TSTP Solution File: GRP440-1 by EQP---0.9e

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : EQP---0.9e
% Problem  : GRP440-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_eqp %s

% Computer : n009.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 08:47:21 EDT 2022

% Result   : Unsatisfiable 1.02s 1.39s
% Output   : Refutation 1.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   48
%            Number of leaves      :    2
% Syntax   : Number of clauses     :  120 ( 120 unt;   0 nHn;   2 RR)
%            Number of literals    :  120 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   14 (   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   :  445 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,plain,
    equal(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))),D),
    file('GRP440-1.p',unknown),
    [] ).

cnf(2,plain,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP440-1.p',unknown),
    [] ).

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

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

cnf(6,plain,
    equal(inverse(multiply(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))),multiply(E,multiply(multiply(inverse(E),multiply(multiply(D,F),inverse(multiply(G,multiply(H,F))))),G)))),H),
    inference(para,[status(thm),theory(equality)],[3,1]),
    [iquote('para(3,1)')] ).

cnf(9,plain,
    equal(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(F,D))))),E)),F)))),C),
    inference(para,[status(thm),theory(equality)],[4,1]),
    [iquote('para(4,1)')] ).

cnf(26,plain,
    equal(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(C,D),inverse(multiply(E,multiply(F,D))))),E)),F)))),multiply(G,multiply(H,multiply(multiply(inverse(H),I),inverse(multiply(C,multiply(G,I))))))),
    inference(para,[status(thm),theory(equality)],[6,1]),
    [iquote('para(6,1)')] ).

cnf(1034,plain,
    equal(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(inverse(D),multiply(A,C)))))),D),
    inference(para,[status(thm),theory(equality)],[26,9]),
    [iquote('para(26,9)')] ).

cnf(1035,plain,
    equal(inverse(multiply(A,multiply(B,multiply(C,inverse(multiply(D,multiply(A,multiply(E,multiply(multiply(inverse(E),F),inverse(multiply(inverse(C),multiply(inverse(B),F)))))))))))),D),
    inference(para,[status(thm),theory(equality)],[1034,1]),
    [iquote('para(1034,1)')] ).

cnf(1043,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,B)))))),C),
    inference(para,[status(thm),theory(equality)],[1034,1035]),
    [iquote('para(1034,1035)')] ).

cnf(1049,plain,
    equal(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D)))),inverse(A)),
    inference(para,[status(thm),theory(equality)],[1043,1]),
    [iquote('para(1043,1)')] ).

cnf(1055,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D)),inverse(E))))),E),
    inference(para,[status(thm),theory(equality)],[1049,1043]),
    [iquote('para(1049,1043)')] ).

cnf(1079,plain,
    equal(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D))),A),
    inference(para,[status(thm),theory(equality)],[1055,1043]),
    [iquote('para(1055,1043)')] ).

cnf(1082,plain,
    equal(inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A)))))),C),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1079,1]),1079]),
    [iquote('para(1079,1),demod([1079])')] ).

cnf(1085,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)))),D),
    inference(para,[status(thm),theory(equality)],[1082,1043]),
    [iquote('para(1082,1043)')] ).

cnf(1086,plain,
    equal(inverse(multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),multiply(D,multiply(inverse(D),C)))),inverse(A)),
    inference(para,[status(thm),theory(equality)],[1043,1082]),
    [iquote('para(1043,1082)')] ).

cnf(1091,plain,
    equal(inverse(multiply(multiply(A,multiply(multiply(inverse(A),multiply(B,inverse(multiply(C,B)))),C)),multiply(D,multiply(inverse(D),inverse(E))))),E),
    inference(para,[status(thm),theory(equality)],[1079,1082]),
    [iquote('para(1079,1082)')] ).

cnf(1105,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),C)),inverse(D))))),multiply(D,multiply(E,inverse(multiply(C,E))))),
    inference(para,[status(thm),theory(equality)],[1086,1043]),
    [iquote('para(1086,1043)')] ).

cnf(1184,plain,
    equal(inverse(multiply(multiply(A,multiply(multiply(inverse(A),multiply(B,inverse(multiply(C,B)))),C)),multiply(D,multiply(inverse(D),E)))),multiply(F,multiply(G,multiply(inverse(G),inverse(multiply(E,F)))))),
    inference(para,[status(thm),theory(equality)],[1082,1091]),
    [iquote('para(1082,1091)')] ).

cnf(1185,plain,
    equal(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A))))),inverse(multiply(multiply(D,multiply(multiply(inverse(D),multiply(E,inverse(multiply(F,E)))),F)),multiply(G,multiply(inverse(G),C))))),
    inference(flip,[status(thm),theory(equality)],[1184]),
    [iquote('flip(1184)')] ).

cnf(1199,plain,
    equal(multiply(multiply(A,multiply(B,multiply(inverse(B),C))),multiply(D,inverse(multiply(C,D)))),A),
    inference(para,[status(thm),theory(equality)],[1105,1043]),
    [iquote('para(1105,1043)')] ).

cnf(1202,plain,
    equal(inverse(multiply(inverse(multiply(A,multiply(B,multiply(inverse(B),C)))),A)),C),
    inference(para,[status(thm),theory(equality)],[1199,1043]),
    [iquote('para(1199,1043)')] ).

cnf(1203,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(B,C)))),inverse(multiply(B,multiply(D,multiply(inverse(D),C))))),
    inference(para,[status(thm),theory(equality)],[1202,1043]),
    [iquote('para(1202,1043)')] ).

cnf(1210,plain,
    equal(inverse(inverse(multiply(multiply(A,multiply(multiply(inverse(A),multiply(B,inverse(multiply(C,B)))),C)),multiply(D,multiply(inverse(D),E))))),E),
    inference(para,[status(thm),theory(equality)],[1079,1202]),
    [iquote('para(1079,1202)')] ).

cnf(1245,plain,
    equal(inverse(multiply(inverse(A),multiply(A,B))),inverse(multiply(B,multiply(C,inverse(C))))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1079,1203]),1079]),
    [iquote('para(1079,1203),demod([1079])')] ).

cnf(1246,plain,
    equal(inverse(multiply(A,multiply(B,inverse(B)))),inverse(multiply(inverse(C),multiply(C,A)))),
    inference(flip,[status(thm),theory(equality)],[1245]),
    [iquote('flip(1245)')] ).

cnf(1250,plain,
    equal(inverse(multiply(multiply(A,inverse(multiply(B,A))),multiply(C,inverse(C)))),B),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1043,1245]),1]),
    [iquote('para(1043,1245),flip(1)')] ).

cnf(1251,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,C),inverse(multiply(C,multiply(D,inverse(D)))))))),inverse(B)),
    inference(para,[status(thm),theory(equality)],[1245,1043]),
    [iquote('para(1245,1043)')] ).

cnf(1253,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(B)),C)))),multiply(D,inverse(multiply(C,D)))),
    inference(para,[status(thm),theory(equality)],[1250,1043]),
    [iquote('para(1250,1043)')] ).

cnf(1256,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(inverse(B),C)))),multiply(D,inverse(multiply(C,D)))),
    inference(para,[status(thm),theory(equality)],[1250,1082]),
    [iquote('para(1250,1082)')] ).

cnf(1257,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(multiply(multiply(C,inverse(C)),multiply(D,multiply(inverse(D),B))))),
    inference(flip,[status(thm),theory(equality)],[1256]),
    [iquote('flip(1256)')] ).

cnf(1271,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),multiply(C,D))))))),D),
    inference(para,[status(thm),theory(equality)],[1246,1082]),
    [iquote('para(1246,1082)')] ).

cnf(1284,plain,
    equal(inverse(multiply(A,multiply(B,inverse(B)))),inverse(multiply(A,multiply(C,inverse(C))))),
    inference(para,[status(thm),theory(equality)],[1245,1245]),
    [iquote('para(1245,1245)')] ).

cnf(1285,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D)))))))),C),
    inference(para,[status(thm),theory(equality)],[1284,1043]),
    [iquote('para(1284,1043)')] ).

cnf(1290,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(inverse(B),inverse(multiply(C,multiply(D,inverse(D)))))))),C),
    inference(para,[status(thm),theory(equality)],[1284,1082]),
    [iquote('para(1284,1082)')] ).

cnf(1293,plain,
    equal(inverse(multiply(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(inverse(B),C)))),multiply(D,inverse(D)))),C),
    inference(para,[status(thm),theory(equality)],[1284,1202]),
    [iquote('para(1284,1202)')] ).

cnf(1323,plain,
    equal(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C)))),multiply(D,inverse(multiply(C,D)))),
    inference(para,[status(thm),theory(equality)],[1250,1]),
    [iquote('para(1250,1)')] ).

cnf(1324,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(C)),B))))),
    inference(flip,[status(thm),theory(equality)],[1323]),
    [iquote('flip(1323)')] ).

cnf(1360,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,inverse(C)))),A))),B),
    inference(para,[status(thm),theory(equality)],[1253,1043]),
    [iquote('para(1253,1043)')] ).

cnf(1399,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,C))),multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(C,multiply(E,inverse(E)))),inverse(B))),D)))),
    inference(para,[status(thm),theory(equality)],[1360,1256]),
    [iquote('para(1360,1256)')] ).

cnf(1400,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,inverse(C)))),inverse(D))),A))),inverse(multiply(multiply(E,inverse(E)),multiply(D,B)))),
    inference(flip,[status(thm),theory(equality)],[1399]),
    [iquote('flip(1399)')] ).

cnf(1402,plain,
    equal(inverse(multiply(inverse(multiply(A,B)),multiply(C,multiply(inverse(C),inverse(inverse(multiply(multiply(D,inverse(D)),multiply(E,multiply(inverse(E),A))))))))),B),
    inference(para,[status(thm),theory(equality)],[1257,1082]),
    [iquote('para(1257,1082)')] ).

cnf(1422,plain,
    equal(inverse(multiply(inverse(A),multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(B)),D))))))),D),
    inference(para,[status(thm),theory(equality)],[1324,1043]),
    [iquote('para(1324,1043)')] ).

cnf(1438,plain,
    equal(inverse(multiply(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,C)))),B),multiply(D,inverse(D)))),C),
    inference(flip,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1085,1245]),1]),
    [iquote('para(1085,1245),flip(1)')] ).

cnf(1440,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(B)),C)))),multiply(multiply(D,multiply(inverse(D),inverse(multiply(E,C)))),E)),
    inference(para,[status(thm),theory(equality)],[1438,1043]),
    [iquote('para(1438,1043)')] ).

cnf(1441,plain,
    equal(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,C)))),B),inverse(multiply(inverse(D),multiply(D,multiply(multiply(E,inverse(E)),C))))),
    inference(flip,[status(thm),theory(equality)],[1440]),
    [iquote('flip(1440)')] ).

cnf(1471,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(multiply(multiply(multiply(C,inverse(C)),B),multiply(D,inverse(D))))),
    inference(para,[status(thm),theory(equality)],[1253,1245]),
    [iquote('para(1253,1245)')] ).

cnf(1474,plain,
    equal(inverse(multiply(inverse(A),multiply(A,inverse(multiply(multiply(multiply(B,inverse(B)),C),multiply(D,inverse(D))))))),C),
    inference(para,[status(thm),theory(equality)],[1471,1043]),
    [iquote('para(1471,1043)')] ).

cnf(1580,plain,
    equal(inverse(multiply(inverse(A),inverse(multiply(multiply(multiply(B,inverse(B)),C),multiply(D,inverse(D)))))),inverse(multiply(inverse(multiply(C,A)),multiply(E,inverse(E))))),
    inference(para,[status(thm),theory(equality)],[1471,1245]),
    [iquote('para(1471,1245)')] ).

cnf(1581,plain,
    equal(inverse(multiply(inverse(multiply(A,B)),multiply(C,inverse(C)))),inverse(multiply(inverse(B),inverse(multiply(multiply(multiply(D,inverse(D)),A),multiply(E,inverse(E))))))),
    inference(flip,[status(thm),theory(equality)],[1580]),
    [iquote('flip(1580)')] ).

cnf(1621,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),D)))))),inverse(multiply(inverse(multiply(D,multiply(E,inverse(E)))),C))),
    inference(para,[status(thm),theory(equality)],[1360,1271]),
    [iquote('para(1360,1271)')] ).

cnf(1622,plain,
    equal(inverse(multiply(inverse(multiply(A,multiply(B,inverse(B)))),C)),inverse(multiply(multiply(D,inverse(D)),multiply(E,multiply(inverse(E),inverse(multiply(inverse(C),A))))))),
    inference(flip,[status(thm),theory(equality)],[1621]),
    [iquote('flip(1621)')] ).

cnf(1630,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(multiply(inverse(multiply(D,multiply(E,multiply(inverse(E),F)))),D),F))))))),C),
    inference(para,[status(thm),theory(equality)],[1202,1285]),
    [iquote('para(1202,1285)')] ).

cnf(1634,plain,
    equal(multiply(A,inverse(A)),multiply(B,inverse(B))),
    inference(demod,[status(thm),theory(equality)],[inference(para,[status(thm),theory(equality)],[1290,1043]),1085]),
    [iquote('para(1290,1043),demod([1085])')] ).

cnf(1639,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(inverse(B),inverse(multiply(C,inverse(C))))))),B),
    inference(para,[status(thm),theory(equality)],[1634,1043]),
    [iquote('para(1634,1043)')] ).

cnf(1642,plain,
    equal(inverse(multiply(inverse(A),multiply(B,multiply(inverse(B),inverse(multiply(C,inverse(C))))))),A),
    inference(para,[status(thm),theory(equality)],[1634,1082]),
    [iquote('para(1634,1082)')] ).

cnf(1692,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(C,inverse(C))))),multiply(D,inverse(multiply(inverse(inverse(B)),D)))),
    inference(para,[status(thm),theory(equality)],[1634,1256]),
    [iquote('para(1634,1256)')] ).

cnf(1693,plain,
    equal(multiply(A,inverse(multiply(inverse(inverse(B)),A))),inverse(multiply(multiply(C,inverse(C)),multiply(B,multiply(D,inverse(D)))))),
    inference(flip,[status(thm),theory(equality)],[1692]),
    [iquote('flip(1692)')] ).

cnf(1696,plain,
    equal(inverse(multiply(A,multiply(B,multiply(C,inverse(C))))),multiply(D,inverse(multiply(inverse(multiply(inverse(B),inverse(A))),D)))),
    inference(para,[status(thm),theory(equality)],[1634,1323]),
    [iquote('para(1634,1323)')] ).

cnf(1697,plain,
    equal(multiply(A,inverse(multiply(inverse(multiply(inverse(B),inverse(C))),A))),inverse(multiply(C,multiply(B,multiply(D,inverse(D)))))),
    inference(flip,[status(thm),theory(equality)],[1696]),
    [iquote('flip(1696)')] ).

cnf(1716,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(B))))),inverse(multiply(C,inverse(C)))),
    inference(para,[status(thm),theory(equality)],[1634,1251]),
    [iquote('para(1634,1251)')] ).

cnf(1756,plain,
    equal(inverse(multiply(inverse(A),multiply(A,inverse(multiply(B,multiply(C,multiply(D,inverse(D)))))))),inverse(multiply(inverse(C),inverse(B)))),
    inference(para,[status(thm),theory(equality)],[1634,1422]),
    [iquote('para(1634,1422)')] ).

cnf(1762,plain,
    equal(inverse(multiply(inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C)))),multiply(D,inverse(D)))),B),
    inference(para,[status(thm),theory(equality)],[1634,1474]),
    [iquote('para(1634,1474)')] ).

cnf(1792,plain,
    equal(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(B))))),multiply(C,multiply(inverse(C),D))),D),
    inference(para,[status(thm),theory(equality)],[1642,1202]),
    [iquote('para(1642,1202)')] ).

cnf(1797,plain,
    equal(inverse(multiply(inverse(A),multiply(inverse(multiply(B,multiply(C,inverse(C)))),B))),A),
    inference(para,[status(thm),theory(equality)],[1360,1642]),
    [iquote('para(1360,1642)')] ).

cnf(1880,plain,
    equal(inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),multiply(C,inverse(C)))),A),
    inference(para,[status(thm),theory(equality)],[1245,1639]),
    [iquote('para(1245,1639)')] ).

cnf(1888,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(inverse(B),C)))),multiply(inverse(C),inverse(multiply(D,inverse(D))))),
    inference(para,[status(thm),theory(equality)],[1880,1082]),
    [iquote('para(1880,1082)')] ).

cnf(1905,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,multiply(C,inverse(C))))),multiply(inverse(inverse(inverse(B))),inverse(multiply(D,inverse(D))))),
    inference(para,[status(thm),theory(equality)],[1634,1888]),
    [iquote('para(1634,1888)')] ).

cnf(1906,plain,
    equal(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,inverse(B)))),inverse(multiply(multiply(C,inverse(C)),multiply(A,multiply(D,inverse(D)))))),
    inference(flip,[status(thm),theory(equality)],[1905]),
    [iquote('flip(1905)')] ).

cnf(1914,plain,
    equal(inverse(multiply(A,inverse(A))),inverse(multiply(multiply(B,inverse(B)),multiply(C,inverse(C))))),
    inference(para,[status(thm),theory(equality)],[1716,1245]),
    [iquote('para(1716,1245)')] ).

cnf(1915,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))),inverse(multiply(C,inverse(C)))),
    inference(flip,[status(thm),theory(equality)],[1914]),
    [iquote('flip(1914)')] ).

cnf(1933,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))))),multiply(D,inverse(D))),
    inference(para,[status(thm),theory(equality)],[1915,1043]),
    [iquote('para(1915,1043)')] ).

cnf(1955,plain,
    equal(inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(B))))),multiply(C,inverse(C))),
    inference(para,[status(thm),theory(equality)],[1634,1933]),
    [iquote('para(1634,1933)')] ).

cnf(2041,plain,
    equal(inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),multiply(multiply(inverse(C),multiply(inverse(multiply(D,multiply(E,inverse(E)))),D)),C))),A),
    inference(para,[status(thm),theory(equality)],[1797,1880]),
    [iquote('para(1797,1880)')] ).

cnf(2042,plain,
    equal(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),
    inference(para,[status(thm),theory(equality)],[1955,1716]),
    [iquote('para(1955,1716)')] ).

cnf(2050,plain,
    equal(inverse(multiply(inverse(A),multiply(B,multiply(inverse(B),inverse(inverse(multiply(C,inverse(C)))))))),A),
    inference(para,[status(thm),theory(equality)],[2042,1082]),
    [iquote('para(2042,1082)')] ).

cnf(2099,plain,
    equal(inverse(multiply(inverse(A),multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C)))))),A),
    inference(para,[status(thm),theory(equality)],[2042,2050]),
    [iquote('para(2042,2050)')] ).

cnf(2102,plain,
    equal(inverse(multiply(inverse(A),multiply(B,inverse(B)))),A),
    inference(para,[status(thm),theory(equality)],[1634,2099]),
    [iquote('para(1634,2099)')] ).

cnf(2106,plain,
    equal(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1762]),2102]),
    [iquote('back_demod(1762),demod([2102])')] ).

cnf(2119,plain,
    equal(inverse(multiply(inverse(A),inverse(B))),multiply(B,A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1581]),2102,2106]),1]),
    [iquote('back_demod(1581),demod([2102,2106]),flip(1)')] ).

cnf(2122,plain,
    equal(inverse(multiply(inverse(A),multiply(A,inverse(multiply(B,multiply(C,multiply(D,inverse(D)))))))),multiply(B,C)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1756]),2119]),
    [iquote('back_demod(1756),demod([2119])')] ).

cnf(2123,plain,
    equal(multiply(A,inverse(multiply(multiply(B,C),A))),inverse(multiply(B,multiply(C,multiply(D,inverse(D)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1697]),2119]),
    [iquote('back_demod(1697),demod([2119])')] ).

cnf(2124,plain,
    equal(inverse(multiply(A,multiply(B,multiply(C,inverse(C))))),multiply(D,inverse(multiply(multiply(A,B),D)))),
    inference(flip,[status(thm),theory(equality)],[2123]),
    [iquote('flip(2123)')] ).

cnf(2137,plain,
    equal(multiply(A,inverse(multiply(multiply(B,multiply(C,multiply(D,inverse(D)))),A))),inverse(multiply(multiply(E,inverse(E)),multiply(B,C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1400]),2119]),
    [iquote('back_demod(1400),demod([2119])')] ).

cnf(2138,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,C))),multiply(D,inverse(multiply(multiply(B,multiply(C,multiply(E,inverse(E)))),D)))),
    inference(flip,[status(thm),theory(equality)],[2137]),
    [iquote('flip(2137)')] ).

cnf(2144,plain,
    equal(inverse(multiply(inverse(A),multiply(A,inverse(B)))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1474]),2106]),
    [iquote('back_demod(1474),demod([2106])')] ).

cnf(2145,plain,
    equal(multiply(A,multiply(B,multiply(C,inverse(C)))),multiply(A,B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2122]),2144]),
    [iquote('back_demod(2122),demod([2144])')] ).

cnf(2160,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,C))),multiply(D,inverse(multiply(multiply(B,C),D)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2138]),2145]),
    [iquote('back_demod(2138),demod([2145])')] ).

cnf(2161,plain,
    equal(multiply(A,inverse(multiply(multiply(B,C),A))),inverse(multiply(multiply(D,inverse(D)),multiply(B,C)))),
    inference(flip,[status(thm),theory(equality)],[2160]),
    [iquote('flip(2160)')] ).

cnf(2162,plain,
    equal(multiply(A,inverse(multiply(multiply(B,C),A))),inverse(multiply(B,C))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2124]),2145]),1]),
    [iquote('back_demod(2124),demod([2145]),flip(1)')] ).

cnf(2163,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),multiply(B,C))),inverse(multiply(B,C))),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2161]),2162]),1]),
    [iquote('back_demod(2161),demod([2162]),flip(1)')] ).

cnf(2189,plain,
    equal(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,inverse(B)))),inverse(multiply(multiply(C,inverse(C)),A))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1906]),2145]),
    [iquote('back_demod(1906),demod([2145])')] ).

cnf(2190,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),B)),multiply(inverse(inverse(inverse(B))),inverse(multiply(C,inverse(C))))),
    inference(flip,[status(thm),theory(equality)],[2189]),
    [iquote('flip(2189)')] ).

cnf(2197,plain,
    equal(multiply(A,inverse(multiply(inverse(inverse(B)),A))),inverse(multiply(multiply(C,inverse(C)),B))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1693]),2145]),
    [iquote('back_demod(1693),demod([2145])')] ).

cnf(2198,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),B)),multiply(C,inverse(multiply(inverse(inverse(B)),C)))),
    inference(flip,[status(thm),theory(equality)],[2197]),
    [iquote('flip(2197)')] ).

cnf(2203,plain,
    equal(inverse(multiply(inverse(multiply(A,multiply(B,inverse(B)))),C)),inverse(multiply(D,multiply(inverse(D),inverse(multiply(inverse(C),A)))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1622]),2163]),
    [iquote('back_demod(1622),demod([2163])')] ).

cnf(2204,plain,
    equal(inverse(multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),C))))),inverse(multiply(inverse(multiply(C,multiply(D,inverse(D)))),B))),
    inference(flip,[status(thm),theory(equality)],[2203]),
    [iquote('flip(2203)')] ).

cnf(2210,plain,
    equal(inverse(multiply(inverse(multiply(A,B)),multiply(C,multiply(inverse(C),inverse(inverse(multiply(D,multiply(inverse(D),A)))))))),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1402]),2163]),
    [iquote('back_demod(1402),demod([2163])')] ).

cnf(2212,plain,
    equal(multiply(A,multiply(inverse(A),B)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1293]),2163,2102]),
    [iquote('back_demod(1293),demod([2163,2102])')] ).

cnf(2214,plain,
    equal(multiply(inverse(A),multiply(A,B)),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2210]),2212,2212,2119]),
    [iquote('back_demod(2210),demod([2212,2212,2119])')] ).

cnf(2226,plain,
    equal(inverse(inverse(A)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2144]),2214]),
    [iquote('back_demod(2144),demod([2214])')] ).

cnf(2228,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),B)),multiply(C,inverse(multiply(B,C)))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2198]),2226]),
    [iquote('back_demod(2198),demod([2226])')] ).

cnf(2229,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(multiply(multiply(C,inverse(C)),B))),
    inference(flip,[status(thm),theory(equality)],[2228]),
    [iquote('flip(2228)')] ).

cnf(2230,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),B)),multiply(inverse(B),inverse(multiply(C,inverse(C))))),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2190]),2226]),
    [iquote('back_demod(2190),demod([2226])')] ).

cnf(2231,plain,
    equal(multiply(inverse(A),inverse(multiply(B,inverse(B)))),inverse(multiply(multiply(C,inverse(C)),A))),
    inference(flip,[status(thm),theory(equality)],[2230]),
    [iquote('flip(2230)')] ).

cnf(2250,plain,
    equal(multiply(multiply(A,multiply(multiply(inverse(A),multiply(B,inverse(multiply(C,B)))),C)),D),D),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1210]),2212,2226]),
    [iquote('back_demod(1210),demod([2212,2226])')] ).

cnf(2251,plain,
    equal(multiply(A,inverse(multiply(B,A))),inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1185]),2212,2212,2250]),
    [iquote('back_demod(1185),demod([2212,2212,2250])')] ).

cnf(2257,plain,
    equal(inverse(multiply(multiply(A,inverse(A)),B)),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2229]),2251]),1]),
    [iquote('back_demod(2229),demod([2251]),flip(1)')] ).

cnf(2258,plain,
    equal(multiply(inverse(A),inverse(multiply(B,inverse(B)))),inverse(A)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2231]),2257]),
    [iquote('back_demod(2231),demod([2257])')] ).

cnf(2259,plain,
    equal(inverse(multiply(inverse(A),multiply(multiply(inverse(B),multiply(inverse(multiply(C,multiply(D,inverse(D)))),C)),B))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2041]),2258]),
    [iquote('back_demod(2041),demod([2258])')] ).

cnf(2268,plain,
    equal(multiply(multiply(A,inverse(A)),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1792]),2258,2212]),
    [iquote('back_demod(1792),demod([2258,2212])')] ).

cnf(2274,plain,
    equal(multiply(A,multiply(B,inverse(B))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2106]),2268]),
    [iquote('back_demod(2106),demod([2268])')] ).

cnf(2275,plain,
    equal(inverse(multiply(inverse(A),multiply(multiply(inverse(B),multiply(inverse(C),C)),B))),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2259]),2274]),
    [iquote('back_demod(2259),demod([2274])')] ).

cnf(2276,plain,
    equal(inverse(multiply(inverse(A),B)),multiply(inverse(B),A)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2204]),2212,2226,2274]),1]),
    [iquote('back_demod(2204),demod([2212,2226,2274]),flip(1)')] ).

cnf(2277,plain,
    equal(multiply(inverse(multiply(multiply(inverse(A),multiply(inverse(B),B)),A)),C),C),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2275]),2276]),
    [iquote('back_demod(2275),demod([2276])')] ).

cnf(2293,plain,
    equal(multiply(A,multiply(multiply(inverse(multiply(B,C)),B),C)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1630]),2212,2268,2214,2226]),
    [iquote('back_demod(1630),demod([2212,2268,2214,2226])')] ).

cnf(2297,plain,
    equal(multiply(inverse(multiply(A,B)),A),inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[1441]),2212,2268,2214]),
    [iquote('back_demod(1441),demod([2212,2268,2214])')] ).

cnf(2298,plain,
    equal(multiply(A,multiply(inverse(B),B)),A),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2293]),2297]),
    [iquote('back_demod(2293),demod([2297])')] ).

cnf(2299,plain,
    equal(multiply(multiply(inverse(A),A),B),B),
    inference(demod,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[2277]),2298,2276]),
    [iquote('back_demod(2277),demod([2298,2276])')] ).

cnf(2300,plain,
    $false,
    inference(conflict,[status(thm)],[2299,2]),
    [iquote('conflict(2299,2)')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP440-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13  % Command  : tptp2X_and_run_eqp %s
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 10:38:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.02/1.39  ----- EQP 0.9e, May 2009 -----
% 1.02/1.39  The job began on n009.cluster.edu, Mon Jun 13 10:38:08 2022
% 1.02/1.39  The command was "./eqp09e".
% 1.02/1.39  
% 1.02/1.39  set(prolog_style_variables).
% 1.02/1.39  set(lrpo).
% 1.02/1.39  set(basic_paramod).
% 1.02/1.39  set(functional_subsume).
% 1.02/1.39  set(ordered_paramod).
% 1.02/1.39  set(prime_paramod).
% 1.02/1.39  set(para_pairs).
% 1.02/1.39  assign(pick_given_ratio,4).
% 1.02/1.39  clear(print_kept).
% 1.02/1.39  clear(print_new_demod).
% 1.02/1.39  clear(print_back_demod).
% 1.02/1.39  clear(print_given).
% 1.02/1.39  assign(max_mem,64000).
% 1.02/1.39  end_of_commands.
% 1.02/1.39  
% 1.02/1.39  Usable:
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Sos:
% 1.02/1.39  0 (wt=-1) [] inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D.
% 1.02/1.39  0 (wt=-1) [] -(multiply(multiply(inverse(b2),b2),a2) = a2).
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Demodulators:
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Passive:
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Starting to process input.
% 1.02/1.39  
% 1.02/1.39  ** KEPT: 1 (wt=18) [] inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D.
% 1.02/1.39  1 is a new demodulator.
% 1.02/1.39  
% 1.02/1.39  ** KEPT: 2 (wt=8) [] -(multiply(multiply(inverse(b2),b2),a2) = a2).
% 1.02/1.39  ---------------- PROOF FOUND ----------------
% 1.02/1.39  % SZS status Unsatisfiable
% 1.02/1.39  
% 1.02/1.39  
% 1.02/1.39  After processing input:
% 1.02/1.39  
% 1.02/1.39  Usable:
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Sos:
% 1.02/1.39  2 (wt=8) [] -(multiply(multiply(inverse(b2),b2),a2) = a2).
% 1.02/1.39  1 (wt=18) [] inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D.
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Demodulators:
% 1.02/1.39  1 (wt=18) [] inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D.
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  Passive:
% 1.02/1.39  end_of_list.
% 1.02/1.39  
% 1.02/1.39  UNIT CONFLICT from 2299 and 2 at   0.28 seconds.
% 1.02/1.39  
% 1.02/1.39  ---------------- PROOF ----------------
% 1.02/1.39  % SZS output start Refutation
% See solution above
% 1.02/1.40  ------------ end of proof -------------
% 1.02/1.40  
% 1.02/1.40  
% 1.02/1.40  ------------- memory usage ------------
% 1.02/1.40  Memory dynamically allocated (tp_alloc): 10253.
% 1.02/1.40    type (bytes each)        gets      frees     in use      avail      bytes
% 1.02/1.40  sym_ent (  96)               56          0         56          0      5.2 K
% 1.02/1.40  term (  16)              237301     120244     117057         43   2278.1 K
% 1.02/1.40  gen_ptr (   8)           832087      21332     810755        119   6335.0 K
% 1.02/1.40  context ( 808)           173944     173942          2          3      3.9 K
% 1.02/1.40  trail (  12)              89609      89609          0         27      0.3 K
% 1.02/1.40  bt_node (  68)            40763      40756          7         66      4.8 K
% 1.02/1.40  ac_position (285432)          0          0          0          0      0.0 K
% 1.02/1.40  ac_match_pos (14044)          0          0          0          0      0.0 K
% 1.02/1.40  ac_match_free_vars_pos (4020)
% 1.02/1.40                                0          0          0          0      0.0 K
% 1.02/1.40  discrim (  12)            76033       6878      69155       4281    860.6 K
% 1.02/1.40  flat (  40)              604717     604717          0        119      4.6 K
% 1.02/1.40  discrim_pos (  12)         2109       2109          0          1      0.0 K
% 1.02/1.40  fpa_head (  12)            4524          0       4524          0     53.0 K
% 1.02/1.40  fpa_tree (  28)           13576      13576          0         27      0.7 K
% 1.02/1.40  fpa_pos (  36)             3623       3623          0          1      0.0 K
% 1.02/1.40  literal (  12)             7031       4732       2299          1     27.0 K
% 1.02/1.40  clause (  24)              7031       4732       2299          1     53.9 K
% 1.02/1.40  list (  12)                1383       1309         74          0      0.9 K
% 1.02/1.40  list_pos (  20)           10824       2208       8616        388    175.9 K
% 1.02/1.40  pair_index (   40)              2          0          2          0      0.1 K
% 1.02/1.40  
% 1.02/1.40  -------------- statistics -------------
% 1.02/1.40  Clauses input                  2
% 1.02/1.40    Usable input                   0
% 1.02/1.40    Sos input                      2
% 1.02/1.40    Demodulators input             0
% 1.02/1.40    Passive input                  0
% 1.02/1.40  
% 1.02/1.40  Processed BS (before search)   2
% 1.02/1.40  Forward subsumed BS            0
% 1.02/1.40  Kept BS                        2
% 1.02/1.40  New demodulators BS            1
% 1.02/1.40  Back demodulated BS            0
% 1.02/1.40  
% 1.02/1.40  Clauses or pairs given      2628
% 1.02/1.40  Clauses generated           3539
% 1.02/1.40  Forward subsumed            1242
% 1.02/1.40  Deleted by weight              0
% 1.02/1.40  Deleted by variable count      0
% 1.02/1.40  Kept                        2297
% 1.02/1.40  New demodulators            1323
% 1.02/1.40  Back demodulated             509
% 1.02/1.40  Ordered paramod prunes         0
% 1.02/1.40  Basic paramod prunes       30254
% 1.02/1.40  Prime paramod prunes           4
% 1.02/1.40  Semantic prunes                0
% 1.02/1.40  
% 1.02/1.40  Rewrite attmepts           92733
% 1.02/1.40  Rewrites                    1320
% 1.02/1.40  
% 1.02/1.40  FPA overloads                  0
% 1.02/1.40  FPA underloads                 0
% 1.02/1.40  
% 1.02/1.40  Usable size                    0
% 1.02/1.40  Sos size                    1789
% 1.02/1.40  Demodulators size           1158
% 1.02/1.40  Passive size                   0
% 1.02/1.40  Disabled size                509
% 1.02/1.40  
% 1.02/1.40  Proofs found                   1
% 1.02/1.40  
% 1.02/1.40  ----------- times (seconds) ----------- Mon Jun 13 10:38:09 2022
% 1.02/1.40  
% 1.02/1.40  user CPU time             0.28   (0 hr, 0 min, 0 sec)
% 1.02/1.40  system CPU time           0.06   (0 hr, 0 min, 0 sec)
% 1.02/1.40  wall-clock time           1      (0 hr, 0 min, 1 sec)
% 1.02/1.40  input time                0.00
% 1.02/1.40  paramodulation time       0.03
% 1.02/1.40  demodulation time         0.02
% 1.02/1.40  orient time               0.01
% 1.02/1.40  weigh time                0.00
% 1.02/1.40  forward subsume time      0.01
% 1.02/1.40  back demod find time      0.04
% 1.02/1.40  conflict time             0.00
% 1.02/1.40  LRPO time                 0.01
% 1.02/1.40  store clause time         0.11
% 1.02/1.40  disable clause time       0.02
% 1.02/1.40  prime paramod time        0.01
% 1.02/1.40  semantics time            0.00
% 1.02/1.40  
% 1.02/1.40  EQP interrupted
%------------------------------------------------------------------------------