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
%------------------------------------------------------------------------------