TSTP Solution File: GRP408-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP408-1 : 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 1.87s 2.06s
% Output   : Refutation 1.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   76 (  76 unt;   0 nHn;   2 RR)
%            Number of literals    :   76 (  75 equ;   1 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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  310 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('GRP408-1.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('GRP408-1.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(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(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(461,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)],[446,195]),
    [iquote('para_from,446.1.1,195.1.1.2')] ).

cnf(483,plain,
    inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(B),B)))) = B,
    inference(para_from,[status(thm),theory(equality)],[446,171]),
    [iquote('para_from,446.1.1,171.1.1.1.1.1')] ).

cnf(525,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)],[446,173]),
    [iquote('para_from,446.1.1,173.1.1.2.2.1.2.1.1')] ).

cnf(530,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)],[446,168]),
    [iquote('para_from,446.1.1,168.1.1.2.2.1.1.1')] ).

cnf(532,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)],[446,151]),
    [iquote('para_from,446.1.1,151.1.1.2')] ).

cnf(544,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)],[446,437]),
    [iquote('para_from,446.1.1,436.1.1.2.2')] ).

cnf(554,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)],[446,390]),
    [iquote('para_from,446.1.1,390.1.1.1.1.1')] ).

cnf(557,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)],[446,164]),
    [iquote('para_from,446.1.1,164.1.1.1.1')] ).

cnf(558,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)],[446,151]),
    [iquote('para_from,446.1.1,151.1.1.1.1')] ).

cnf(572,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)],[461])]),
    [iquote('copy,461,flip.1')] ).

cnf(590,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)],[532])]),
    [iquote('copy,532,flip.1')] ).

cnf(597,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)],[554])]),
    [iquote('copy,554,flip.1')] ).

cnf(598,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)],[557])]),
    [iquote('copy,557,flip.1')] ).

cnf(599,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)],[558])]),
    [iquote('copy,558,flip.1')] ).

cnf(607,plain,
    inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),multiply(inverse(C),C)))) = B,
    inference(para_into,[status(thm),theory(equality)],[483,446]),
    [iquote('para_into,483.1.1.1.2.2,446.1.1')] ).

cnf(616,plain,
    inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(B),B)))) = B,
    inference(para_into,[status(thm),theory(equality)],[483,151]),
    [iquote('para_into,483.1.1.1,151.1.1')] ).

cnf(618,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)],[597]),607]),
    [iquote('back_demod,597,demod,607')] ).

cnf(621,plain,
    multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[530]),607]),
    [iquote('back_demod,530,demod,607')] ).

cnf(625,plain,
    inverse(multiply(inverse(A),multiply(inverse(A),A))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[616]),621]),
    [iquote('back_demod,616,demod,621')] ).

cnf(656,plain,
    inverse(multiply(inverse(A),multiply(inverse(B),B))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[618]),621]),
    [iquote('back_demod,618,demod,621')] ).

cnf(667,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)],[599]),621])]),
    [iquote('back_demod,599,demod,621,flip.1')] ).

cnf(669,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)],[598]),621,667]),
    [iquote('back_demod,598,demod,621,667')] ).

cnf(675,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)],[590]),621])]),
    [iquote('back_demod,590,demod,621,flip.1')] ).

cnf(686,plain,
    multiply(A,multiply(inverse(A),B)) = multiply(B,multiply(inverse(C),C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[572]),621,621,625]),
    [iquote('back_demod,572,demod,621,621,625')] ).

cnf(691,plain,
    multiply(inverse(inverse(A)),multiply(inverse(B),B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[544]),621,621]),
    [iquote('back_demod,544,demod,621,621')] ).

cnf(694,plain,
    multiply(inverse(multiply(inverse(A),A)),B) = B,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[525]),621,667,656,621]),
    [iquote('back_demod,525,demod,621,667,656,621')] ).

cnf(742,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]),669,621,621,621])]),
    [iquote('back_demod,350,demod,669,621,621,621,flip.1')] ).

cnf(752,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]),621,621,742,625,621])]),
    [iquote('back_demod,327,demod,621,621,742,625,621,flip.1')] ).

cnf(756,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]),621,621,694,621,621])]),
    [iquote('back_demod,325,demod,621,621,694,621,621,flip.1')] ).

cnf(765,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]),621,621,621,752,621,621]),
    [iquote('back_demod,278,demod,621,621,621,752,621,621')] ).

cnf(782,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]),621,765,621,621,625])]),
    [iquote('back_demod,257,demod,621,765,621,621,625,flip.1')] ).

cnf(793,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]),621,782,691,756,621])]),
    [iquote('back_demod,206,demod,621,782,691,756,621,flip.1')] ).

cnf(796,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]),782,742,765,656,621,793,742])]),
    [iquote('back_demod,203,demod,782,742,765,656,621,793,742,flip.1')] ).

cnf(850,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]),793,782,765,782,782,796,782,793,782,782,621,621,621,782,782,793]),
    [iquote('back_demod,63,demod,793,782,765,782,782,796,782,793,782,782,621,621,621,782,782,793')] ).

cnf(862,plain,
    multiply(A,multiply(inverse(B),B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[686])]),756]),
    [iquote('copy,686,flip.1,demod,756')] ).

cnf(902,plain,
    inverse(multiply(inverse(A),B)) = multiply(inverse(B),A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[675]),862]),
    [iquote('back_demod,675,demod,862')] ).

cnf(928,plain,
    inverse(inverse(A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[656]),862]),
    [iquote('back_demod,655,demod,862')] ).

cnf(929,plain,
    multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[850]),862,902,902,928,902,928]),
    [iquote('back_demod,850,demod,862,902,902,928,902,928')] ).

cnf(931,plain,
    $false,
    inference(binary,[status(thm)],[929,1]),
    [iquote('binary,929.1,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP408-1 : 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 05:30:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.87/2.06  ----- Otter 3.3f, August 2004 -----
% 1.87/2.06  The process was started by sandbox2 on n018.cluster.edu,
% 1.87/2.06  Wed Jul 27 05:30:31 2022
% 1.87/2.06  The command was "./otter".  The process ID is 18516.
% 1.87/2.06  
% 1.87/2.06  set(prolog_style_variables).
% 1.87/2.06  set(auto).
% 1.87/2.06     dependent: set(auto1).
% 1.87/2.06     dependent: set(process_input).
% 1.87/2.06     dependent: clear(print_kept).
% 1.87/2.06     dependent: clear(print_new_demod).
% 1.87/2.06     dependent: clear(print_back_demod).
% 1.87/2.06     dependent: clear(print_back_sub).
% 1.87/2.06     dependent: set(control_memory).
% 1.87/2.06     dependent: assign(max_mem, 12000).
% 1.87/2.06     dependent: assign(pick_given_ratio, 4).
% 1.87/2.06     dependent: assign(stats_level, 1).
% 1.87/2.06     dependent: assign(max_seconds, 10800).
% 1.87/2.06  clear(print_given).
% 1.87/2.06  
% 1.87/2.06  list(usable).
% 1.87/2.06  0 [] A=A.
% 1.87/2.06  0 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 1.87/2.06  0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.87/2.06  end_of_list.
% 1.87/2.06  
% 1.87/2.06  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.87/2.06  
% 1.87/2.06  All clauses are units, and equality is present; the
% 1.87/2.06  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.87/2.06  
% 1.87/2.06     dependent: set(knuth_bendix).
% 1.87/2.06     dependent: set(anl_eq).
% 1.87/2.06     dependent: set(para_from).
% 1.87/2.06     dependent: set(para_into).
% 1.87/2.06     dependent: clear(para_from_right).
% 1.87/2.06     dependent: clear(para_into_right).
% 1.87/2.06     dependent: set(para_from_vars).
% 1.87/2.06     dependent: set(eq_units_both_ways).
% 1.87/2.06     dependent: set(dynamic_demod_all).
% 1.87/2.06     dependent: set(dynamic_demod).
% 1.87/2.06     dependent: set(order_eq).
% 1.87/2.06     dependent: set(back_demod).
% 1.87/2.06     dependent: set(lrpo).
% 1.87/2.06  
% 1.87/2.06  ------------> process usable:
% 1.87/2.06  ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.87/2.06  
% 1.87/2.06  ------------> process sos:
% 1.87/2.06  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.87/2.06  ** KEPT (pick-wt=20): 3 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 1.87/2.06  ---> 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.
% 1.87/2.06    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.87/2.06  >>>> Starting back demodulation with 4.
% 1.87/2.06  
% 1.87/2.06  ======= end of input processing =======
% 1.87/2.06  
% 1.87/2.06  =========== start of search ===========
% 1.87/2.06  
% 1.87/2.06  
% 1.87/2.06  Resetting weight limit to 40.
% 1.87/2.06  
% 1.87/2.06  
% 1.87/2.06  Resetting weight limit to 40.
% 1.87/2.06  
% 1.87/2.06  sos_size=66
% 1.87/2.06  
% 1.87/2.06  
% 1.87/2.06  Resetting weight limit to 30.
% 1.87/2.06  
% 1.87/2.06  
% 1.87/2.06  Resetting weight limit to 30.
% 1.87/2.06  
% 1.87/2.06  sos_size=246
% 1.87/2.06  
% 1.87/2.06  -------- PROOF -------- 
% 1.87/2.06  
% 1.87/2.06  ----> UNIT CONFLICT at   0.19 sec ----> 931 [binary,929.1,1.1] $F.
% 1.87/2.06  
% 1.87/2.06  Length of proof is 73.  Level of proof is 25.
% 1.87/2.06  
% 1.87/2.06  ---------------- PROOF ----------------
% 1.87/2.06  % SZS status Unsatisfiable
% 1.87/2.06  % SZS output start Refutation
% See solution above
% 1.87/2.06  ------------ end of proof -------------
% 1.87/2.06  
% 1.87/2.06  
% 1.87/2.06  Search stopped by max_proofs option.
% 1.87/2.06  
% 1.87/2.06  
% 1.87/2.06  Search stopped by max_proofs option.
% 1.87/2.06  
% 1.87/2.06  ============ end of search ============
% 1.87/2.06  
% 1.87/2.06  -------------- statistics -------------
% 1.87/2.06  clauses given                 34
% 1.87/2.06  clauses generated           3437
% 1.87/2.06  clauses kept                 675
% 1.87/2.06  clauses forward subsumed    1230
% 1.87/2.06  clauses back subsumed         72
% 1.87/2.06  Kbytes malloced             6835
% 1.87/2.06  
% 1.87/2.06  ----------- times (seconds) -----------
% 1.87/2.06  user CPU time          0.19          (0 hr, 0 min, 0 sec)
% 1.87/2.06  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.87/2.06  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.87/2.06  
% 1.87/2.06  That finishes the proof of the theorem.
% 1.87/2.06  
% 1.87/2.06  Process 18516 finished Wed Jul 27 05:30:33 2022
% 1.87/2.06  Otter interrupted
% 1.87/2.06  PROOF FOUND
%------------------------------------------------------------------------------