TSTP Solution File: GRP058-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP058-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:45:05 EDT 2022
% Result : Unsatisfiable 16.46s 16.68s
% Output : Refutation 16.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of clauses : 106 ( 103 unt; 0 nHn; 106 RR)
% Number of literals : 112 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(v,multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,v))),u)))),x),
file('GRP058-1.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('GRP058-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,v))),y))),multiply(multiply(multiply(z,inverse(z)),inverse(x)),u)))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,x))),multiply(y,inverse(y))),multiply(w,u)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,z)))))),inverse(multiply(z,w))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(9,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(w))),multiply(multiply(multiply(multiply(x,inverse(x)),inverse(multiply(y,v))),multiply(z,inverse(z))),u)))),multiply(y,multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(16,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(w))),multiply(x,u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(v,x))),multiply(z,inverse(z)))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(30,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,multiply(w,inverse(multiply(multiply(x,multiply(y,inverse(y))),multiply(v,w))))))),x),
inference(spr,[status(thm),theory(equality)],[16,1]),
[iquote('0:SpR:16.0,1.0')] ).
cnf(35,plain,
equal(multiply(u,inverse(multiply(multiply(v,inverse(multiply(multiply(w,multiply(x,inverse(x))),multiply(y,v)))),multiply(w,u)))),y),
inference(spr,[status(thm),theory(equality)],[16,4]),
[iquote('0:SpR:16.0,4.0')] ).
cnf(66,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(multiply(x,inverse(x)),inverse(multiply(v,multiply(w,multiply(y,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[1,35]),
[iquote('0:SpR:1.0,35.0')] ).
cnf(90,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,w))),multiply(multiply(x,inverse(x)),inverse(multiply(v,w)))),
inference(spr,[status(thm),theory(equality)],[4,30]),
[iquote('0:SpR:4.0,30.0')] ).
cnf(125,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(multiply(multiply(y,inverse(y)),inverse(multiply(v,w))))),u)))),multiply(z,inverse(z))),
inference(spr,[status(thm),theory(equality)],[90,1]),
[iquote('0:SpR:90.0,1.0')] ).
cnf(158,plain,
equal(multiply(multiply(u,inverse(u)),inverse(v)),multiply(multiply(w,inverse(w)),inverse(v))),
inference(spr,[status(thm),theory(equality)],[1,90]),
[iquote('0:SpR:1.0,90.0')] ).
cnf(170,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[1,125]),
[iquote('0:Rew:1.0,125.0')] ).
cnf(178,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(multiply(w,inverse(w)),u)))),v),
inference(spr,[status(thm),theory(equality)],[170,1]),
[iquote('0:SpR:170.0,1.0')] ).
cnf(179,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(x,u)))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[170,4]),
[iquote('0:SpR:170.0,4.0')] ).
cnf(269,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),inverse(multiply(z,inverse(z)))),y),
inference(spr,[status(thm),theory(equality)],[170,6]),
[iquote('0:SpR:170.0,6.0')] ).
cnf(333,plain,
equal(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[158,170]),
[iquote('0:SpR:158.0,170.0')] ).
cnf(394,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(x),u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(multiply(z,inverse(z)),inverse(x)))),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[158,16]),
[iquote('0:SpR:158.0,16.0')] ).
cnf(408,plain,
equal(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(multiply(v,inverse(v)),inverse(w)))),multiply(x,inverse(x))),inverse(inverse(w))),
inference(rew,[status(thm),theory(equality)],[179,394]),
[iquote('0:Rew:179.0,394.0')] ).
cnf(448,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(multiply(v,inverse(v)),inverse(multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))))),multiply(y,inverse(y))),multiply(z,u)))),inverse(z)),
inference(spr,[status(thm),theory(equality)],[333,4]),
[iquote('0:SpR:333.0,4.0')] ).
cnf(489,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(multiply(x,inverse(x))),u)))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(z,inverse(z)))),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[333,16]),
[iquote('0:SpR:333.0,16.0')] ).
cnf(505,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[408,448]),
[iquote('0:Rew:408.0,448.0')] ).
cnf(506,plain,
equal(inverse(inverse(multiply(u,inverse(u)))),multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[179,489]),
[iquote('0:Rew:179.0,489.0')] ).
cnf(725,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(inverse(w),multiply(multiply(z,inverse(z)),multiply(multiply(x1,inverse(x1)),inverse(multiply(y,v))))))),
inference(spr,[status(thm),theory(equality)],[178,3]),
[iquote('0:SpR:178.0,3.0')] ).
cnf(734,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(multiply(z,inverse(z)),inverse(multiply(y,v))))),
inference(spr,[status(thm),theory(equality)],[170,3]),
[iquote('0:SpR:170.0,3.0')] ).
cnf(765,plain,
equal(inverse(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(inverse(multiply(w,inverse(w)))))))),v),
inference(spr,[status(thm),theory(equality)],[505,1]),
[iquote('0:SpR:505.0,1.0')] ).
cnf(777,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(u,inverse(u)))),multiply(v,w))),inverse(multiply(inverse(inverse(multiply(x,inverse(x)))),inverse(v)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[505]),
[iquote('0:SpR:505.0,505.0')] ).
cnf(794,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[170,505]),
[iquote('0:SpR:170.0,505.0')] ).
cnf(961,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(multiply(x,inverse(inverse(multiply(y,inverse(y)))))),u)))),multiply(multiply(multiply(z,inverse(z)),x),multiply(x1,inverse(x1)))),
inference(spr,[status(thm),theory(equality)],[765,16]),
[iquote('0:SpR:765.0,16.0')] ).
cnf(995,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),v)),
inference(spr,[status(thm),theory(equality)],[765,158]),
[iquote('0:SpR:765.0,158.0')] ).
cnf(1050,plain,
equal(inverse(inverse(multiply(u,inverse(inverse(multiply(v,inverse(v))))))),multiply(multiply(multiply(w,inverse(w)),u),multiply(x,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[179,961]),
[iquote('0:Rew:179.0,961.0')] ).
cnf(1276,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(u,multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[9]),
[iquote('0:SpR:9.0,9.0')] ).
cnf(1619,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))))),u),
inference(spr,[status(thm),theory(equality)],[765,794]),
[iquote('0:SpR:765.0,794.0')] ).
cnf(1639,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),multiply(inverse(inverse(multiply(x,inverse(x)))),u)))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1619,4]),
[iquote('0:SpR:1619.0,4.0')] ).
cnf(1651,plain,
equal(multiply(u,inverse(u)),multiply(inverse(inverse(multiply(v,inverse(v)))),multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1619,170]),
[iquote('0:SpR:1619.0,170.0')] ).
cnf(1729,plain,
equal(inverse(inverse(inverse(multiply(u,inverse(u))))),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[179,1639]),
[iquote('0:Rew:179.0,1639.0')] ).
cnf(1791,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(inverse(inverse(inverse(multiply(w,inverse(w))))),v)),
inference(spr,[status(thm),theory(equality)],[1729,995]),
[iquote('0:SpR:1729.0,995.0')] ).
cnf(1792,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(u,inverse(inverse(inverse(multiply(w,inverse(w))))))),
inference(spr,[status(thm),theory(equality)],[1729,1276]),
[iquote('0:SpR:1729.0,1276.0')] ).
cnf(1815,plain,
equal(inverse(inverse(inverse(multiply(u,inverse(u))))),inverse(inverse(inverse(multiply(v,inverse(v)))))),
inference(spr,[status(thm),theory(equality)],[1729]),
[iquote('0:SpR:1729.0,1729.0')] ).
cnf(1829,plain,
equal(inverse(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u)))))))),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[1729]),
[iquote('0:SpR:1729.0,1729.0')] ).
cnf(1838,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,inverse(multiply(multiply(u,multiply(w,inverse(w))),multiply(x,v)))),inverse(inverse(inverse(multiply(y,inverse(y)))))))),x),
inference(spr,[status(thm),theory(equality)],[1729,35]),
[iquote('0:SpR:1729.0,35.0')] ).
cnf(1841,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(w,inverse(w))),inverse(inverse(inverse(multiply(x,inverse(x)))))))),multiply(multiply(multiply(y,inverse(y)),inverse(multiply(v,u))),multiply(z,inverse(z)))),
inference(spr,[status(thm),theory(equality)],[1729,16]),
[iquote('0:SpR:1729.0,16.0')] ).
cnf(1851,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),inverse(inverse(inverse(inverse(multiply(z,inverse(z))))))),y),
inference(spr,[status(thm),theory(equality)],[1729,6]),
[iquote('0:SpR:1729.0,6.0')] ).
cnf(2458,plain,
equal(multiply(multiply(inverse(inverse(multiply(u,inverse(u)))),inverse(inverse(inverse(multiply(v,inverse(v)))))),w),multiply(multiply(x,inverse(x)),w)),
inference(spr,[status(thm),theory(equality)],[1815,995]),
[iquote('0:SpR:1815.0,995.0')] ).
cnf(2846,plain,
equal(multiply(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(z,inverse(z)))))))))),y),
inference(spr,[status(thm),theory(equality)],[1829,6]),
[iquote('0:SpR:1829.0,6.0')] ).
cnf(3508,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[1651,1619]),
[iquote('0:SpR:1651.0,1619.0')] ).
cnf(3724,plain,
equal(inverse(multiply(u,multiply(multiply(multiply(v,inverse(v)),inverse(multiply(inverse(w),u))),multiply(multiply(x,inverse(x)),inverse(multiply(y,w)))))),y),
inference(rew,[status(thm),theory(equality)],[3508,269]),
[iquote('0:Rew:3508.0,269.0')] ).
cnf(3845,plain,
equal(inverse(inverse(multiply(u,inverse(u)))),multiply(multiply(v,inverse(v)),multiply(w,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[3508,506]),
[iquote('0:Rew:3508.0,506.0')] ).
cnf(3963,plain,
equal(multiply(u,inverse(inverse(inverse(inverse(multiply(v,inverse(v))))))),u),
inference(rew,[status(thm),theory(equality)],[3724,1851]),
[iquote('0:Rew:3724.0,1851.0')] ).
cnf(3964,plain,
equal(multiply(u,inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(v,inverse(v)))))))))),u),
inference(rew,[status(thm),theory(equality)],[3724,2846]),
[iquote('0:Rew:3724.0,2846.0')] ).
cnf(4944,plain,
equal(multiply(u,inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(inverse(multiply(x,inverse(x))))))),w))))))))),u),
inference(spr,[status(thm),theory(equality)],[765,3964]),
[iquote('0:SpR:765.0,3964.0')] ).
cnf(5284,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(inverse(inverse(inverse(multiply(multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(inverse(multiply(y,inverse(y))))))),x)))),v)),
inference(spr,[status(thm),theory(equality)],[765,1791]),
[iquote('0:SpR:765.0,1791.0')] ).
cnf(6258,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(v,inverse(v)),multiply(w,inverse(w)))))),u),
inference(spr,[status(thm),theory(equality)],[3845,3963]),
[iquote('0:SpR:3845.0,3963.0')] ).
cnf(6266,plain,
equal(inverse(multiply(multiply(u,inverse(u)),multiply(v,inverse(v)))),multiply(w,inverse(w))),
inference(spr,[status(thm),theory(equality)],[3845,1729]),
[iquote('0:SpR:3845.0,1729.0')] ).
cnf(6280,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(inverse(v),inverse(inverse(multiply(w,inverse(w))))))),v),
inference(spr,[status(thm),theory(equality)],[3845,1]),
[iquote('0:SpR:3845.0,1.0')] ).
cnf(6632,plain,
equal(multiply(inverse(inverse(multiply(multiply(u,inverse(u)),multiply(v,inverse(v))))),inverse(multiply(multiply(w,inverse(multiply(multiply(x,multiply(y,inverse(y))),multiply(z,w)))),x))),z),
inference(spr,[status(thm),theory(equality)],[6258,35]),
[iquote('0:SpR:6258.0,35.0')] ).
cnf(6681,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(v,inverse(v)),inverse(inverse(inverse(multiply(w,inverse(w))))))))),u),
inference(spr,[status(thm),theory(equality)],[1729,6258]),
[iquote('0:SpR:1729.0,6258.0')] ).
cnf(6760,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(v,inverse(v)),multiply(multiply(multiply(w,inverse(w)),multiply(x,inverse(x))),y))),multiply(multiply(multiply(z,inverse(z)),inverse(multiply(x1,inverse(x1)))),u)))),y),
inference(spr,[status(thm),theory(equality)],[6266,3]),
[iquote('0:SpR:6266.0,3.0')] ).
cnf(6794,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(v,inverse(v)),multiply(multiply(multiply(w,inverse(w)),multiply(x,inverse(x))),multiply(y,inverse(y))))))),u),
inference(spr,[status(thm),theory(equality)],[6266,6258]),
[iquote('0:SpR:6266.0,6258.0')] ).
cnf(7118,plain,
equal(multiply(multiply(u,inverse(u)),multiply(multiply(multiply(v,inverse(v)),multiply(w,inverse(w))),x)),x),
inference(rew,[status(thm),theory(equality)],[178,6760,3508]),
[iquote('0:Rew:178.0,6760.0,3508.0,6760.0')] ).
cnf(7121,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(v))))),u),
inference(rew,[status(thm),theory(equality)],[7118,6794]),
[iquote('0:Rew:7118.0,6794.0')] ).
cnf(7124,plain,
equal(inverse(multiply(multiply(u,inverse(u)),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[7121,765]),
[iquote('0:Rew:7121.0,765.0')] ).
cnf(7165,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(inverse(inverse(inverse(multiply(multiply(multiply(w,inverse(w)),inverse(x)),x)))),v)),
inference(rew,[status(thm),theory(equality)],[7121,5284]),
[iquote('0:Rew:7121.0,5284.0')] ).
cnf(7204,plain,
equal(multiply(multiply(u,inverse(u)),inverse(inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[7121,6280]),
[iquote('0:Rew:7121.0,6280.0')] ).
cnf(7347,plain,
equal(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w))),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[7121,1050]),
[iquote('0:Rew:7121.0,1050.0')] ).
cnf(7357,plain,
equal(multiply(u,inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(multiply(multiply(v,inverse(v)),inverse(w)),w))))))))),u),
inference(rew,[status(thm),theory(equality)],[7121,4944]),
[iquote('0:Rew:7121.0,4944.0')] ).
cnf(7391,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),u),
inference(rew,[status(thm),theory(equality)],[7124,6681]),
[iquote('0:Rew:7124.0,6681.0')] ).
cnf(7439,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),multiply(y,v)),
inference(rew,[status(thm),theory(equality)],[7124,734]),
[iquote('0:Rew:7124.0,734.0')] ).
cnf(7524,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[7391,1792]),
[iquote('0:Rew:7391.0,1792.0')] ).
cnf(7591,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(u)))),v),multiply(multiply(w,inverse(w)),v)),
inference(rew,[status(thm),theory(equality)],[7391,2458]),
[iquote('0:Rew:7391.0,2458.0')] ).
cnf(7611,plain,
equal(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(w))))),multiply(multiply(multiply(x,inverse(x)),inverse(multiply(v,u))),multiply(y,inverse(y)))),
inference(rew,[status(thm),theory(equality)],[7391,1841]),
[iquote('0:Rew:7391.0,1841.0')] ).
cnf(7623,plain,
equal(multiply(inverse(u),inverse(multiply(v,inverse(multiply(multiply(u,multiply(w,inverse(w))),multiply(x,v)))))),x),
inference(rew,[status(thm),theory(equality)],[7391,1838]),
[iquote('0:Rew:7391.0,1838.0')] ).
cnf(7876,plain,
equal(multiply(inverse(inverse(multiply(multiply(u,inverse(u)),multiply(v,inverse(v))))),inverse(multiply(multiply(w,inverse(multiply(x,multiply(y,w)))),x))),y),
inference(rew,[status(thm),theory(equality)],[7524,6632]),
[iquote('0:Rew:7524.0,6632.0')] ).
cnf(7996,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(multiply(x,inverse(x)),inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[7524,66]),
[iquote('0:Rew:7524.0,66.0')] ).
cnf(8673,plain,
equal(multiply(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),w)),w),
inference(rew,[status(thm),theory(equality)],[7524,7118]),
[iquote('0:Rew:7524.0,7118.0')] ).
cnf(8924,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,w)),multiply(multiply(multiply(x,inverse(x)),inverse(y)),u)))),inverse(multiply(inverse(w),inverse(multiply(y,v))))),
inference(rew,[status(thm),theory(equality)],[8673,725]),
[iquote('0:Rew:8673.0,725.0')] ).
cnf(8948,plain,
equal(multiply(multiply(u,inverse(u)),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[7524,7347]),
[iquote('0:Rew:7524.0,7347.0')] ).
cnf(8968,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[8948,7204]),
[iquote('0:Rew:8948.0,7204.0')] ).
cnf(9102,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(u)))),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[8948,7591]),
[iquote('0:Rew:8948.0,7591.0')] ).
cnf(9106,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(u,inverse(u)))),multiply(v,w))),inverse(inverse(inverse(inverse(v))))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[9102,777]),
[iquote('0:Rew:9102.0,777.0')] ).
cnf(9315,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),inverse(inverse(inverse(multiply(v,w))))),
inference(rew,[status(thm),theory(equality)],[8948,7996]),
[iquote('0:Rew:8948.0,7996.0')] ).
cnf(9391,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[8968,7623,9315,7524]),
[iquote('0:Rew:8968.0,7623.0,9315.0,7623.0,7524.0,7623.0')] ).
cnf(9451,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8968,7357,8948]),
[iquote('0:Rew:8968.0,7357.0,8948.0,7357.0')] ).
cnf(9508,plain,
equal(multiply(inverse(inverse(inverse(multiply(u,v)))),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[9102,9106,8968]),
[iquote('0:Rew:9102.0,9106.0,8968.0,9106.0')] ).
cnf(9516,plain,
equal(multiply(inverse(inverse(inverse(multiply(inverse(inverse(inverse(u))),u)))),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[8948,7165]),
[iquote('0:Rew:8948.0,7165.0,8948.0,7165.0')] ).
cnf(9634,plain,
equal(inverse(inverse(inverse(multiply(inverse(u),inverse(inverse(inverse(v))))))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[9315,7439,7524,8948]),
[iquote('0:Rew:9315.0,7439.0,7524.0,7439.0,8948.0,7439.0')] ).
cnf(9679,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),multiply(inverse(v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[7524,7611,8948]),
[iquote('0:Rew:7524.0,7611.0,7524.0,7611.0,8948.0,7611.0')] ).
cnf(9683,plain,
equal(multiply(multiply(inverse(u),inverse(v)),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[9679,9508]),
[iquote('0:Rew:9679.0,9508.0')] ).
cnf(9686,plain,
equal(multiply(u,multiply(inverse(v),inverse(inverse(inverse(inverse(v)))))),u),
inference(rew,[status(thm),theory(equality)],[9679,9451]),
[iquote('0:Rew:9679.0,9451.0')] ).
cnf(9690,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),multiply(inverse(w),inverse(v))),
inference(rew,[status(thm),theory(equality)],[9679,9315]),
[iquote('0:Rew:9679.0,9315.0')] ).
cnf(9694,plain,
equal(multiply(multiply(inverse(u),inverse(inverse(inverse(inverse(u))))),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[9679,9516]),
[iquote('0:Rew:9679.0,9516.0')] ).
cnf(9699,plain,
equal(multiply(inverse(inverse(inverse(inverse(u)))),inverse(inverse(v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[9679,9634]),
[iquote('0:Rew:9679.0,9634.0')] ).
cnf(9705,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[8968,9686]),
[iquote('0:Rew:8968.0,9686.0')] ).
cnf(9707,plain,
equal(multiply(u,inverse(inverse(v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[8968,9699]),
[iquote('0:Rew:8968.0,9699.0')] ).
cnf(9716,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[8968,9694]),
[iquote('0:Rew:8968.0,9694.0')] ).
cnf(9717,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[9716,2]),
[iquote('0:Rew:9716.0,2.2')] ).
cnf(9730,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[9102,7876,9707,7524,9683,9690]),
[iquote('0:Rew:9102.0,7876.0,9707.0,7876.0,7524.0,7876.0,9683.0,7876.0,9690.0,7876.0')] ).
cnf(9745,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[9730,8948]),
[iquote('0:Rew:9730.0,8948.0')] ).
cnf(9757,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[9730,9679]),
[iquote('0:Rew:9730.0,9679.0')] ).
cnf(9767,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),inverse(multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[9757,9690]),
[iquote('0:Rew:9757.0,9690.0')] ).
cnf(9869,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[9730,8924,9757,9767,9745]),
[iquote('0:Rew:9730.0,8924.0,9757.0,8924.0,9767.0,8924.0,9745.0,8924.0,9730.0,8924.0,9757.0,8924.0')] ).
cnf(9968,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[9730,9717,9869]),
[iquote('0:Rew:9730.0,9717.2,9869.0,9717.1')] ).
cnf(9969,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[9968]),
[iquote('0:Obv:9968.2')] ).
cnf(11270,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[9705,9391]),
[iquote('0:SpR:9705.0,9391.0')] ).
cnf(11277,plain,
$false,
inference(unc,[status(thm)],[11270,9969]),
[iquote('0:UnC:11270.0,9969.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP058-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 04:01:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 16.46/16.68
% 16.46/16.68 SPASS V 3.9
% 16.46/16.68 SPASS beiseite: Proof found.
% 16.46/16.68 % SZS status Theorem
% 16.46/16.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.46/16.68 SPASS derived 8252 clauses, backtracked 0 clauses, performed 0 splits and kept 2547 clauses.
% 16.46/16.68 SPASS allocated 88242 KBytes.
% 16.46/16.68 SPASS spent 0:0:16.32 on the problem.
% 16.46/16.68 0:00:00.03 for the input.
% 16.46/16.68 0:00:00.00 for the FLOTTER CNF translation.
% 16.46/16.68 0:00:00.08 for inferences.
% 16.46/16.68 0:00:00.00 for the backtracking.
% 16.46/16.68 0:0:16.18 for the reduction.
% 16.46/16.68
% 16.46/16.68
% 16.46/16.68 Here is a proof with depth 14, length 106 :
% 16.46/16.68 % SZS output start Refutation
% See solution above
% 16.66/16.83 Formulae used in the proof : single_axiom prove_these_axioms
% 16.66/16.83
%------------------------------------------------------------------------------