TSTP Solution File: GRP431-1 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP431-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n029.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  : 600s
% DateTime : Sat Jul 16 08:47:08 EDT 2022

% Result   : Unsatisfiable 0.88s 1.28s
% Output   : Refutation 0.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :    2
% Syntax   : Number of clauses     :  100 ( 100 unt;   0 nHn;   2 RR)
%            Number of literals    :  100 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   15 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  421 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))),D),
    file('GRP431-1.p',unknown),
    [] ).

cnf(2,plain,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP431-1.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),E))),multiply(multiply(multiply(F,inverse(F)),inverse(D)),A)))),E),
    inference(para,[status(thm),theory(equality)],[1,1]),
    [iquote('para(1,1)')] ).

cnf(4,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),multiply(E,inverse(E))),multiply(C,A)))),D),
    inference(para,[status(thm),theory(equality)],[1,1]),
    [iquote('para(1,1)')] ).

cnf(7,plain,
    equal(multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),multiply(E,A)))),inverse(multiply(F,multiply(multiply(multiply(G,inverse(G)),inverse(multiply(C,F))),E)))),
    inference(para,[status(thm),theory(equality)],[3,1]),
    [iquote('para(3,1)')] ).

cnf(8,plain,
    equal(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),D))),multiply(E,inverse(multiply(multiply(multiply(multiply(F,inverse(F)),inverse(C)),multiply(G,inverse(G))),multiply(D,E))))),
    inference(flip,[status(thm),theory(equality)],[7]),
    [iquote('flip(7)')] ).

cnf(10,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,multiply(multiply(multiply(E,inverse(E)),inverse(multiply(F,D))),multiply(G,inverse(G)))),B))),H))),multiply(F,A)))),H),
    inference(para,[status(thm),theory(equality)],[1,3]),
    [iquote('para(1,3)')] ).

cnf(11,plain,
    equal(multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(E))))),inverse(multiply(inverse(multiply(F,multiply(multiply(multiply(G,inverse(G)),inverse(multiply(E,F))),H))),C))),H),
    inference(para,[status(thm),theory(equality)],[1,3]),
    [iquote('para(1,3)')] ).

cnf(14,plain,
    equal(multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))),multiply(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))),multiply(F,inverse(F)))),
    inference(para,[status(thm),theory(equality)],[4,1]),
    [iquote('para(4,1)')] ).

cnf(15,plain,
    equal(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))),multiply(E,inverse(multiply(multiply(B,multiply(F,inverse(F))),multiply(C,E))))),
    inference(flip,[status(thm),theory(equality)],[14]),
    [iquote('flip(14)')] ).

cnf(33,plain,
    equal(multiply(A,inverse(multiply(multiply(B,inverse(B)),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(multiply(multiply(E,multiply(F,inverse(F))),multiply(G,D)))))),A)))),multiply(multiply(H,inverse(H)),inverse(multiply(E,G)))),
    inference(para,[status(thm),theory(equality)],[15,1]),
    [iquote('para(15,1)')] ).

cnf(34,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(multiply(multiply(E,inverse(E)),multiply(multiply(multiply(F,inverse(F)),inverse(multiply(G,inverse(multiply(multiply(B,multiply(H,inverse(H))),multiply(C,G)))))),D))))),
    inference(flip,[status(thm),theory(equality)],[33]),
    [iquote('flip(33)')] ).

cnf(35,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(D,multiply(E,inverse(E))),multiply(B,C))))))),D),
    inference(para,[status(thm),theory(equality)],[15,1]),
    [iquote('para(15,1)')] ).

cnf(41,plain,
    equal(multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(E),C))),E),
    inference(para,[status(thm),theory(equality)],[35,1]),
    [iquote('para(35,1)')] ).

cnf(43,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,multiply(E,inverse(E)))))),C))),D),
    inference(para,[status(thm),theory(equality)],[1,35]),
    [iquote('para(1,35)')] ).

cnf(52,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(multiply(multiply(D,inverse(D)),inverse(B)),A)))),inverse(multiply(E,multiply(F,inverse(multiply(multiply(C,multiply(G,inverse(G))),multiply(E,F))))))),
    inference(para,[status(thm),theory(equality)],[41,1]),
    [iquote('para(41,1)')] ).

cnf(53,plain,
    equal(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),multiply(E,inverse(multiply(inverse(multiply(inverse(F),C)),multiply(multiply(multiply(G,inverse(G)),inverse(F)),E))))),
    inference(flip,[status(thm),theory(equality)],[52]),
    [iquote('flip(52)')] ).

cnf(56,plain,
    equal(multiply(A,inverse(multiply(B,multiply(C,A)))),multiply(multiply(D,inverse(D)),inverse(multiply(B,multiply(C,multiply(E,inverse(E))))))),
    inference(para,[status(thm),theory(equality)],[43,1]),
    [iquote('para(43,1)')] ).

cnf(58,plain,
    equal(multiply(inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,multiply(D,inverse(D)))))),B)),inverse(multiply(inverse(E),C))),E),
    inference(para,[status(thm),theory(equality)],[43,1]),
    [iquote('para(43,1)')] ).

cnf(68,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),multiply(E,inverse(E)))))),D),
    inference(para,[status(thm),theory(equality)],[56,1]),
    [iquote('para(56,1)')] ).

cnf(89,plain,
    equal(multiply(A,inverse(A)),multiply(B,inverse(B))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[68,1]),3]),
    [iquote('para(68,1),demod([3])')] ).

cnf(92,plain,
    equal(multiply(A,inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),A)))),B),
    inference(para,[status(thm),theory(equality)],[89,1]),
    [iquote('para(89,1)')] ).

cnf(93,plain,
    equal(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,C)))),inverse(multiply(C,multiply(D,inverse(D))))),B),
    inference(para,[status(thm),theory(equality)],[89,1]),
    [iquote('para(89,1)')] ).

cnf(96,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),inverse(multiply(inverse(B),multiply(C,inverse(C))))),B),
    inference(para,[status(thm),theory(equality)],[89,92]),
    [iquote('para(89,92)')] ).

cnf(130,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),D))),multiply(multiply(multiply(E,inverse(E)),inverse(B)),A)))),D),
    inference(para,[status(thm),theory(equality)],[92,1]),
    [iquote('para(92,1)')] ).

cnf(136,plain,
    equal(multiply(A,multiply(B,inverse(multiply(multiply(multiply(multiply(C,inverse(C)),inverse(D)),multiply(E,inverse(E))),multiply(A,B))))),D),
    inference(para,[status(thm),theory(equality)],[8,1]),
    [iquote('para(8,1)')] ).

cnf(141,plain,
    equal(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(C))))),multiply(multiply(D,inverse(D)),inverse(multiply(B,multiply(A,multiply(E,inverse(E))))))),
    inference(para,[status(thm),theory(equality)],[89,56]),
    [iquote('para(89,56)')] ).

cnf(142,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,multiply(D,inverse(D)))))),multiply(inverse(C),inverse(multiply(B,multiply(E,inverse(E)))))),
    inference(flip,[status(thm),theory(equality)],[141]),
    [iquote('flip(141)')] ).

cnf(143,plain,
    equal(multiply(A,multiply(inverse(A),inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),multiply(E,inverse(E)))))),C),
    inference(para,[status(thm),theory(equality)],[89,136]),
    [iquote('para(89,136)')] ).

cnf(161,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),C)),C),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[89,130]),92]),
    [iquote('para(89,130),demod([92])')] ).

cnf(164,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))),inverse(multiply(C,inverse(C)))),
    inference(para,[status(thm),theory(equality)],[89,161]),
    [iquote('para(89,161)')] ).

cnf(170,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),B),inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))))),
    inference(para,[status(thm),theory(equality)],[92,161]),
    [iquote('para(92,161)')] ).

cnf(171,plain,
    equal(inverse(multiply(inverse(A),multiply(multiply(B,inverse(B)),multiply(C,inverse(C))))),multiply(inverse(multiply(D,inverse(D))),A)),
    inference(flip,[status(thm),theory(equality)],[170]),
    [iquote('flip(170)')] ).

cnf(175,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(multiply(B,inverse(B))))),multiply(C,inverse(C))),
    inference(para,[status(thm),theory(equality)],[161,96]),
    [iquote('para(161,96)')] ).

cnf(176,plain,
    equal(multiply(A,inverse(A)),multiply(inverse(multiply(B,inverse(B))),inverse(inverse(multiply(C,inverse(C)))))),
    inference(flip,[status(thm),theory(equality)],[175]),
    [iquote('flip(175)')] ).

cnf(192,plain,
    equal(multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))),inverse(multiply(E,multiply(multiply(multiply(F,inverse(F)),inverse(multiply(multiply(G,multiply(multiply(multiply(H,inverse(H)),inverse(multiply(B,G))),multiply(I,inverse(I)))),E))),D)))),
    inference(para,[status(thm),theory(equality)],[10,1]),
    [iquote('para(10,1)')] ).

cnf(193,plain,
    equal(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,C))),multiply(F,inverse(F)))),A))),G))),multiply(H,inverse(multiply(multiply(E,multiply(I,inverse(I))),multiply(G,H))))),
    inference(flip,[status(thm),theory(equality)],[192]),
    [iquote('flip(192)')] ).

cnf(256,plain,
    equal(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(multiply(C,inverse(C))))))),inverse(inverse(multiply(D,inverse(D))))),B),
    inference(para,[status(thm),theory(equality)],[164,1]),
    [iquote('para(164,1)')] ).

cnf(397,plain,
    equal(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(multiply(B,inverse(B)),inverse(C)),D))),multiply(E,inverse(E))),inverse(multiply(F,multiply(multiply(multiply(G,inverse(G)),inverse(multiply(C,F))),D)))),
    inference(para,[status(thm),theory(equality)],[14,7]),
    [iquote('para(14,7)')] ).

cnf(398,plain,
    equal(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),D))),multiply(multiply(multiply(E,inverse(E)),inverse(multiply(multiply(multiply(F,inverse(F)),inverse(C)),D))),multiply(G,inverse(G)))),
    inference(flip,[status(thm),theory(equality)],[397]),
    [iquote('flip(397)')] ).

cnf(418,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),D))),E)),inverse(multiply(multiply(F,multiply(G,inverse(G))),D))),multiply(multiply(multiply(H,inverse(H)),inverse(multiply(F,inverse(multiply(I,multiply(multiply(multiply(J,inverse(J)),inverse(multiply(E,I))),multiply(multiply(K,inverse(K)),inverse(C)))))))),multiply(L,inverse(L)))),
    inference(para,[status(thm),theory(equality)],[11,14]),
    [iquote('para(11,14)')] ).

cnf(419,plain,
    equal(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,C))),multiply(multiply(F,inverse(F)),inverse(G)))))))),multiply(H,inverse(H))),multiply(inverse(multiply(inverse(multiply(I,multiply(multiply(multiply(J,inverse(J)),inverse(multiply(G,I))),K))),E)),inverse(multiply(multiply(B,multiply(L,inverse(L))),K)))),
    inference(flip,[status(thm),theory(equality)],[418]),
    [iquote('flip(418)')] ).

cnf(431,plain,
    equal(multiply(multiply(A,inverse(A)),multiply(inverse(multiply(B,inverse(B))),C)),C),
    inference(para,[status(thm),theory(equality)],[171,92]),
    [iquote('para(171,92)')] ).

cnf(438,plain,
    equal(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(multiply(inverse(C),B))),C),
    inference(para,[status(thm),theory(equality)],[431,92]),
    [iquote('para(431,92)')] ).

cnf(466,plain,
    equal(multiply(multiply(A,inverse(A)),B),inverse(multiply(inverse(B),multiply(C,inverse(C))))),
    inference(para,[status(thm),theory(equality)],[96,431]),
    [iquote('para(96,431)')] ).

cnf(468,plain,
    equal(inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),multiply(B,inverse(B)))),multiply(C,inverse(C))),
    inference(para,[status(thm),theory(equality)],[466,89]),
    [iquote('para(466,89)')] ).

cnf(469,plain,
    equal(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))))),
    inference(flip,[status(thm),theory(equality)],[468]),
    [iquote('flip(468)')] ).

cnf(477,plain,
    equal(multiply(A,inverse(multiply(inverse(B),inverse(multiply(inverse(A),multiply(C,inverse(C))))))),B),
    inference(para,[status(thm),theory(equality)],[466,92]),
    [iquote('para(466,92)')] ).

cnf(512,plain,
    equal(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C)))))),inverse(multiply(inverse(D),A))),D),
    inference(para,[status(thm),theory(equality)],[477,92]),
    [iquote('para(477,92)')] ).

cnf(515,plain,
    equal(multiply(multiply(A,inverse(A)),B),inverse(multiply(inverse(B),inverse(multiply(inverse(inverse(multiply(C,inverse(C)))),multiply(D,inverse(D))))))),
    inference(para,[status(thm),theory(equality)],[477,431]),
    [iquote('para(477,431)')] ).

cnf(516,plain,
    equal(inverse(multiply(inverse(A),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,inverse(C)))))),multiply(multiply(D,inverse(D)),A)),
    inference(flip,[status(thm),theory(equality)],[515]),
    [iquote('flip(515)')] ).

cnf(567,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),inverse(multiply(inverse(B),inverse(multiply(inverse(inverse(multiply(C,inverse(C)))),multiply(D,inverse(D))))))),B),
    inference(para,[status(thm),theory(equality)],[469,92]),
    [iquote('para(469,92)')] ).

cnf(568,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))))),inverse(inverse(multiply(D,inverse(D))))),
    inference(para,[status(thm),theory(equality)],[469,431]),
    [iquote('para(469,431)')] ).

cnf(569,plain,
    equal(inverse(inverse(multiply(A,inverse(A)))),multiply(multiply(B,inverse(B)),inverse(multiply(inverse(inverse(multiply(C,inverse(C)))),multiply(D,inverse(D)))))),
    inference(flip,[status(thm),theory(equality)],[568]),
    [iquote('flip(568)')] ).

cnf(607,plain,
    equal(multiply(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))),inverse(multiply(inverse(multiply(C,inverse(C))),inverse(inverse(multiply(D,inverse(D))))))),B),
    inference(para,[status(thm),theory(equality)],[176,438]),
    [iquote('para(176,438)')] ).

cnf(659,plain,
    equal(multiply(inverse(multiply(inverse(inverse(inverse(A))),inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C)))))),inverse(multiply(D,inverse(D)))),A),
    inference(para,[status(thm),theory(equality)],[89,512]),
    [iquote('para(89,512)')] ).

cnf(664,plain,
    equal(inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,inverse(C)))))),multiply(D,inverse(D))),
    inference(para,[status(thm),theory(equality)],[515,89]),
    [iquote('para(515,89)')] ).

cnf(665,plain,
    equal(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),inverse(multiply(inverse(inverse(multiply(C,inverse(C)))),multiply(D,inverse(D))))))),
    inference(flip,[status(thm),theory(equality)],[664]),
    [iquote('flip(664)')] ).

cnf(710,plain,
    equal(multiply(A,inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,A)))),inverse(C)),
    inference(para,[status(thm),theory(equality)],[438,1]),
    [iquote('para(438,1)')] ).

cnf(713,plain,
    equal(multiply(inverse(A),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))))),inverse(A)),
    inference(para,[status(thm),theory(equality)],[89,710]),
    [iquote('para(89,710)')] ).

cnf(716,plain,
    equal(multiply(A,inverse(A)),inverse(inverse(inverse(multiply(B,inverse(B)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[665]),713]),
    [iquote('back_demod(665),demod([713])')] ).

cnf(717,plain,
    equal(inverse(inverse(inverse(multiply(A,inverse(A))))),multiply(B,inverse(B))),
    inference(flip,[status(thm),theory(equality)],[716]),
    [iquote('flip(716)')] ).

cnf(718,plain,
    equal(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[567]),713]),
    [iquote('back_demod(567),demod([713])')] ).

cnf(720,plain,
    equal(multiply(A,inverse(multiply(B,inverse(B)))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[607]),718,718]),
    [iquote('back_demod(607),demod([718,718])')] ).

cnf(722,plain,
    equal(inverse(multiply(inverse(inverse(inverse(A))),inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C)))))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[659]),720]),
    [iquote('back_demod(659),demod([720])')] ).

cnf(730,plain,
    equal(multiply(inverse(multiply(multiply(A,inverse(A)),inverse(B))),inverse(inverse(multiply(C,inverse(C))))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[256]),720]),
    [iquote('back_demod(256),demod([720])')] ).

cnf(736,plain,
    equal(inverse(inverse(A)),multiply(multiply(B,inverse(B)),A)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[516]),713]),
    [iquote('back_demod(516),demod([713])')] ).

cnf(737,plain,
    equal(multiply(multiply(A,inverse(A)),B),inverse(inverse(B))),
    inference(flip,[status(thm),theory(equality)],[736]),
    [iquote('flip(736)')] ).

cnf(744,plain,
    equal(multiply(A,inverse(inverse(inverse(inverse(multiply(B,inverse(B))))))),A),
    inference(para,[status(thm),theory(equality)],[737,720]),
    [iquote('para(737,720)')] ).

cnf(756,plain,
    equal(multiply(A,inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))))),A),
    inference(para,[status(thm),theory(equality)],[717,720]),
    [iquote('para(717,720)')] ).

cnf(757,plain,
    equal(inverse(inverse(multiply(A,inverse(A)))),multiply(B,inverse(B))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[569]),756]),
    [iquote('back_demod(569),demod([756])')] ).

cnf(763,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C))))),A),
    inference(para,[status(thm),theory(equality)],[757,720]),
    [iquote('para(757,720)')] ).

cnf(764,plain,
    equal(inverse(inverse(inverse(inverse(A)))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[722]),763]),
    [iquote('back_demod(722),demod([763])')] ).

cnf(765,plain,
    equal(multiply(A,multiply(B,inverse(B))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[744]),764]),
    [iquote('back_demod(744),demod([764])')] ).

cnf(766,plain,
    equal(multiply(A,inverse(inverse(multiply(B,inverse(B))))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[763]),765]),
    [iquote('back_demod(763),demod([765])')] ).

cnf(767,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),inverse(B))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[730]),766]),
    [iquote('back_demod(730),demod([766])')] ).

cnf(771,plain,
    equal(multiply(multiply(A,B),inverse(B)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[93]),767,765]),
    [iquote('back_demod(93),demod([767,765])')] ).

cnf(978,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,C))),multiply(multiply(F,inverse(F)),inverse(G)))))))),multiply(inverse(multiply(inverse(multiply(H,multiply(multiply(multiply(I,inverse(I)),inverse(multiply(G,H))),J))),E)),inverse(multiply(B,J)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[419]),765,765]),
    [iquote('back_demod(419),demod([765,765])')] ).

cnf(979,plain,
    equal(multiply(inverse(multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),D))),E)),inverse(multiply(F,D))),multiply(multiply(G,inverse(G)),inverse(multiply(F,inverse(multiply(H,multiply(multiply(multiply(I,inverse(I)),inverse(multiply(E,H))),multiply(multiply(J,inverse(J)),inverse(C))))))))),
    inference(flip,[status(thm),theory(equality)],[978]),
    [iquote('flip(978)')] ).

cnf(988,plain,
    equal(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),D))),multiply(multiply(E,inverse(E)),inverse(multiply(multiply(multiply(F,inverse(F)),inverse(C)),D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[398]),765]),
    [iquote('back_demod(398),demod([765])')] ).

cnf(989,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(multiply(B,inverse(B)),inverse(C)),D))),inverse(multiply(E,multiply(multiply(multiply(F,inverse(F)),inverse(multiply(C,E))),D)))),
    inference(flip,[status(thm),theory(equality)],[988]),
    [iquote('flip(988)')] ).

cnf(1088,plain,
    equal(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,multiply(multiply(D,inverse(D)),inverse(multiply(E,C)))),A))),F))),multiply(G,inverse(multiply(E,multiply(F,G))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[193]),765,765]),
    [iquote('back_demod(193),demod([765,765])')] ).

cnf(1089,plain,
    equal(multiply(A,inverse(multiply(B,multiply(C,A)))),inverse(multiply(D,multiply(multiply(multiply(E,inverse(E)),inverse(multiply(multiply(F,multiply(multiply(G,inverse(G)),inverse(multiply(B,F)))),D))),C)))),
    inference(flip,[status(thm),theory(equality)],[1088]),
    [iquote('flip(1088)')] ).

cnf(1106,plain,
    equal(multiply(A,multiply(inverse(A),B)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[143]),765,765,767]),
    [iquote('back_demod(143),demod([765,765,767])')] ).

cnf(1107,plain,
    equal(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(inverse(C),inverse(B))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[142]),765,765]),
    [iquote('back_demod(142),demod([765,765])')] ).

cnf(1118,plain,
    equal(multiply(A,inverse(multiply(B,multiply(C,A)))),inverse(multiply(D,multiply(multiply(inverse(D),inverse(inverse(B))),C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1089]),1107,1106,1107]),
    [iquote('back_demod(1089),demod([1107,1106,1107])')] ).

cnf(1119,plain,
    equal(inverse(multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),C))),multiply(D,inverse(multiply(B,multiply(C,D))))),
    inference(flip,[status(thm),theory(equality)],[1118]),
    [iquote('flip(1118)')] ).

cnf(1208,plain,
    equal(inverse(multiply(A,multiply(multiply(inverse(A),inverse(B)),C))),multiply(inverse(C),B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[989]),1107,767,1107]),1]),
    [iquote('back_demod(989),demod([1107,767,1107]),flip(1)')] ).

cnf(1260,plain,
    equal(multiply(A,inverse(multiply(B,multiply(C,A)))),multiply(inverse(C),inverse(B))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1119]),1208]),1]),
    [iquote('back_demod(1119),demod([1208]),flip(1)')] ).

cnf(1331,plain,
    equal(multiply(A,inverse(inverse(multiply(inverse(A),B)))),inverse(inverse(B))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[53]),765,1260,1106,1260,767]),1]),
    [iquote('back_demod(53),demod([765,1260,1106,1260,767]),flip(1)')] ).

cnf(1335,plain,
    equal(inverse(multiply(inverse(inverse(A)),inverse(inverse(B)))),multiply(inverse(B),inverse(A))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[34]),1107,765,1260,1107,1260,720]),1]),
    [iquote('back_demod(34),demod([1107,765,1260,1107,1260,720]),flip(1)')] ).

cnf(1344,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),B),C)),inverse(multiply(D,A))),multiply(inverse(multiply(B,C)),inverse(D))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[979]),1107,1208,1107,1208,767,1107]),
    [iquote('back_demod(979),demod([1107,1208,1107,1208,767,1107])')] ).

cnf(1357,plain,
    equal(multiply(inverse(multiply(inverse(A),A)),inverse(inverse(B))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[58]),765,1107,1344]),
    [iquote('back_demod(58),demod([765,1107,1344])')] ).

cnf(1361,plain,
    equal(multiply(A,inverse(inverse(B))),multiply(A,B)),
    inference(para,[status(thm),theory(equality)],[771,771]),
    [iquote('para(771,771)')] ).

cnf(1363,plain,
    equal(multiply(inverse(multiply(inverse(A),A)),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1357]),1361]),
    [iquote('back_demod(1357),demod([1361])')] ).

cnf(1367,plain,
    equal(inverse(multiply(inverse(inverse(A)),B)),multiply(inverse(B),inverse(A))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1335]),1361]),
    [iquote('back_demod(1335),demod([1361])')] ).

cnf(1370,plain,
    equal(inverse(inverse(A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1331]),1361,1106]),1]),
    [iquote('back_demod(1331),demod([1361,1106]),flip(1)')] ).

cnf(1371,plain,
    equal(inverse(multiply(A,B)),multiply(inverse(B),inverse(A))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1367]),1370]),
    [iquote('back_demod(1367),demod([1370])')] ).

cnf(1373,plain,
    equal(multiply(multiply(inverse(A),A),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1363]),1371,1370]),
    [iquote('back_demod(1363),demod([1371,1370])')] ).

cnf(1374,plain,
    $false,
    inference(conflict,[status(thm)],[1373,2]),
    [iquote('conflict(1373,2)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP431-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12  % Command  : tptp2X_and_run_eqp %s
% 0.12/0.33  % Computer : n029.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  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 19:52:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.88/1.28  ----- EQP 0.9e, May 2009 -----
% 0.88/1.28  The job began on n029.cluster.edu, Mon Jun 13 19:52:56 2022
% 0.88/1.28  The command was "./eqp09e".
% 0.88/1.28  
% 0.88/1.28  set(prolog_style_variables).
% 0.88/1.28  set(lrpo).
% 0.88/1.28  set(basic_paramod).
% 0.88/1.28  set(functional_subsume).
% 0.88/1.28  set(ordered_paramod).
% 0.88/1.28  set(prime_paramod).
% 0.88/1.28  set(para_pairs).
% 0.88/1.28  assign(pick_given_ratio,4).
% 0.88/1.28  clear(print_kept).
% 0.88/1.28  clear(print_new_demod).
% 0.88/1.28  clear(print_back_demod).
% 0.88/1.28  clear(print_given).
% 0.88/1.28  assign(max_mem,64000).
% 0.88/1.28  end_of_commands.
% 0.88/1.28  
% 0.88/1.28  Usable:
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Sos:
% 0.88/1.28  0 (wt=-1) [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D.
% 0.88/1.28  0 (wt=-1) [] -(multiply(multiply(inverse(b2),b2),a2) = a2).
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Demodulators:
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Passive:
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Starting to process input.
% 0.88/1.28  
% 0.88/1.28  ** KEPT: 1 (wt=18) [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D.
% 0.88/1.28  1 is a new demodulator.
% 0.88/1.28  
% 0.88/1.28  ** KEPT: 2 (wt=8) [] -(multiply(multiply(inverse(b2),b2),a2) = a2).
% 0.88/1.28  ---------------- PROOF FOUND ----------------
% 0.88/1.28  % SZS status Unsatisfiable
% 0.88/1.28  
% 0.88/1.28  
% 0.88/1.28  After processing input:
% 0.88/1.28  
% 0.88/1.28  Usable:
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Sos:
% 0.88/1.28  2 (wt=8) [] -(multiply(multiply(inverse(b2),b2),a2) = a2).
% 0.88/1.28  1 (wt=18) [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D.
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Demodulators:
% 0.88/1.28  1 (wt=18) [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D.
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  Passive:
% 0.88/1.28  end_of_list.
% 0.88/1.28  
% 0.88/1.28  UNIT CONFLICT from 1373 and 2 at   0.17 seconds.
% 0.88/1.28  
% 0.88/1.28  ---------------- PROOF ----------------
% 0.88/1.28  % SZS output start Refutation
% See solution above
% 0.88/1.28  ------------ end of proof -------------
% 0.88/1.28  
% 0.88/1.28  
% 0.88/1.28  ------------- memory usage ------------
% 0.88/1.28  Memory dynamically allocated (tp_alloc): 4882.
% 0.88/1.28    type (bytes each)        gets      frees     in use      avail      bytes
% 0.88/1.28  sym_ent (  96)               56          0         56          0      5.2 K
% 0.88/1.28  term (  16)              148196      94084      54112         61   1052.7 K
% 0.88/1.28  gen_ptr (   8)           446832      95954     350878         99   2742.0 K
% 0.88/1.28  context ( 808)            91392      91390          2          4      4.7 K
% 0.88/1.28  trail (  12)              38078      38078          0         18      0.2 K
% 0.88/1.28  bt_node (  68)            13624      13621          3         46      3.3 K
% 0.88/1.28  ac_position (285432)          0          0          0          0      0.0 K
% 0.88/1.28  ac_match_pos (14044)          0          0          0          0      0.0 K
% 0.88/1.28  ac_match_free_vars_pos (4020)
% 0.88/1.28                                0          0          0          0      0.0 K
% 0.88/1.28  discrim (  12)            47956      45813       2143      24031    306.7 K
% 0.88/1.28  flat (  40)              523138     523138          0         93      3.6 K
% 0.88/1.28  discrim_pos (  12)         4739       4739          0          1      0.0 K
% 0.88/1.28  fpa_head (  12)            6181          0       6181          0     72.4 K
% 0.88/1.28  fpa_tree (  28)            8128       8128          0         23      0.6 K
% 0.88/1.28  fpa_pos (  36)             2264       2264          0          1      0.0 K
% 0.88/1.28  literal (  12)             4674       3301       1373          1     16.1 K
% 0.88/1.28  clause (  24)              4674       3301       1373          1     32.2 K
% 0.88/1.28  list (  12)                 950        891         59          5      0.8 K
% 0.88/1.28  list_pos (  20)            7875       5939       1936       1238     62.0 K
% 0.88/1.28  pair_index (   40)              2          0          2          0      0.1 K
% 0.88/1.28  
% 0.88/1.28  -------------- statistics -------------
% 0.88/1.28  Clauses input                  2
% 0.88/1.28    Usable input                   0
% 0.88/1.28    Sos input                      2
% 0.88/1.28    Demodulators input             0
% 0.88/1.28    Passive input                  0
% 0.88/1.28  
% 0.88/1.28  Processed BS (before search)   2
% 0.88/1.28  Forward subsumed BS            0
% 0.88/1.28  Kept BS                        2
% 0.88/1.28  New demodulators BS            1
% 0.88/1.28  Back demodulated BS            0
% 0.88/1.28  
% 0.88/1.28  Clauses or pairs given       929
% 0.88/1.28  Clauses generated           2609
% 0.88/1.28  Forward subsumed            1238
% 0.88/1.28  Deleted by weight              0
% 0.88/1.28  Deleted by variable count      0
% 0.88/1.28  Kept                        1371
% 0.88/1.28  New demodulators             890
% 0.88/1.28  Back demodulated            1225
% 0.88/1.28  Ordered paramod prunes         0
% 0.88/1.28  Basic paramod prunes        8564
% 0.88/1.28  Prime paramod prunes           0
% 0.88/1.28  Semantic prunes                0
% 0.88/1.28  
% 0.88/1.28  Rewrite attmepts           66453
% 0.88/1.28  Rewrites                    4108
% 0.88/1.28  
% 0.88/1.28  FPA overloads                  0
% 0.88/1.28  FPA underloads                 0
% 0.88/1.28  
% 0.88/1.28  Usable size                    0
% 0.88/1.28  Sos size                     147
% 0.88/1.28  Demodulators size             93
% 0.88/1.28  Passive size                   0
% 0.88/1.28  Disabled size               1225
% 0.88/1.28  
% 0.88/1.28  Proofs found                   1
% 0.88/1.28  
% 0.88/1.28  ----------- times (seconds) ----------- Mon Jun 13 19:52:56 2022
% 0.88/1.28  
% 0.88/1.28  user CPU time             0.17   (0 hr, 0 min, 0 sec)
% 0.88/1.28  system CPU time           0.05   (0 hr, 0 min, 0 sec)
% 0.88/1.28  wall-clock time           0      (0 hr, 0 min, 0 sec)
% 0.88/1.28  input time                0.00
% 0.88/1.28  paramodulation time       0.01
% 0.88/1.28  demodulation time         0.03
% 0.88/1.28  orient time               0.01
% 0.88/1.28  weigh time                0.00
% 0.88/1.28  forward subsume time      0.00
% 0.88/1.28  back demod find time      0.02
% 0.88/1.28  conflict time             0.00
% 0.88/1.28  LRPO time                 0.00
% 0.88/1.28  store clause time         0.06
% 0.88/1.28  disable clause time       0.01
% 0.88/1.28  prime paramod time        0.01
% 0.88/1.28  semantics time            0.00
% 0.88/1.28  
% 0.88/1.28  EQP interrupted
%------------------------------------------------------------------------------