TSTP Solution File: GRP428-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP428-1 : 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 11:47:25 EDT 2022
% Result : Unsatisfiable 24.05s 24.27s
% Output : Refutation 24.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 2
% Syntax : Number of clauses : 110 ( 110 unt; 0 nHn; 110 RR)
% Number of literals : 110 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(u),w))),x),inverse(multiply(v,x))))),w),
file('GRP428-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP428-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(v,x))))),inverse(multiply(multiply(inverse(multiply(inverse(y),multiply(inverse(inverse(u)),w))),z),inverse(multiply(y,z))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(59,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(inverse(inverse(v)),multiply(inverse(v),w)))),x),inverse(multiply(u,x)))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(68,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(v,x)))))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(71,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(v,x))))),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(y),w)),z),inverse(multiply(y,z)))))),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(162,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(inverse(inverse(w)),multiply(inverse(w),v))),
inference(spr,[status(thm),theory(equality)],[59,68]),
[iquote('0:SpR:59.0,68.0')] ).
cnf(177,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(inverse(v),multiply(v,w)))),x),inverse(multiply(u,x)))),w),
inference(spr,[status(thm),theory(equality)],[59]),
[iquote('0:SpR:59.0,59.0')] ).
cnf(234,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),x),inverse(multiply(inverse(u),x))))),w),
inference(spr,[status(thm),theory(equality)],[162,1]),
[iquote('0:SpR:162.0,1.0')] ).
cnf(242,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(inverse(w),multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[162]),
[iquote('0:SpR:162.0,162.0')] ).
cnf(293,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,w))),multiply(inverse(inverse(v)),multiply(inverse(x),multiply(x,w)))),
inference(spr,[status(thm),theory(equality)],[242]),
[iquote('0:SpR:242.0,242.0')] ).
cnf(300,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),x),inverse(multiply(y,x)))))),multiply(y,w)),
inference(spr,[status(thm),theory(equality)],[242,68]),
[iquote('0:SpR:242.0,68.0')] ).
cnf(304,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(v),multiply(v,w)),inverse(multiply(x,multiply(multiply(inverse(x),y),w))))))),y),
inference(spr,[status(thm),theory(equality)],[242,68]),
[iquote('0:SpR:242.0,68.0')] ).
cnf(541,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(v),multiply(v,w))),multiply(inverse(inverse(u)),multiply(inverse(x),multiply(x,w)))),
inference(spr,[status(thm),theory(equality)],[242,293]),
[iquote('0:SpR:242.0,293.0')] ).
cnf(607,plain,
equal(multiply(inverse(u),multiply(u,multiply(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(w),multiply(w,x)))),y),inverse(multiply(v,y))),z))),multiply(inverse(x),multiply(inverse(x1),multiply(x1,z)))),
inference(spr,[status(thm),theory(equality)],[177,293]),
[iquote('0:SpR:177.0,293.0')] ).
cnf(735,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(v),multiply(v,w)),inverse(multiply(inverse(u),multiply(multiply(inverse(x),multiply(x,y)),w)))))),y),
inference(spr,[status(thm),theory(equality)],[242,234]),
[iquote('0:SpR:242.0,234.0')] ).
cnf(1082,plain,
equal(multiply(inverse(u),multiply(inverse(v),multiply(v,w))),multiply(inverse(u),multiply(inverse(x),multiply(x,w)))),
inference(spr,[status(thm),theory(equality)],[177,541]),
[iquote('0:SpR:177.0,541.0')] ).
cnf(1304,plain,
equal(multiply(u,multiply(inverse(v),multiply(v,w))),multiply(u,multiply(inverse(x),multiply(x,w)))),
inference(spr,[status(thm),theory(equality)],[177,1082]),
[iquote('0:SpR:177.0,1082.0')] ).
cnf(1491,plain,
equal(multiply(inverse(u),multiply(u,multiply(inverse(v),multiply(v,w)))),multiply(inverse(x),multiply(x,multiply(inverse(y),multiply(y,w))))),
inference(spr,[status(thm),theory(equality)],[1304,242]),
[iquote('0:SpR:1304.0,242.0')] ).
cnf(3899,plain,
equal(multiply(multiply(inverse(u),multiply(u,v)),inverse(multiply(multiply(inverse(w),multiply(w,inverse(multiply(multiply(inverse(multiply(inverse(x),y)),z),inverse(multiply(x,z)))))),inverse(y)))),v),
inference(spr,[status(thm),theory(equality)],[68,735]),
[iquote('0:SpR:68.0,735.0')] ).
cnf(3956,plain,
equal(multiply(multiply(inverse(u),multiply(u,v)),inverse(multiply(w,inverse(w)))),v),
inference(rew,[status(thm),theory(equality)],[68,3899]),
[iquote('0:Rew:68.0,3899.0')] ).
cnf(4021,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,inverse(multiply(w,inverse(w)))))),multiply(inverse(inverse(v)),multiply(inverse(multiply(inverse(x),multiply(x,y))),y))),
inference(spr,[status(thm),theory(equality)],[3956,293]),
[iquote('0:SpR:3956.0,293.0')] ).
cnf(4028,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(u,multiply(inverse(x),multiply(x,inverse(multiply(y,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[3956,1304]),
[iquote('0:SpR:3956.0,1304.0')] ).
cnf(4030,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),w),inverse(multiply(x,multiply(multiply(inverse(x),y),inverse(multiply(z,inverse(z)))))))))),y),
inference(spr,[status(thm),theory(equality)],[3956,304]),
[iquote('0:SpR:3956.0,304.0')] ).
cnf(4039,plain,
equal(multiply(inverse(multiply(inverse(u),multiply(u,v))),v),multiply(inverse(multiply(inverse(w),multiply(w,x))),x)),
inference(spr,[status(thm),theory(equality)],[3956,300]),
[iquote('0:SpR:3956.0,300.0')] ).
cnf(4091,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,inverse(w)))),inverse(multiply(multiply(inverse(multiply(inverse(x),multiply(x,v))),y),inverse(multiply(u,y))))),
inference(spr,[status(thm),theory(equality)],[300,3956]),
[iquote('0:SpR:300.0,3956.0')] ).
cnf(4505,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),w),inverse(multiply(x,y)))))),multiply(x,y)),
inference(spr,[status(thm),theory(equality)],[4039,300]),
[iquote('0:SpR:4039.0,300.0')] ).
cnf(4527,plain,
equal(multiply(inverse(inverse(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(v,x)))))))),multiply(inverse(multiply(inverse(y),multiply(y,z))),z)),w),
inference(spr,[status(thm),theory(equality)],[4039,68]),
[iquote('0:SpR:4039.0,68.0')] ).
cnf(4672,plain,
equal(multiply(u,multiply(multiply(inverse(u),v),inverse(multiply(w,inverse(w))))),v),
inference(rew,[status(thm),theory(equality)],[4505,4030]),
[iquote('0:Rew:4505.0,4030.0')] ).
cnf(4675,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),u),
inference(rew,[status(thm),theory(equality)],[68,4527]),
[iquote('0:Rew:68.0,4527.0')] ).
cnf(4686,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,inverse(multiply(w,inverse(w)))))),v),
inference(rew,[status(thm),theory(equality)],[4675,4021]),
[iquote('0:Rew:4675.0,4021.0')] ).
cnf(4833,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,inverse(w))))),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(x),v)),y),inverse(multiply(x,y)))))),
inference(spr,[status(thm),theory(equality)],[68,4672]),
[iquote('0:SpR:68.0,4672.0')] ).
cnf(4921,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),multiply(u,inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[4686,3956]),
[iquote('0:SpR:4686.0,3956.0')] ).
cnf(4926,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(v),w),inverse(multiply(inverse(u),w))))),multiply(v,inverse(multiply(x,inverse(x))))),
inference(spr,[status(thm),theory(equality)],[4686,234]),
[iquote('0:SpR:4686.0,234.0')] ).
cnf(4964,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,multiply(w,inverse(multiply(x,inverse(x))))))),multiply(inverse(inverse(v)),w)),
inference(spr,[status(thm),theory(equality)],[4686,242]),
[iquote('0:SpR:4686.0,242.0')] ).
cnf(4991,plain,
equal(multiply(inverse(u),multiply(u,multiply(inverse(v),multiply(v,inverse(multiply(w,inverse(w))))))),multiply(inverse(inverse(inverse(x))),x)),
inference(spr,[status(thm),theory(equality)],[4686,1491]),
[iquote('0:SpR:4686.0,1491.0')] ).
cnf(5036,plain,
equal(multiply(inverse(inverse(inverse(u))),u),multiply(inverse(inverse(inverse(v))),v)),
inference(rew,[status(thm),theory(equality)],[4964,4991]),
[iquote('0:Rew:4964.0,4991.0')] ).
cnf(5101,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(inverse(inverse(inverse(inverse(v)))),multiply(inverse(inverse(inverse(w))),w))),
inference(spr,[status(thm),theory(equality)],[5036,242]),
[iquote('0:SpR:5036.0,242.0')] ).
cnf(5151,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(v))),v)),w),inverse(multiply(inverse(inverse(multiply(inverse(u),x))),w))))),x),
inference(spr,[status(thm),theory(equality)],[5036,1]),
[iquote('0:SpR:5036.0,1.0')] ).
cnf(5160,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(u))),u)),v),inverse(multiply(inverse(inverse(multiply(inverse(w),multiply(w,x)))),v)))),x),
inference(spr,[status(thm),theory(equality)],[5036,177]),
[iquote('0:SpR:5036.0,177.0')] ).
cnf(5165,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(v,x))))),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(y))),y)),z),inverse(multiply(inverse(inverse(w)),z)))))),
inference(spr,[status(thm),theory(equality)],[5036,71]),
[iquote('0:SpR:5036.0,71.0')] ).
cnf(5174,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),x),inverse(multiply(inverse(inverse(inverse(y))),y)))))),multiply(inverse(inverse(inverse(x))),w)),
inference(spr,[status(thm),theory(equality)],[5036,300]),
[iquote('0:SpR:5036.0,300.0')] ).
cnf(5179,plain,
equal(multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),v)),w),inverse(multiply(u,w)))))))),multiply(inverse(inverse(inverse(x))),x)),v),
inference(spr,[status(thm),theory(equality)],[5036,68]),
[iquote('0:SpR:5036.0,68.0')] ).
cnf(5192,plain,
equal(multiply(multiply(inverse(inverse(inverse(inverse(u)))),multiply(inverse(inverse(inverse(v))),v)),inverse(multiply(w,inverse(w)))),u),
inference(spr,[status(thm),theory(equality)],[5036,3956]),
[iquote('0:SpR:5036.0,3956.0')] ).
cnf(5197,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,w))),multiply(inverse(inverse(v)),multiply(inverse(inverse(inverse(inverse(w)))),multiply(inverse(inverse(inverse(x))),x)))),
inference(spr,[status(thm),theory(equality)],[5036,293]),
[iquote('0:SpR:5036.0,293.0')] ).
cnf(5962,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),inverse(multiply(x,inverse(x))))),u),
inference(spr,[status(thm),theory(equality)],[3956,4675]),
[iquote('0:SpR:3956.0,4675.0')] ).
cnf(6018,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(multiply(inverse(multiply(inverse(x),multiply(inverse(y),multiply(y,u)))),z),inverse(multiply(x,z)))),
inference(spr,[status(thm),theory(equality)],[177,4675]),
[iquote('0:SpR:177.0,4675.0')] ).
cnf(6214,plain,
equal(multiply(u,inverse(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))))),multiply(u,inverse(multiply(x,inverse(x))))),
inference(spr,[status(thm),theory(equality)],[4921]),
[iquote('0:SpR:4921.0,4921.0')] ).
cnf(6231,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,inverse(v)))),inverse(multiply(w,inverse(w))))),inverse(multiply(x,inverse(x)))),
inference(spr,[status(thm),theory(equality)],[4921,4672]),
[iquote('0:SpR:4921.0,4672.0')] ).
cnf(6251,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(multiply(inverse(v),multiply(v,inverse(multiply(w,inverse(w)))))),inverse(multiply(x,inverse(x))))),u),
inference(spr,[status(thm),theory(equality)],[4921,4675]),
[iquote('0:SpR:4921.0,4675.0')] ).
cnf(6279,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[4672,6231]),
[iquote('0:Rew:4672.0,6231.0')] ).
cnf(6382,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),multiply(inverse(x),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[6279,242]),
[iquote('0:SpR:6279.0,242.0')] ).
cnf(6487,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(u)))),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(x,inverse(x))),
inference(spr,[status(thm),theory(equality)],[6279,4675]),
[iquote('0:SpR:6279.0,4675.0')] ).
cnf(6495,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(multiply(u,inverse(u))),multiply(inverse(v),multiply(v,w)))),x),inverse(multiply(multiply(y,inverse(y)),x)))),w),
inference(spr,[status(thm),theory(equality)],[6279,177]),
[iquote('0:SpR:6279.0,177.0')] ).
cnf(6575,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[4675,6487]),
[iquote('0:Rew:4675.0,6487.0')] ).
cnf(6624,plain,
equal(multiply(u,multiply(v,inverse(v))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6575,4672]),
[iquote('0:SpR:6575.0,4672.0')] ).
cnf(6641,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),multiply(inverse(v),multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[6575,242]),
[iquote('0:SpR:6575.0,242.0')] ).
cnf(6647,plain,
equal(multiply(u,multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6575,4672]),
[iquote('0:SpR:6575.0,4672.0')] ).
cnf(6693,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(inverse(multiply(inverse(w),x))))))))),x),
inference(spr,[status(thm),theory(equality)],[6575,68]),
[iquote('0:SpR:6575.0,68.0')] ).
cnf(6755,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(w,inverse(w)))),x),inverse(multiply(inverse(u),x))))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[6575,234]),
[iquote('0:SpR:6575.0,234.0')] ).
cnf(6797,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[6624,6641]),
[iquote('0:Rew:6624.0,6641.0')] ).
cnf(6800,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),v)),w),inverse(multiply(u,w)))))),v),
inference(rew,[status(thm),theory(equality)],[6797,68]),
[iquote('0:Rew:6797.0,68.0')] ).
cnf(6803,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(u,inverse(inverse(inverse(multiply(x,inverse(x))))))),
inference(rew,[status(thm),theory(equality)],[6797,4028]),
[iquote('0:Rew:6797.0,4028.0')] ).
cnf(6812,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(inverse(inverse(inverse(multiply(v,inverse(v)))))),inverse(multiply(w,inverse(w))))),u),
inference(rew,[status(thm),theory(equality)],[6797,6251]),
[iquote('0:Rew:6797.0,6251.0')] ).
cnf(6840,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(u,v))),w),inverse(multiply(inverse(inverse(inverse(x))),x)))))),multiply(inverse(inverse(inverse(w))),v)),
inference(rew,[status(thm),theory(equality)],[6797,5174]),
[iquote('0:Rew:6797.0,5174.0')] ).
cnf(7044,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(inverse(inverse(v))),v)),u),
inference(rew,[status(thm),theory(equality)],[6800,5179]),
[iquote('0:Rew:6800.0,5179.0')] ).
cnf(7051,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[7044,5192]),
[iquote('0:Rew:7044.0,5192.0')] ).
cnf(7065,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,w))),multiply(inverse(inverse(v)),inverse(inverse(w)))),
inference(rew,[status(thm),theory(equality)],[7044,5197]),
[iquote('0:Rew:7044.0,5197.0')] ).
cnf(7070,plain,
equal(multiply(inverse(u),multiply(u,v)),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[7044,5101]),
[iquote('0:Rew:7044.0,5101.0')] ).
cnf(7665,plain,
equal(multiply(inverse(u),multiply(u,multiply(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(w),multiply(w,x)))),y),inverse(multiply(v,y))),z))),multiply(inverse(x),inverse(inverse(z)))),
inference(rew,[status(thm),theory(equality)],[7070,607]),
[iquote('0:Rew:7070.0,607.0')] ).
cnf(7692,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(multiply(inverse(multiply(inverse(x),inverse(inverse(u)))),y),inverse(multiply(x,y)))),
inference(rew,[status(thm),theory(equality)],[7070,6018]),
[iquote('0:Rew:7070.0,6018.0')] ).
cnf(7850,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),inverse(inverse(w))),
inference(rew,[status(thm),theory(equality)],[7070,6382]),
[iquote('0:Rew:7070.0,6382.0')] ).
cnf(7958,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,inverse(w)))),inverse(multiply(multiply(inverse(inverse(inverse(v))),x),inverse(multiply(u,x))))),
inference(rew,[status(thm),theory(equality)],[7070,4091]),
[iquote('0:Rew:7070.0,4091.0')] ).
cnf(8025,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(u))),u)),v),inverse(multiply(inverse(inverse(inverse(inverse(w)))),v)))),w),
inference(rew,[status(thm),theory(equality)],[7070,5160]),
[iquote('0:Rew:7070.0,5160.0')] ).
cnf(8086,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(multiply(inverse(inverse(inverse(v))),v)),inverse(multiply(w,inverse(w))))),u),
inference(rew,[status(thm),theory(equality)],[7070,5962]),
[iquote('0:Rew:7070.0,5962.0')] ).
cnf(8155,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(v)))),w),inverse(multiply(multiply(x,inverse(x)),w)))),v),
inference(rew,[status(thm),theory(equality)],[7070,6495]),
[iquote('0:Rew:7070.0,6495.0')] ).
cnf(8244,plain,
equal(multiply(inverse(inverse(u)),inverse(inverse(v))),inverse(inverse(multiply(u,v)))),
inference(rew,[status(thm),theory(equality)],[7070,7065]),
[iquote('0:Rew:7070.0,7065.0')] ).
cnf(8286,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[6624,6812,8244,7051]),
[iquote('0:Rew:6624.0,6812.0,8244.0,6812.0,7051.0,6812.0')] ).
cnf(8329,plain,
equal(multiply(u,multiply(inverse(inverse(inverse(v))),v)),multiply(u,inverse(inverse(inverse(multiply(w,inverse(w))))))),
inference(rew,[status(thm),theory(equality)],[7070,6803]),
[iquote('0:Rew:7070.0,6803.0')] ).
cnf(8343,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(u))),u)),v),inverse(multiply(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[8286,8025]),
[iquote('0:Rew:8286.0,8025.0')] ).
cnf(8349,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(v,x))))),multiply(u,inverse(inverse(w)))),
inference(rew,[status(thm),theory(equality)],[8343,5165]),
[iquote('0:Rew:8343.0,5165.0')] ).
cnf(8351,plain,
equal(multiply(u,inverse(inverse(multiply(inverse(u),v)))),v),
inference(rew,[status(thm),theory(equality)],[8343,5151]),
[iquote('0:Rew:8343.0,5151.0')] ).
cnf(8514,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,inverse(w))))),multiply(u,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[8349,4833]),
[iquote('0:Rew:8349.0,4833.0')] ).
cnf(8873,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(v))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8514,6647]),
[iquote('0:Rew:8514.0,6647.0')] ).
cnf(8900,plain,
equal(multiply(inverse(inverse(u)),inverse(inverse(inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8514,8086]),
[iquote('0:Rew:8514.0,8086.0')] ).
cnf(8903,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8244,8900]),
[iquote('0:Rew:8244.0,8900.0')] ).
cnf(8909,plain,
equal(multiply(u,inverse(multiply(multiply(v,w),inverse(multiply(inverse(u),w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[8286,6755,6624]),
[iquote('0:Rew:8286.0,6755.0,6624.0,6755.0')] ).
cnf(8914,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8909,4926]),
[iquote('0:Rew:8909.0,4926.0')] ).
cnf(8927,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),multiply(u,inverse(multiply(w,inverse(w))))),
inference(rew,[status(thm),theory(equality)],[8914,6214]),
[iquote('0:Rew:8914.0,6214.0')] ).
cnf(9018,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8914,8927]),
[iquote('0:Rew:8914.0,8927.0')] ).
cnf(9020,plain,
equal(multiply(u,multiply(inverse(inverse(inverse(v))),v)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[9018,8329]),
[iquote('0:Rew:9018.0,8329.0')] ).
cnf(9032,plain,
equal(inverse(inverse(inverse(multiply(multiply(u,inverse(u)),inverse(v))))),v),
inference(rew,[status(thm),theory(equality)],[7070,6693,8351]),
[iquote('0:Rew:7070.0,6693.0,8351.0,6693.0')] ).
cnf(9068,plain,
equal(inverse(multiply(multiply(inverse(inverse(inverse(u))),v),inverse(multiply(w,v)))),inverse(inverse(multiply(w,u)))),
inference(rew,[status(thm),theory(equality)],[8914,7958]),
[iquote('0:Rew:8914.0,7958.0')] ).
cnf(9287,plain,
equal(inverse(multiply(inverse(inverse(inverse(u))),v)),multiply(inverse(inverse(inverse(v))),u)),
inference(rew,[status(thm),theory(equality)],[8903,6840,7070]),
[iquote('0:Rew:8903.0,6840.0,7070.0,6840.0')] ).
cnf(9319,plain,
equal(multiply(multiply(inverse(multiply(inverse(u),inverse(inverse(v)))),w),inverse(multiply(u,w))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[9020,7692,7070]),
[iquote('0:Rew:9020.0,7692.0,7070.0,7692.0')] ).
cnf(9605,plain,
equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[9287,7665,7070,9319]),
[iquote('0:Rew:9287.0,7665.0,9287.0,7665.0,7070.0,7665.0,9319.0,7665.0,7070.0,7665.0')] ).
cnf(9607,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(multiply(w,v)))),inverse(inverse(multiply(w,u)))),
inference(rew,[status(thm),theory(equality)],[9605,9068]),
[iquote('0:Rew:9605.0,9068.0')] ).
cnf(9608,plain,
equal(inverse(multiply(inverse(u),inverse(inverse(v)))),multiply(inverse(inverse(inverse(v))),u)),
inference(rew,[status(thm),theory(equality)],[9605,9287]),
[iquote('0:Rew:9605.0,9287.0')] ).
cnf(9641,plain,
equal(inverse(multiply(inverse(u),inverse(inverse(v)))),multiply(inverse(v),inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[9605,9608]),
[iquote('0:Rew:9605.0,9608.0')] ).
cnf(9652,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),inverse(inverse(multiply(v,inverse(v))))),w),inverse(multiply(multiply(x,inverse(x)),w)))),u),
inference(rew,[status(thm),theory(equality)],[9641,8155]),
[iquote('0:Rew:9641.0,8155.0')] ).
cnf(9666,plain,
equal(inverse(inverse(multiply(multiply(u,inverse(u)),v))),v),
inference(rew,[status(thm),theory(equality)],[9607,9652,9605,8873]),
[iquote('0:Rew:9607.0,9652.0,9605.0,9652.0,8873.0,9652.0')] ).
cnf(9670,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[9666,9032]),
[iquote('0:Rew:9666.0,9032.0')] ).
cnf(9687,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),w),
inference(rew,[status(thm),theory(equality)],[9670,7850]),
[iquote('0:Rew:9670.0,7850.0')] ).
cnf(9732,plain,
equal(multiply(inverse(u),inverse(inverse(v))),inverse(multiply(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[9670,9641]),
[iquote('0:Rew:9670.0,9641.0')] ).
cnf(9755,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[9670,9666]),
[iquote('0:Rew:9670.0,9666.0')] ).
cnf(9771,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[9670,9732]),
[iquote('0:Rew:9670.0,9732.0')] ).
cnf(9782,plain,
equal(multiply(inverse(multiply(u,inverse(u))),v),v),
inference(rew,[status(thm),theory(equality)],[9755,9687]),
[iquote('0:Rew:9755.0,9687.0')] ).
cnf(11803,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(spr,[status(thm),theory(equality)],[9670,9782]),
[iquote('0:SpR:9670.0,9782.0')] ).
cnf(11811,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[9771,11803]),
[iquote('0:Rew:9771.0,11803.0')] ).
cnf(11812,plain,
$false,
inference(unc,[status(thm)],[11811,2]),
[iquote('0:UnC:11811.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP428-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 11:46:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 24.05/24.27
% 24.05/24.27 SPASS V 3.9
% 24.05/24.27 SPASS beiseite: Proof found.
% 24.05/24.27 % SZS status Theorem
% 24.05/24.27 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.05/24.27 SPASS derived 8312 clauses, backtracked 0 clauses, performed 0 splits and kept 2654 clauses.
% 24.05/24.27 SPASS allocated 102758 KBytes.
% 24.05/24.27 SPASS spent 0:0:23.89 on the problem.
% 24.05/24.27 0:00:00.03 for the input.
% 24.05/24.27 0:00:00.00 for the FLOTTER CNF translation.
% 24.05/24.27 0:00:00.10 for inferences.
% 24.05/24.27 0:00:00.00 for the backtracking.
% 24.05/24.27 0:0:23.74 for the reduction.
% 24.05/24.27
% 24.05/24.27
% 24.05/24.27 Here is a proof with depth 12, length 110 :
% 24.05/24.27 % SZS output start Refutation
% See solution above
% 24.34/24.57 Formulae used in the proof : single_axiom prove_these_axioms_2
% 24.34/24.57
%------------------------------------------------------------------------------