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(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(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(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(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(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(1307,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(1309,plain,
    $false,
    inference(binary,[status(thm)],[1307,1]),
    [iquote('binary,1307.1,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP438-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Wed Jul 27 04:38:48 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 1.78/1.99  ----- Otter 3.3f, August 2004 -----
% 1.78/1.99  The process was started by sandbox2 on n017.cluster.edu,
% 1.78/1.99  Wed Jul 27 04:38:48 2022
% 1.78/1.99  The command was "./otter".  The process ID is 28072.
% 1.78/1.99  
% 1.78/1.99  set(prolog_style_variables).
% 1.78/1.99  set(auto).
% 1.78/1.99     dependent: set(auto1).
% 1.78/1.99     dependent: set(process_input).
% 1.78/1.99     dependent: clear(print_kept).
% 1.78/1.99     dependent: clear(print_new_demod).
% 1.78/1.99     dependent: clear(print_back_demod).
% 1.78/1.99     dependent: clear(print_back_sub).
% 1.78/1.99     dependent: set(control_memory).
% 1.78/1.99     dependent: assign(max_mem, 12000).
% 1.78/1.99     dependent: assign(pick_given_ratio, 4).
% 1.78/1.99     dependent: assign(stats_level, 1).
% 1.78/1.99     dependent: assign(max_seconds, 10800).
% 1.78/1.99  clear(print_given).
% 1.78/1.99  
% 1.78/1.99  list(usable).
% 1.78/1.99  0 [] A=A.
% 1.78/1.99  0 [] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.78/1.99  0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.78/1.99  end_of_list.
% 1.78/1.99  
% 1.78/1.99  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.78/1.99  
% 1.78/1.99  All clauses are units, and equality is present; the
% 1.78/1.99  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.78/1.99  
% 1.78/1.99     dependent: set(knuth_bendix).
% 1.78/1.99     dependent: set(anl_eq).
% 1.78/1.99     dependent: set(para_from).
% 1.78/1.99     dependent: set(para_into).
% 1.78/1.99     dependent: clear(para_from_right).
% 1.78/1.99     dependent: clear(para_into_right).
% 1.78/1.99     dependent: set(para_from_vars).
% 1.78/1.99     dependent: set(eq_units_both_ways).
% 1.78/1.99     dependent: set(dynamic_demod_all).
% 1.78/1.99     dependent: set(dynamic_demod).
% 1.78/1.99     dependent: set(order_eq).
% 1.78/1.99     dependent: set(back_demod).
% 1.78/1.99     dependent: set(lrpo).
% 1.78/1.99  
% 1.78/1.99  ------------> process usable:
% 1.78/1.99  ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.78/1.99  
% 1.78/1.99  ------------> process sos:
% 1.78/1.99  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.78/1.99  ** KEPT (pick-wt=18): 3 [] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.78/1.99  ---> New Demodulator: 4 [new_demod,3] multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A)))))=D.
% 1.78/1.99    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.78/1.99  >>>> Starting back demodulation with 4.
% 1.78/1.99  
% 1.78/1.99  ======= end of input processing =======
% 1.78/1.99  
% 1.78/1.99  =========== start of search ===========
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 31.
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 31.
% 1.78/1.99  
% 1.78/1.99  sos_size=100
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 29.
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 29.
% 1.78/1.99  
% 1.78/1.99  sos_size=124
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 22.
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 22.
% 1.78/1.99  
% 1.78/1.99  sos_size=342
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 16.
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Resetting weight limit to 16.
% 1.78/1.99  
% 1.78/1.99  sos_size=526
% 1.78/1.99  
% 1.78/1.99  -------- PROOF -------- 
% 1.78/1.99  
% 1.78/1.99  ----> UNIT CONFLICT at   0.19 sec ----> 1309 [binary,1307.1,1.1] $F.
% 1.78/1.99  
% 1.78/1.99  Length of proof is 75.  Level of proof is 31.
% 1.78/1.99  
% 1.78/1.99  ---------------- PROOF ----------------
% 1.78/1.99  % SZS status Unsatisfiable
% 1.78/1.99  % SZS output start Refutation
% See solution above
% 1.78/1.99  ------------ end of proof -------------
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Search stopped by max_proofs option.
% 1.78/1.99  
% 1.78/1.99  
% 1.78/1.99  Search stopped by max_proofs option.
% 1.78/1.99  
% 1.78/1.99  ============ end of search ============
% 1.78/1.99  
% 1.78/1.99  -------------- statistics -------------
% 1.78/1.99  clauses given                 77
% 1.78/1.99  clauses generated           8918
% 1.78/1.99  clauses kept                 922
% 1.78/1.99  clauses forward subsumed    1930
% 1.78/1.99  clauses back subsumed         11
% 1.78/1.99  Kbytes malloced            10742
% 1.78/1.99  
% 1.78/1.99  ----------- times (seconds) -----------
% 1.78/1.99  user CPU time          0.19          (0 hr, 0 min, 0 sec)
% 1.78/1.99  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 1.78/1.99  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.78/1.99  
% 1.78/1.99  That finishes the proof of the theorem.
% 1.78/1.99  
% 1.78/1.99  Process 28072 finished Wed Jul 27 04:38:49 2022
% 1.78/1.99  Otter interrupted
% 1.78/1.99  PROOF FOUND
%------------------------------------------------------------------------------