TSTP Solution File: GRP051-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP051-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 11:45:00 EDT 2022

% Result   : Unsatisfiable 1.08s 1.26s
% Output   : Refutation 1.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :    2
% Syntax   : Number of clauses     :  110 ( 105 unt;   0 nHn; 110 RR)
%            Number of literals    :  118 (   0 equ;  15 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   16 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  13 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),v),
    file('GRP051-1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
    | ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
    | ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
    file('GRP051-1.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),multiply(inverse(multiply(x,inverse(multiply(v,w)))),multiply(x,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(4,plain,
    equal(multiply(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(x,multiply(inverse(w),w))))),v),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),x),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(63,plain,
    equal(multiply(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w)))),multiply(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(inverse(multiply(inverse(w),w))))),inverse(inverse(multiply(inverse(y),y))))),inverse(multiply(inverse(inverse(multiply(inverse(y),y))),inverse(multiply(inverse(y),y))))),multiply(inverse(multiply(z,inverse(multiply(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))),y)))),multiply(z,inverse(y)))),
    inference(spr,[status(thm),theory(equality)],[3]),
    [iquote('0:SpR:3.0,3.0')] ).

cnf(64,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),w)))),multiply(u,inverse(w))),v),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(65,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(multiply(v,w)))),multiply(x,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[3]),
    [iquote('0:SpR:3.0,3.0')] ).

cnf(77,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(w),w))),v),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(92,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(multiply(w,x)))),multiply(v,inverse(x)))))),multiply(u,inverse(inverse(multiply(inverse(inverse(multiply(inverse(x),x))),inverse(multiply(inverse(x),x))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(x),x))),inverse(multiply(inverse(x),x))))),inverse(multiply(inverse(inverse(multiply(inverse(x),x))),inverse(multiply(inverse(x),x))))))),multiply(inverse(multiply(y,inverse(w))),multiply(y,inverse(inverse(multiply(inverse(x),x)))))),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(101,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),inverse(multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x))))),inverse(multiply(w,inverse(multiply(multiply(v,inverse(multiply(inverse(x),x))),x))))),
    inference(spr,[status(thm),theory(equality)],[64,1]),
    [iquote('0:SpR:64.0,1.0')] ).

cnf(124,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))))),inverse(multiply(multiply(inverse(multiply(x,inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w))))),w)))),multiply(x,inverse(w))),inverse(multiply(v,multiply(inverse(w),w)))))),
    inference(spr,[status(thm),theory(equality)],[4,64]),
    [iquote('0:SpR:4.0,64.0')] ).

cnf(188,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),multiply(inverse(multiply(y,inverse(v))),multiply(y,inverse(multiply(w,inverse(x)))))),
    inference(spr,[status(thm),theory(equality)],[64,65]),
    [iquote('0:SpR:64.0,65.0')] ).

cnf(268,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[4,188]),
    [iquote('0:SpR:4.0,188.0')] ).

cnf(272,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),multiply(inverse(multiply(multiply(inverse(multiply(x,inverse(y))),multiply(x,inverse(inverse(multiply(inverse(w),w))))),inverse(v))),multiply(inverse(multiply(z,inverse(multiply(y,w)))),multiply(z,inverse(w))))),
    inference(spr,[status(thm),theory(equality)],[3,188]),
    [iquote('0:SpR:3.0,188.0')] ).

cnf(348,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x)))))),multiply(u,inverse(multiply(y,inverse(x))))),inverse(multiply(inverse(multiply(y,inverse(x))),multiply(y,inverse(x))))),inverse(multiply(y,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[268,1]),
    [iquote('0:SpR:268.0,1.0')] ).

cnf(387,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(y,v)))),multiply(x,inverse(v)))),multiply(multiply(inverse(multiply(z,inverse(y))),multiply(z,inverse(inverse(multiply(inverse(v),v))))),inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[3,268]),
    [iquote('0:SpR:3.0,268.0')] ).

cnf(390,plain,
    equal(inverse(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x))),inverse(multiply(inverse(x),x))),x)))),inverse(multiply(u,inverse(w)))),
    inference(rew,[status(thm),theory(equality)],[101,348]),
    [iquote('0:Rew:101.0,348.0')] ).

cnf(422,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(w),w))),multiply(multiply(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(y))),inverse(multiply(inverse(y),y))),y)),
    inference(spr,[status(thm),theory(equality)],[390,77]),
    [iquote('0:SpR:390.0,77.0')] ).

cnf(463,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),w),v),
    inference(rew,[status(thm),theory(equality)],[77,422]),
    [iquote('0:Rew:77.0,422.0')] ).

cnf(527,plain,
    equal(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(x))),multiply(inverse(multiply(y,inverse(multiply(v,w)))),multiply(y,inverse(w)))),inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))),x),
    inference(spr,[status(thm),theory(equality)],[3,463]),
    [iquote('0:SpR:3.0,463.0')] ).

cnf(529,plain,
    equal(multiply(multiply(multiply(inverse(u),multiply(multiply(inverse(multiply(v,inverse(multiply(u,w)))),multiply(v,inverse(w))),inverse(x))),inverse(multiply(inverse(x),x))),x),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[1,463]),
    [iquote('0:SpR:1.0,463.0')] ).

cnf(615,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),multiply(inverse(v),v)),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[1,529]),
    [iquote('0:SpR:1.0,529.0')] ).

cnf(687,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[615,64]),
    [iquote('0:SpR:615.0,64.0')] ).

cnf(720,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[687]),
    [iquote('0:SpR:687.0,687.0')] ).

cnf(732,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(multiply(inverse(y),y)))))),v),
    inference(spr,[status(thm),theory(equality)],[687,1]),
    [iquote('0:SpR:687.0,1.0')] ).

cnf(785,plain,
    equal(multiply(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(multiply(inverse(y),y))))))),v),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),inverse(multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[687,4]),
    [iquote('0:SpR:687.0,4.0')] ).

cnf(808,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),inverse(multiply(inverse(v),v))),
    inference(rew,[status(thm),theory(equality)],[732,785]),
    [iquote('0:Rew:732.0,785.0')] ).

cnf(855,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),v),v),
    inference(spr,[status(thm),theory(equality)],[720,463]),
    [iquote('0:SpR:720.0,463.0')] ).

cnf(867,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(inverse(x),x))),v),
    inference(spr,[status(thm),theory(equality)],[720,1]),
    [iquote('0:SpR:720.0,1.0')] ).

cnf(870,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),x)))),multiply(u,inverse(x))),v),
    inference(spr,[status(thm),theory(equality)],[720,64]),
    [iquote('0:SpR:720.0,64.0')] ).

cnf(873,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[720,1]),
    [iquote('0:SpR:720.0,1.0')] ).

cnf(877,plain,
    equal(multiply(multiply(multiply(inverse(inverse(u)),multiply(multiply(inverse(multiply(v,inverse(multiply(inverse(w),w)))),multiply(v,inverse(u))),inverse(x))),inverse(multiply(inverse(x),x))),x),multiply(inverse(u),u)),
    inference(spr,[status(thm),theory(equality)],[720,529]),
    [iquote('0:SpR:720.0,529.0')] ).

cnf(885,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),w))),inverse(w))),v),
    inference(spr,[status(thm),theory(equality)],[720,64]),
    [iquote('0:SpR:720.0,64.0')] ).

cnf(894,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(multiply(inverse(v),v),w)))),multiply(u,inverse(w))),inverse(inverse(multiply(inverse(w),w)))),
    inference(spr,[status(thm),theory(equality)],[720,64]),
    [iquote('0:SpR:720.0,64.0')] ).

cnf(899,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(inverse(w)),inverse(v))),multiply(inverse(x),x))),
    inference(spr,[status(thm),theory(equality)],[720,268]),
    [iquote('0:SpR:720.0,268.0')] ).

cnf(905,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))),multiply(inverse(multiply(w,inverse(multiply(inverse(multiply(inverse(v),v)),v)))),multiply(w,inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[720,3]),
    [iquote('0:SpR:720.0,3.0')] ).

cnf(917,plain,
    ( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
    | ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
    | ~ equal(multiply(multiply(inverse(u),u),a2),a2) ),
    inference(spl,[status(thm),theory(equality)],[720,2]),
    [iquote('0:SpL:720.0,2.2')] ).

cnf(918,plain,
    equal(multiply(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w)))),multiply(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(inverse(multiply(inverse(w),w))))),inverse(inverse(multiply(inverse(y),y))))),inverse(multiply(inverse(inverse(multiply(inverse(y),y))),inverse(multiply(inverse(y),y))))),inverse(inverse(multiply(inverse(w),w)))),
    inference(rew,[status(thm),theory(equality)],[870,63]),
    [iquote('0:Rew:870.0,63.0')] ).

cnf(967,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(inverse(v)),inverse(v)))),inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[855,268]),
    [iquote('0:SpR:855.0,268.0')] ).

cnf(971,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),w),w),
    inference(spr,[status(thm),theory(equality)],[720,855]),
    [iquote('0:SpR:720.0,855.0')] ).

cnf(977,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),inverse(w))),
    inference(rew,[status(thm),theory(equality)],[971,967]),
    [iquote('0:Rew:971.0,967.0')] ).

cnf(989,plain,
    equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(inverse(w),w)),multiply(inverse(inverse(v)),inverse(u))),
    inference(rew,[status(thm),theory(equality)],[977,899]),
    [iquote('0:Rew:977.0,899.0')] ).

cnf(1002,plain,
    equal(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(x))),multiply(inverse(multiply(y,inverse(multiply(v,w)))),multiply(y,inverse(w)))),multiply(inverse(inverse(x)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),
    inference(rew,[status(thm),theory(equality)],[977,272]),
    [iquote('0:Rew:977.0,272.0')] ).

cnf(1015,plain,
    equal(multiply(inverse(inverse(multiply(multiply(u,inverse(multiply(inverse(v),v))),w))),inverse(w)),u),
    inference(rew,[status(thm),theory(equality)],[977,870]),
    [iquote('0:Rew:977.0,870.0')] ).

cnf(1021,plain,
    equal(multiply(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(w)))),inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(w))))),inverse(multiply(v,inverse(multiply(multiply(u,inverse(multiply(inverse(w),w))),w))))),
    inference(rew,[status(thm),theory(equality)],[977,101]),
    [iquote('0:Rew:977.0,101.0')] ).

cnf(1034,plain,
    equal(multiply(inverse(inverse(multiply(multiply(inverse(u),u),v))),inverse(v)),inverse(inverse(multiply(inverse(v),v)))),
    inference(rew,[status(thm),theory(equality)],[977,894]),
    [iquote('0:Rew:977.0,894.0')] ).

cnf(1035,plain,
    equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w)))),multiply(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(inverse(multiply(inverse(w),w))))),inverse(y))),multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),inverse(y))),
    inference(rew,[status(thm),theory(equality)],[977,387]),
    [iquote('0:Rew:977.0,387.0')] ).

cnf(1041,plain,
    equal(multiply(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(v)),inverse(multiply(inverse(v),v))),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[977,873]),
    [iquote('0:Rew:977.0,873.0')] ).

cnf(1052,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),v))),inverse(v))),
    inference(rew,[status(thm),theory(equality)],[977,905]),
    [iquote('0:Rew:977.0,905.0')] ).

cnf(1056,plain,
    equal(multiply(multiply(multiply(inverse(inverse(u)),multiply(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(u)),inverse(w))),inverse(multiply(inverse(w),w))),w),multiply(inverse(u),u)),
    inference(rew,[status(thm),theory(equality)],[977,877]),
    [iquote('0:Rew:977.0,877.0')] ).

cnf(1057,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))))),inverse(multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w))))),w))),inverse(w)),inverse(multiply(v,multiply(inverse(w),w)))))),
    inference(rew,[status(thm),theory(equality)],[977,124]),
    [iquote('0:Rew:977.0,124.0')] ).

cnf(1066,plain,
    equal(multiply(multiply(inverse(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))))),inverse(inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(inverse(multiply(inverse(w),w)))))),
    inference(rew,[status(thm),theory(equality)],[977,92]),
    [iquote('0:Rew:977.0,92.0')] ).

cnf(1099,plain,
    equal(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(x))),multiply(inverse(multiply(y,inverse(multiply(v,w)))),multiply(y,inverse(w)))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))),x),
    inference(rew,[status(thm),theory(equality)],[977,527]),
    [iquote('0:Rew:977.0,527.0')] ).

cnf(1162,plain,
    equal(multiply(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w)))),multiply(multiply(inverse(inverse(v)),inverse(inverse(multiply(inverse(w),w)))),inverse(inverse(multiply(inverse(x),x))))),inverse(multiply(inverse(inverse(multiply(inverse(x),x))),inverse(multiply(inverse(x),x))))),inverse(inverse(multiply(inverse(w),w)))),
    inference(rew,[status(thm),theory(equality)],[977,918]),
    [iquote('0:Rew:977.0,918.0')] ).

cnf(1172,plain,
    equal(multiply(multiply(inverse(inverse(multiply(u,v))),inverse(v)),inverse(multiply(inverse(w),w))),u),
    inference(rew,[status(thm),theory(equality)],[977,867]),
    [iquote('0:Rew:977.0,867.0')] ).

cnf(1174,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),v),v),
    inference(rew,[status(thm),theory(equality)],[1015,885]),
    [iquote('0:Rew:1015.0,885.0')] ).

cnf(1183,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))),
    inference(rew,[status(thm),theory(equality)],[1174,808]),
    [iquote('0:Rew:1174.0,808.0')] ).

cnf(1213,plain,
    equal(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))),multiply(inverse(inverse(u)),inverse(u))),
    inference(rew,[status(thm),theory(equality)],[1183,1052,1174]),
    [iquote('0:Rew:1183.0,1052.0,1174.0,1052.0')] ).

cnf(1227,plain,
    equal(multiply(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(w)))),inverse(multiply(inverse(inverse(w)),inverse(w)))),inverse(multiply(v,inverse(multiply(multiply(u,inverse(multiply(inverse(w),w))),w))))),
    inference(rew,[status(thm),theory(equality)],[977,1021]),
    [iquote('0:Rew:977.0,1021.0')] ).

cnf(1275,plain,
    equal(multiply(inverse(multiply(multiply(inverse(inverse(u)),inverse(inverse(multiply(inverse(v),v)))),inverse(w))),multiply(inverse(inverse(multiply(u,v))),inverse(v))),multiply(inverse(inverse(w)),multiply(inverse(inverse(v)),inverse(v)))),
    inference(rew,[status(thm),theory(equality)],[977,1002,1213]),
    [iquote('0:Rew:977.0,1002.0,977.0,1002.0,1213.0,1002.0')] ).

cnf(1278,plain,
    equal(multiply(inverse(multiply(inverse(inverse(multiply(u,v))),inverse(v))),multiply(multiply(inverse(inverse(u)),inverse(inverse(multiply(inverse(v),v)))),inverse(w))),inverse(w)),
    inference(rew,[status(thm),theory(equality)],[977,1035,1174,1213]),
    [iquote('0:Rew:977.0,1035.0,977.0,1035.0,1174.0,1035.0,1213.0,1035.0')] ).

cnf(1292,plain,
    equal(multiply(inverse(inverse(multiply(inverse(u),u))),multiply(inverse(inverse(u)),inverse(u))),inverse(inverse(multiply(inverse(v),v)))),
    inference(rew,[status(thm),theory(equality)],[1278,1162,977,1213]),
    [iquote('0:Rew:1278.0,1162.0,977.0,1162.0,1213.0,1162.0')] ).

cnf(1311,plain,
    equal(multiply(multiply(multiply(inverse(inverse(u)),multiply(inverse(inverse(v)),inverse(v))),multiply(inverse(inverse(v)),inverse(v))),multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))),u),
    inference(rew,[status(thm),theory(equality)],[1275,1099,977,1213]),
    [iquote('0:Rew:1275.0,1099.0,977.0,1099.0,977.0,1099.0,1213.0,1099.0')] ).

cnf(1316,plain,
    equal(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(v,multiply(inverse(u),u))))),multiply(inverse(inverse(v)),inverse(inverse(multiply(inverse(u),u))))),
    inference(rew,[status(thm),theory(equality)],[977,1057,1034,1213,1174]),
    [iquote('0:Rew:977.0,1057.0,1034.0,1057.0,1213.0,1057.0,1174.0,1057.0')] ).

cnf(1346,plain,
    equal(multiply(inverse(inverse(u)),inverse(inverse(multiply(inverse(v),v)))),inverse(multiply(inverse(inverse(v)),inverse(multiply(u,v))))),
    inference(rew,[status(thm),theory(equality)],[1172,1066,1227,977,1174,1213]),
    [iquote('0:Rew:1172.0,1066.0,1227.0,1066.0,977.0,1066.0,1174.0,1066.0,1213.0,1066.0,977.0,1066.0')] ).

cnf(1358,plain,
    equal(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(v,multiply(inverse(u),u))))),inverse(multiply(inverse(inverse(u)),inverse(multiply(v,u))))),
    inference(rew,[status(thm),theory(equality)],[1346,1316]),
    [iquote('0:Rew:1346.0,1316.0')] ).

cnf(1458,plain,
    equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),v))),inverse(v)),inverse(multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[1174,1015]),
    [iquote('0:SpR:1174.0,1015.0')] ).

cnf(1464,plain,
    equal(multiply(inverse(inverse(u)),inverse(u)),inverse(multiply(inverse(v),v))),
    inference(rew,[status(thm),theory(equality)],[1174,1458]),
    [iquote('0:Rew:1174.0,1458.0')] ).

cnf(1483,plain,
    equal(multiply(inverse(inverse(multiply(inverse(u),u))),multiply(inverse(v),v)),inverse(inverse(multiply(inverse(w),w)))),
    inference(spr,[status(thm),theory(equality)],[720,1292]),
    [iquote('0:SpR:720.0,1292.0')] ).

cnf(1492,plain,
    equal(inverse(multiply(inverse(u),u)),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[1464,720]),
    [iquote('0:SpR:1464.0,720.0')] ).

cnf(1493,plain,
    equal(multiply(inverse(inverse(multiply(inverse(u),u))),v),v),
    inference(spr,[status(thm),theory(equality)],[1464,1174]),
    [iquote('0:SpR:1464.0,1174.0')] ).

cnf(1537,plain,
    equal(multiply(inverse(u),u),inverse(inverse(multiply(inverse(v),v)))),
    inference(rew,[status(thm),theory(equality)],[1493,1483]),
    [iquote('0:Rew:1493.0,1483.0')] ).

cnf(1539,plain,
    equal(inverse(multiply(inverse(inverse(u)),inverse(multiply(v,u)))),inverse(inverse(multiply(v,multiply(inverse(u),u))))),
    inference(rew,[status(thm),theory(equality)],[1493,1358]),
    [iquote('0:Rew:1493.0,1358.0')] ).

cnf(1547,plain,
    equal(multiply(multiply(multiply(inverse(inverse(u)),multiply(inverse(inverse(v)),inverse(v))),multiply(inverse(inverse(v)),inverse(v))),inverse(multiply(inverse(v),v))),u),
    inference(rew,[status(thm),theory(equality)],[1493,1311]),
    [iquote('0:Rew:1493.0,1311.0')] ).

cnf(1555,plain,
    equal(multiply(multiply(multiply(inverse(inverse(u)),multiply(inverse(u),inverse(v))),inverse(multiply(inverse(v),v))),v),multiply(inverse(u),u)),
    inference(rew,[status(thm),theory(equality)],[1493,1056]),
    [iquote('0:Rew:1493.0,1056.0')] ).

cnf(1556,plain,
    equal(multiply(inverse(u),inverse(multiply(inverse(u),u))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[1493,1041]),
    [iquote('0:Rew:1493.0,1041.0')] ).

cnf(1567,plain,
    equal(multiply(inverse(inverse(u)),inverse(inverse(multiply(inverse(v),v)))),inverse(inverse(multiply(u,multiply(inverse(v),v))))),
    inference(rew,[status(thm),theory(equality)],[1539,1346]),
    [iquote('0:Rew:1539.0,1346.0')] ).

cnf(1627,plain,
    equal(multiply(multiply(inverse(u),u),v),v),
    inference(spr,[status(thm),theory(equality)],[1492,1174]),
    [iquote('0:SpR:1492.0,1174.0')] ).

cnf(1630,plain,
    equal(multiply(inverse(inverse(multiply(multiply(u,multiply(inverse(v),v)),w))),inverse(w)),u),
    inference(spr,[status(thm),theory(equality)],[1492,1015]),
    [iquote('0:SpR:1492.0,1015.0')] ).

cnf(1651,plain,
    ( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
    | ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
    | ~ equal(a2,a2) ),
    inference(rew,[status(thm),theory(equality)],[1627,917]),
    [iquote('0:Rew:1627.0,917.2')] ).

cnf(1663,plain,
    ( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
    | ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
    inference(obv,[status(thm),theory(equality)],[1651]),
    [iquote('0:Obv:1651.2')] ).

cnf(1867,plain,
    equal(multiply(inverse(inverse(u)),multiply(inverse(v),v)),inverse(inverse(multiply(u,multiply(inverse(w),w))))),
    inference(spr,[status(thm),theory(equality)],[1537,1567]),
    [iquote('0:SpR:1537.0,1567.0')] ).

cnf(1927,plain,
    equal(multiply(inverse(u),multiply(inverse(v),v)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[1492,1556]),
    [iquote('0:SpR:1492.0,1556.0')] ).

cnf(1935,plain,
    equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[1927,1867]),
    [iquote('0:Rew:1927.0,1867.0')] ).

cnf(1939,plain,
    equal(multiply(multiply(inverse(inverse(u)),multiply(inverse(inverse(v)),inverse(v))),inverse(multiply(inverse(v),v))),u),
    inference(rew,[status(thm),theory(equality)],[1927,1547]),
    [iquote('0:Rew:1927.0,1547.0')] ).

cnf(1940,plain,
    equal(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(inverse(inverse(v)),inverse(u))),
    inference(rew,[status(thm),theory(equality)],[1927,989]),
    [iquote('0:Rew:1927.0,989.0')] ).

cnf(1957,plain,
    equal(inverse(multiply(inverse(inverse(u)),inverse(multiply(v,u)))),inverse(inverse(v))),
    inference(rew,[status(thm),theory(equality)],[1935,1539]),
    [iquote('0:Rew:1935.0,1539.0')] ).

cnf(1961,plain,
    equal(multiply(inverse(inverse(multiply(u,v))),inverse(v)),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[1940,1957]),
    [iquote('0:Rew:1940.0,1957.0')] ).

cnf(1964,plain,
    equal(multiply(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(w)))),multiply(inverse(inverse(w)),inverse(w))),inverse(multiply(v,inverse(multiply(multiply(u,inverse(multiply(inverse(w),w))),w))))),
    inference(rew,[status(thm),theory(equality)],[1940,1227]),
    [iquote('0:Rew:1940.0,1227.0')] ).

cnf(1974,plain,
    equal(inverse(inverse(multiply(u,inverse(multiply(inverse(v),v))))),u),
    inference(rew,[status(thm),theory(equality)],[1961,1015]),
    [iquote('0:Rew:1961.0,1015.0')] ).

cnf(1975,plain,
    equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),u),
    inference(rew,[status(thm),theory(equality)],[1961,1630]),
    [iquote('0:Rew:1961.0,1630.0')] ).

cnf(1990,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[1935,1975]),
    [iquote('0:Rew:1935.0,1975.0')] ).

cnf(1996,plain,
    equal(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(v,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[1990,1940]),
    [iquote('0:Rew:1990.0,1940.0')] ).

cnf(2000,plain,
    equal(multiply(multiply(multiply(u,multiply(inverse(u),inverse(v))),inverse(multiply(inverse(v),v))),v),multiply(inverse(u),u)),
    inference(rew,[status(thm),theory(equality)],[1990,1555]),
    [iquote('0:Rew:1990.0,1555.0')] ).

cnf(2003,plain,
    equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),u),
    inference(rew,[status(thm),theory(equality)],[1990,1935]),
    [iquote('0:Rew:1990.0,1935.0')] ).

cnf(2010,plain,
    equal(multiply(u,multiply(inverse(v),v)),u),
    inference(rew,[status(thm),theory(equality)],[1990,2003]),
    [iquote('0:Rew:1990.0,2003.0')] ).

cnf(2013,plain,
    equal(multiply(u,inverse(multiply(inverse(v),v))),u),
    inference(rew,[status(thm),theory(equality)],[1990,1974]),
    [iquote('0:Rew:1990.0,1974.0')] ).

cnf(2022,plain,
    equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[1990,1996]),
    [iquote('0:Rew:1990.0,1996.0')] ).

cnf(2040,plain,
    equal(multiply(u,multiply(v,inverse(v))),u),
    inference(rew,[status(thm),theory(equality)],[2013,1939,1990]),
    [iquote('0:Rew:2013.0,1939.0,1990.0,1939.0,1990.0,1939.0')] ).

cnf(2050,plain,
    equal(multiply(multiply(u,multiply(inverse(u),inverse(v))),v),multiply(inverse(u),u)),
    inference(rew,[status(thm),theory(equality)],[2013,2000]),
    [iquote('0:Rew:2013.0,2000.0')] ).

cnf(2069,plain,
    equal(multiply(multiply(u,v),inverse(w)),multiply(u,multiply(v,inverse(w)))),
    inference(rew,[status(thm),theory(equality)],[2040,1964,1990,2022,2013]),
    [iquote('0:Rew:2040.0,1964.0,1990.0,1964.0,2022.0,1964.0,1990.0,1964.0,2022.0,1964.0,2013.0,1964.0')] ).

cnf(2110,plain,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    inference(spr,[status(thm),theory(equality)],[1990,2069]),
    [iquote('0:SpR:1990.0,2069.0')] ).

cnf(2121,plain,
    ( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
    | ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
    inference(rew,[status(thm),theory(equality)],[2110,1663]),
    [iquote('0:Rew:2110.0,1663.1')] ).

cnf(2122,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(v)),v)),multiply(inverse(u),u)),
    inference(rew,[status(thm),theory(equality)],[2110,2050]),
    [iquote('0:Rew:2110.0,2050.0')] ).

cnf(2128,plain,
    equal(multiply(inverse(u),u),multiply(u,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[2010,2122,2110]),
    [iquote('0:Rew:2010.0,2122.0,2110.0,2122.0')] ).

cnf(2129,plain,
    equal(multiply(inverse(u),u),multiply(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[2128,720]),
    [iquote('0:Rew:2128.0,720.0')] ).

cnf(2137,plain,
    equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[2128,2129]),
    [iquote('0:Rew:2128.0,2129.0')] ).

cnf(2150,plain,
    ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    inference(obv,[status(thm),theory(equality)],[2121]),
    [iquote('0:Obv:2121.1')] ).

cnf(2151,plain,
    ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
    inference(rew,[status(thm),theory(equality)],[2128,2150]),
    [iquote('0:Rew:2128.0,2150.0,2128.0,2150.0')] ).

cnf(2152,plain,
    $false,
    inference(unc,[status(thm)],[2151,2137]),
    [iquote('0:UnC:2151.0,2137.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP051-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 18:39:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.08/1.26  
% 1.08/1.26  SPASS V 3.9 
% 1.08/1.26  SPASS beiseite: Proof found.
% 1.08/1.26  % SZS status Theorem
% 1.08/1.26  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.08/1.26  SPASS derived 1640 clauses, backtracked 0 clauses, performed 0 splits and kept 653 clauses.
% 1.08/1.26  SPASS allocated 70694 KBytes.
% 1.08/1.26  SPASS spent	0:00:00.91 on the problem.
% 1.08/1.26  		0:00:00.04 for the input.
% 1.08/1.26  		0:00:00.00 for the FLOTTER CNF translation.
% 1.08/1.26  		0:00:00.03 for inferences.
% 1.08/1.26  		0:00:00.00 for the backtracking.
% 1.08/1.26  		0:00:00.83 for the reduction.
% 1.08/1.26  
% 1.08/1.26  
% 1.08/1.26  Here is a proof with depth 15, length 110 :
% 1.08/1.26  % SZS output start Refutation
% See solution above
% 1.08/1.29  Formulae used in the proof : single_axiom prove_these_axioms
% 1.08/1.29  
%------------------------------------------------------------------------------