TSTP Solution File: GRP416-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP416-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:47:22 EDT 2022
% Result : Unsatisfiable 27.58s 27.74s
% Output : Refutation 27.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 62 RR)
% Number of literals : 62 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,inverse(w)))),inverse(multiply(inverse(u),u)))))),w),
file('GRP416-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP416-1.p',unknown),
[] ).
cnf(4,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v)))),inverse(multiply(inverse(multiply(w,multiply(v,inverse(x)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v)))))))))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,w))),inverse(multiply(inverse(u),u)))))),multiply(x,inverse(multiply(inverse(multiply(inverse(multiply(y,x)),multiply(y,inverse(w)))),inverse(multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(11,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,inverse(inverse(w))))),inverse(multiply(inverse(u),u))))),w),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(21,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),multiply(v,w))),inverse(multiply(inverse(u),u))))))),w),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(107,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),w)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[11,1]),
[iquote('0:SpR:11.0,1.0')] ).
cnf(113,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,u)),w)),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(v),v))))),
inference(spr,[status(thm),theory(equality)],[11,21]),
[iquote('0:SpR:11.0,21.0')] ).
cnf(151,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(inverse(multiply(v,inverse(w))))))),inverse(multiply(inverse(v),v))),w),
inference(spr,[status(thm),theory(equality)],[107,1]),
[iquote('0:SpR:107.0,1.0')] ).
cnf(153,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(inverse(multiply(v,w)))))),inverse(multiply(inverse(v),v)))),w),
inference(spr,[status(thm),theory(equality)],[107,21]),
[iquote('0:SpR:107.0,21.0')] ).
cnf(182,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(inverse(v),v)))))))),w),
inference(spr,[status(thm),theory(equality)],[107,11]),
[iquote('0:SpR:107.0,11.0')] ).
cnf(268,plain,
equal(inverse(multiply(inverse(multiply(u,multiply(v,inverse(w)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(u)))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(u)))),inverse(multiply(inverse(v),v)))))))),multiply(inverse(multiply(inverse(multiply(x,v)),multiply(x,inverse(u)))),inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(w,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))),
inference(spr,[status(thm),theory(equality)],[4,182]),
[iquote('0:SpR:4.0,182.0')] ).
cnf(269,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(x)))),inverse(multiply(inverse(inverse(multiply(v,w))),inverse(multiply(v,w)))))),multiply(v,inverse(inverse(multiply(w,inverse(multiply(x,inverse(multiply(inverse(w),w))))))))),
inference(spr,[status(thm),theory(equality)],[1,182]),
[iquote('0:SpR:1.0,182.0')] ).
cnf(287,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(inverse(v),v)))),multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(x,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))))))))),x),
inference(rew,[status(thm),theory(equality)],[268,4]),
[iquote('0:Rew:268.0,4.0')] ).
cnf(390,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))),inverse(multiply(w,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))))))))))),w),
inference(spr,[status(thm),theory(equality)],[287]),
[iquote('0:SpR:287.0,287.0')] ).
cnf(494,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,inverse(inverse(multiply(w,inverse(x))))))),u)),x)),inverse(multiply(inverse(u),u)))))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[151,1]),
[iquote('0:SpR:151.0,1.0')] ).
cnf(1617,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))),multiply(inverse(u),u)),
inference(spr,[status(thm),theory(equality)],[153,494]),
[iquote('0:SpR:153.0,494.0')] ).
cnf(1658,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))),w),
inference(spr,[status(thm),theory(equality)],[1617,11]),
[iquote('0:SpR:1617.0,11.0')] ).
cnf(1667,plain,
equal(multiply(inverse(u),inverse(inverse(multiply(u,inverse(multiply(multiply(inverse(u),u),inverse(multiply(inverse(u),u)))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),
inference(spr,[status(thm),theory(equality)],[1617,182]),
[iquote('0:SpR:1617.0,182.0')] ).
cnf(1673,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),inverse(multiply(inverse(multiply(multiply(inverse(u),u),w)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))))))),w),
inference(spr,[status(thm),theory(equality)],[1617,182]),
[iquote('0:SpR:1617.0,182.0')] ).
cnf(1679,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))))),
inference(spr,[status(thm),theory(equality)],[1617,107]),
[iquote('0:SpR:1617.0,107.0')] ).
cnf(1917,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),w)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))))),inverse(multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(v),v)))),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),
inference(spr,[status(thm),theory(equality)],[1617,113]),
[iquote('0:SpR:1617.0,113.0')] ).
cnf(2000,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))))))),
inference(spr,[status(thm),theory(equality)],[1617,113]),
[iquote('0:SpR:1617.0,113.0')] ).
cnf(2071,plain,
equal(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),w)),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))))))),multiply(inverse(v),inverse(inverse(multiply(v,inverse(multiply(inverse(w),inverse(multiply(inverse(v),v))))))))),
inference(rew,[status(thm),theory(equality)],[269,1917]),
[iquote('0:Rew:269.0,1917.0')] ).
cnf(2073,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(u),inverse(inverse(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(u),u))))))))),v),
inference(rew,[status(thm),theory(equality)],[2071,1673]),
[iquote('0:Rew:2071.0,1673.0')] ).
cnf(2509,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(u),v)),multiply(inverse(multiply(w,u)),multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[21,2073]),
[iquote('0:SpR:21.0,2073.0')] ).
cnf(2594,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(inverse(multiply(v,inverse(multiply(inverse(w),inverse(multiply(inverse(v),v))))))))),w),
inference(spr,[status(thm),theory(equality)],[2509,2073]),
[iquote('0:SpR:2509.0,2073.0')] ).
cnf(2601,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[2509]),
[iquote('0:SpR:2509.0,2509.0')] ).
cnf(3223,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)],[1617,2594]),
[iquote('0:SpR:1617.0,2594.0')] ).
cnf(3724,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[3223]),
[iquote('0:SpR:3223.0,3223.0')] ).
cnf(4029,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(u),u))))))),u),
inference(spr,[status(thm),theory(equality)],[3724,21]),
[iquote('0:SpR:3724.0,21.0')] ).
cnf(4102,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[3724,2601]),
[iquote('0:SpR:3724.0,2601.0')] ).
cnf(4112,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(inverse(w),v)),multiply(inverse(x),x))),
inference(spr,[status(thm),theory(equality)],[3724,2601]),
[iquote('0:SpR:3724.0,2601.0')] ).
cnf(4137,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(u)),inverse(u))))))),u),
inference(spr,[status(thm),theory(equality)],[3724,1]),
[iquote('0:SpR:3724.0,1.0')] ).
cnf(4272,plain,
~ equal(multiply(multiply(inverse(u),u),a2),a2),
inference(spl,[status(thm),theory(equality)],[3724,2]),
[iquote('0:SpL:3724.0,2.0')] ).
cnf(4293,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(w),w))))))),u),
inference(spr,[status(thm),theory(equality)],[3724,4029]),
[iquote('0:SpR:3724.0,4029.0')] ).
cnf(4424,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(w),w))),inverse(multiply(inverse(x),x))))))),u),
inference(spr,[status(thm),theory(equality)],[4102,4293]),
[iquote('0:SpR:4102.0,4293.0')] ).
cnf(4452,plain,
~ equal(multiply(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),v)),a2),a2),
inference(spl,[status(thm),theory(equality)],[4102,4272]),
[iquote('0:SpL:4102.0,4272.0')] ).
cnf(4796,plain,
equal(multiply(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(w)),inverse(w))))))),multiply(inverse(x),x)),multiply(w,multiply(inverse(w),u))),
inference(spr,[status(thm),theory(equality)],[4137,4112]),
[iquote('0:SpR:4137.0,4112.0')] ).
cnf(4814,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(w),w)))))),u),
inference(spr,[status(thm),theory(equality)],[3724,4137]),
[iquote('0:SpR:3724.0,4137.0')] ).
cnf(4837,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),inverse(multiply(inverse(multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))),w),
inference(rew,[status(thm),theory(equality)],[4814,1658]),
[iquote('0:Rew:4814.0,1658.0')] ).
cnf(4844,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))),
inference(rew,[status(thm),theory(equality)],[4814,1679]),
[iquote('0:Rew:4814.0,1679.0')] ).
cnf(4845,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u))))))),inverse(multiply(inverse(multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))))),
inference(rew,[status(thm),theory(equality)],[4814,2000]),
[iquote('0:Rew:4814.0,2000.0')] ).
cnf(4852,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(w),u))),
inference(rew,[status(thm),theory(equality)],[4814,4796]),
[iquote('0:Rew:4814.0,4796.0')] ).
cnf(4853,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),w),
inference(rew,[status(thm),theory(equality)],[4814,4837]),
[iquote('0:Rew:4814.0,4837.0')] ).
cnf(4863,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),u)),x)),inverse(multiply(inverse(u),u))))))),multiply(multiply(inverse(w),w),multiply(inverse(multiply(inverse(w),w)),inverse(inverse(x))))),
inference(rew,[status(thm),theory(equality)],[4814,4845]),
[iquote('0:Rew:4814.0,4845.0')] ).
cnf(5161,plain,
equal(inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))),inverse(multiply(v,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))),multiply(inverse(w),w))),v),
inference(spr,[status(thm),theory(equality)],[4112,390]),
[iquote('0:SpR:4112.0,390.0')] ).
cnf(5165,plain,
equal(inverse(multiply(u,multiply(inverse(u),inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))),inverse(multiply(w,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v))))))))),w),
inference(spr,[status(thm),theory(equality)],[4852,390]),
[iquote('0:SpR:4852.0,390.0')] ).
cnf(5412,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(v),v)),inverse(multiply(inverse(multiply(inverse(w),w)),inverse(multiply(inverse(x),x)))))))),u),
inference(spr,[status(thm),theory(equality)],[4814]),
[iquote('0:SpR:4814.0,4814.0')] ).
cnf(5479,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[4814,5412]),
[iquote('0:Rew:4814.0,5412.0')] ).
cnf(5480,plain,
equal(multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))),inverse(multiply(v,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u)))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(u),u))))),v),
inference(rew,[status(thm),theory(equality)],[5479,5161]),
[iquote('0:Rew:5479.0,5161.0')] ).
cnf(5482,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),w))))))),u),
inference(rew,[status(thm),theory(equality)],[5479,4424]),
[iquote('0:Rew:5479.0,4424.0')] ).
cnf(5552,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[5482,1667]),
[iquote('0:Rew:5482.0,1667.0')] ).
cnf(5564,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(v),v),u)),w)),inverse(multiply(inverse(u),u)))))),multiply(inverse(multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[5552,4844]),
[iquote('0:Rew:5552.0,4844.0')] ).
cnf(5565,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(v),v),u)),w)),inverse(multiply(inverse(u),u))))))),multiply(multiply(inverse(v),v),multiply(inverse(multiply(inverse(v),v)),inverse(inverse(w))))),
inference(rew,[status(thm),theory(equality)],[5552,4863]),
[iquote('0:Rew:5552.0,4863.0')] ).
cnf(5569,plain,
equal(multiply(multiply(inverse(u),u),multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v))))),v),
inference(rew,[status(thm),theory(equality)],[5552,4853]),
[iquote('0:Rew:5552.0,4853.0')] ).
cnf(6692,plain,
equal(inverse(multiply(u,multiply(inverse(u),inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[5480,5165]),
[iquote('0:Rew:5480.0,5165.0')] ).
cnf(6717,plain,
equal(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(v),v),u)),w)),inverse(multiply(inverse(u),u)))))),multiply(inverse(w),multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[6692,5564]),
[iquote('0:Rew:6692.0,5564.0')] ).
cnf(6722,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v)))),inverse(multiply(inverse(v),multiply(inverse(u),u)))),
inference(rew,[status(thm),theory(equality)],[6717,5565]),
[iquote('0:Rew:6717.0,5565.0')] ).
cnf(6723,plain,
equal(multiply(multiply(inverse(u),u),multiply(inverse(multiply(inverse(u),u)),inverse(inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[5479,6722]),
[iquote('0:Rew:5479.0,6722.0')] ).
cnf(6724,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[6723,5569]),
[iquote('0:Rew:6723.0,5569.0')] ).
cnf(6725,plain,
$false,
inference(unc,[status(thm)],[6724,4452]),
[iquote('0:UnC:6724.0,4452.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : GRP416-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.08 % Command : run_spass %d %s
% 0.07/0.26 % Computer : n028.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Tue Jun 14 13:27:54 EDT 2022
% 0.07/0.26 % CPUTime :
% 27.58/27.74
% 27.58/27.74 SPASS V 3.9
% 27.58/27.74 SPASS beiseite: Proof found.
% 27.58/27.74 % SZS status Theorem
% 27.58/27.74 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.58/27.74 SPASS derived 6132 clauses, backtracked 0 clauses, performed 0 splits and kept 2773 clauses.
% 27.58/27.74 SPASS allocated 118398 KBytes.
% 27.58/27.74 SPASS spent 0:0:27.47 on the problem.
% 27.58/27.74 0:00:00.02 for the input.
% 27.58/27.74 0:00:00.00 for the FLOTTER CNF translation.
% 27.58/27.74 0:00:00.12 for inferences.
% 27.58/27.74 0:00:00.00 for the backtracking.
% 27.58/27.74 0:0:27.30 for the reduction.
% 27.58/27.74
% 27.58/27.74
% 27.58/27.74 Here is a proof with depth 14, length 62 :
% 27.58/27.74 % SZS output start Refutation
% See solution above
% 27.91/28.10 Formulae used in the proof : single_axiom prove_these_axioms_2
% 27.91/28.10
%------------------------------------------------------------------------------