TSTP Solution File: GRP411-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP411-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 11:47:15 EDT 2022
% Result : Unsatisfiable 1.04s 1.26s
% Output : Refutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 2
% Syntax : Number of clauses : 92 ( 92 unt; 0 nHn; 92 RR)
% Number of literals : 92 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 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('GRP411-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP411-1.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(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(916,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(965,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(969,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(975,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),inverse(w))),
inference(rew,[status(thm),theory(equality)],[969,965]),
[iquote('0:Rew:969.0,965.0')] ).
cnf(991,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)],[975,527]),
[iquote('0:Rew:975.0,527.0')] ).
cnf(1003,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)],[975,899]),
[iquote('0:Rew:975.0,899.0')] ).
cnf(1022,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)],[975,272]),
[iquote('0:Rew:975.0,272.0')] ).
cnf(1028,plain,
equal(multiply(inverse(inverse(multiply(multiply(u,inverse(multiply(inverse(v),v))),w))),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[975,870]),
[iquote('0:Rew:975.0,870.0')] ).
cnf(1034,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)],[975,101]),
[iquote('0:Rew:975.0,101.0')] ).
cnf(1046,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)],[975,894]),
[iquote('0:Rew:975.0,894.0')] ).
cnf(1047,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)],[975,387]),
[iquote('0:Rew:975.0,387.0')] ).
cnf(1053,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)],[975,873]),
[iquote('0:Rew:975.0,873.0')] ).
cnf(1064,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)],[975,92]),
[iquote('0:Rew:975.0,92.0')] ).
cnf(1066,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)],[975,905]),
[iquote('0:Rew:975.0,905.0')] ).
cnf(1076,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)],[975,124]),
[iquote('0:Rew:975.0,124.0')] ).
cnf(1123,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)],[975,916]),
[iquote('0:Rew:975.0,916.0')] ).
cnf(1170,plain,
equal(multiply(multiply(inverse(inverse(multiply(u,v))),inverse(v)),inverse(multiply(inverse(w),w))),u),
inference(rew,[status(thm),theory(equality)],[975,867]),
[iquote('0:Rew:975.0,867.0')] ).
cnf(1172,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[1028,885]),
[iquote('0:Rew:1028.0,885.0')] ).
cnf(1181,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[1172,808]),
[iquote('0:Rew:1172.0,808.0')] ).
cnf(1211,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)],[1181,1066,1172]),
[iquote('0:Rew:1181.0,1066.0,1172.0,1066.0')] ).
cnf(1225,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)],[975,1034]),
[iquote('0:Rew:975.0,1034.0')] ).
cnf(1274,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)],[975,1022,1211]),
[iquote('0:Rew:975.0,1022.0,975.0,1022.0,1211.0,1022.0')] ).
cnf(1276,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)],[975,1047,1172,1211]),
[iquote('0:Rew:975.0,1047.0,975.0,1047.0,1172.0,1047.0,1211.0,1047.0')] ).
cnf(1290,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)],[1276,1123,975,1211]),
[iquote('0:Rew:1276.0,1123.0,975.0,1123.0,1211.0,1123.0')] ).
cnf(1307,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)],[1274,991,975,1211]),
[iquote('0:Rew:1274.0,991.0,975.0,991.0,975.0,991.0,1211.0,991.0')] ).
cnf(1314,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)],[975,1076,1046,1211,1172]),
[iquote('0:Rew:975.0,1076.0,1046.0,1076.0,1211.0,1076.0,1172.0,1076.0')] ).
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)],[1170,1064,1225,975,1172,1211]),
[iquote('0:Rew:1170.0,1064.0,1225.0,1064.0,975.0,1064.0,1172.0,1064.0,1211.0,1064.0,975.0,1064.0')] ).
cnf(1352,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)],[1346,1314]),
[iquote('0:Rew:1346.0,1314.0')] ).
cnf(1454,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)],[1172,1028]),
[iquote('0:SpR:1172.0,1028.0')] ).
cnf(1460,plain,
equal(multiply(inverse(inverse(u)),inverse(u)),inverse(multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[1172,1454]),
[iquote('0:Rew:1172.0,1454.0')] ).
cnf(1479,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)],[720,1290]),
[iquote('0:SpR:720.0,1290.0')] ).
cnf(1488,plain,
equal(inverse(multiply(inverse(u),u)),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[1460,720]),
[iquote('0:SpR:1460.0,720.0')] ).
cnf(1489,plain,
equal(multiply(inverse(inverse(multiply(inverse(u),u))),v),v),
inference(spr,[status(thm),theory(equality)],[1460,1172]),
[iquote('0:SpR:1460.0,1172.0')] ).
cnf(1533,plain,
equal(multiply(inverse(u),u),inverse(inverse(multiply(inverse(v),v)))),
inference(rew,[status(thm),theory(equality)],[1489,1479]),
[iquote('0:Rew:1489.0,1479.0')] ).
cnf(1536,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)],[1489,1352]),
[iquote('0:Rew:1489.0,1352.0')] ).
cnf(1538,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)],[1489,1307]),
[iquote('0:Rew:1489.0,1307.0')] ).
cnf(1552,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(u),u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1489,1053]),
[iquote('0:Rew:1489.0,1053.0')] ).
cnf(1563,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)],[1536,1346]),
[iquote('0:Rew:1536.0,1346.0')] ).
cnf(1626,plain,
equal(multiply(inverse(inverse(multiply(multiply(u,multiply(inverse(v),v)),w))),inverse(w)),u),
inference(spr,[status(thm),theory(equality)],[1488,1028]),
[iquote('0:SpR:1488.0,1028.0')] ).
cnf(1861,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(v),v)),inverse(inverse(multiply(u,multiply(inverse(w),w))))),
inference(spr,[status(thm),theory(equality)],[1533,1563]),
[iquote('0:SpR:1533.0,1563.0')] ).
cnf(1921,plain,
equal(multiply(inverse(u),multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1488,1552]),
[iquote('0:SpR:1488.0,1552.0')] ).
cnf(1929,plain,
equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[1921,1861]),
[iquote('0:Rew:1921.0,1861.0')] ).
cnf(1933,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)],[1921,1538]),
[iquote('0:Rew:1921.0,1538.0')] ).
cnf(1934,plain,
equal(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(inverse(inverse(v)),inverse(u))),
inference(rew,[status(thm),theory(equality)],[1921,1003]),
[iquote('0:Rew:1921.0,1003.0')] ).
cnf(1951,plain,
equal(inverse(multiply(inverse(inverse(u)),inverse(multiply(v,u)))),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[1929,1536]),
[iquote('0:Rew:1929.0,1536.0')] ).
cnf(1955,plain,
equal(multiply(inverse(inverse(multiply(u,v))),inverse(v)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[1934,1951]),
[iquote('0:Rew:1934.0,1951.0')] ).
cnf(1958,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)],[1934,1225]),
[iquote('0:Rew:1934.0,1225.0')] ).
cnf(1968,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(v),v))))),u),
inference(rew,[status(thm),theory(equality)],[1955,1028]),
[iquote('0:Rew:1955.0,1028.0')] ).
cnf(1970,plain,
equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),u),
inference(rew,[status(thm),theory(equality)],[1955,1626]),
[iquote('0:Rew:1955.0,1626.0')] ).
cnf(1984,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[1929,1970]),
[iquote('0:Rew:1929.0,1970.0')] ).
cnf(1990,plain,
equal(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[1984,1934]),
[iquote('0:Rew:1984.0,1934.0')] ).
cnf(2007,plain,
equal(multiply(u,inverse(multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[1984,1968]),
[iquote('0:Rew:1984.0,1968.0')] ).
cnf(2016,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[1984,1990]),
[iquote('0:Rew:1984.0,1990.0')] ).
cnf(2034,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[2007,1933,1984]),
[iquote('0:Rew:2007.0,1933.0,1984.0,1933.0,1984.0,1933.0')] ).
cnf(2063,plain,
equal(multiply(multiply(u,v),inverse(w)),multiply(u,multiply(v,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[2034,1958,1984,2016,2007]),
[iquote('0:Rew:2034.0,1958.0,1984.0,1958.0,2016.0,1958.0,1984.0,1958.0,2016.0,1958.0,2007.0,1958.0')] ).
cnf(2104,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1984,2063]),
[iquote('0:SpR:1984.0,2063.0')] ).
cnf(2110,plain,
$false,
inference(unc,[status(thm)],[2104,2]),
[iquote('0:UnC:2104.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP411-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 00:04:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.04/1.26
% 1.04/1.26 SPASS V 3.9
% 1.04/1.26 SPASS beiseite: Proof found.
% 1.04/1.26 % SZS status Theorem
% 1.04/1.26 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.04/1.26 SPASS derived 1618 clauses, backtracked 0 clauses, performed 0 splits and kept 644 clauses.
% 1.04/1.26 SPASS allocated 70588 KBytes.
% 1.04/1.26 SPASS spent 0:00:00.92 on the problem.
% 1.04/1.26 0:00:00.04 for the input.
% 1.04/1.26 0:00:00.00 for the FLOTTER CNF translation.
% 1.04/1.26 0:00:00.03 for inferences.
% 1.04/1.26 0:00:00.00 for the backtracking.
% 1.04/1.26 0:00:00.84 for the reduction.
% 1.04/1.26
% 1.04/1.26
% 1.04/1.26 Here is a proof with depth 15, length 92 :
% 1.04/1.26 % SZS output start Refutation
% See solution above
% 1.09/1.30 Formulae used in the proof : single_axiom prove_these_axioms_3
% 1.09/1.30
%------------------------------------------------------------------------------