TSTP Solution File: GRP413-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP413-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 29.52s 29.69s
% Output : Refutation 29.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 2
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 77 RR)
% Number of literals : 77 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),w),
file('GRP413-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP413-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v))),inverse(multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),inverse(x))),w))),x))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(24,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(29,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),inverse(u))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(w),w),inverse(x))),y))),x)))),u)),multiply(v,inverse(multiply(y,w)))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(39,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,v)))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),w))),x)),
inference(spr,[status(thm),theory(equality)],[1,24]),
[iquote('0:SpR:1.0,24.0')] ).
cnf(57,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(multiply(multiply(multiply(inverse(w),w),inverse(multiply(inverse(multiply(v,inverse(w))),x))),w)))),inverse(u))),multiply(inverse(x),y)))),u)),y),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(62,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,v)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x)),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x)),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x))),
inference(spr,[status(thm),theory(equality)],[4,24]),
[iquote('0:SpR:4.0,24.0')] ).
cnf(88,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),inverse(multiply(inverse(x),y))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))))),y),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(99,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),inverse(u))),multiply(inverse(v),w)))),u)),w),
inference(rew,[status(thm),theory(equality)],[1,57]),
[iquote('0:Rew:1.0,57.0')] ).
cnf(107,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,inverse(u))),multiply(v,w)))),u)),w),
inference(spr,[status(thm),theory(equality)],[99]),
[iquote('0:SpR:99.0,99.0')] ).
cnf(151,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,w)),multiply(inverse(multiply(x,inverse(v))),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[107,24]),
[iquote('0:SpR:107.0,24.0')] ).
cnf(211,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[107,151]),
[iquote('0:SpR:107.0,151.0')] ).
cnf(223,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(w,inverse(v))),x))),v)))),multiply(u,y)),multiply(inverse(x),multiply(w,y))),
inference(spr,[status(thm),theory(equality)],[1,151]),
[iquote('0:SpR:1.0,151.0')] ).
cnf(275,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(multiply(x,v)),multiply(x,y))),multiply(inverse(multiply(z,w)),multiply(z,multiply(u,y)))),
inference(spr,[status(thm),theory(equality)],[211]),
[iquote('0:SpR:211.0,211.0')] ).
cnf(297,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(x,multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(y,inverse(v))),multiply(y,x)))),w))),
inference(spr,[status(thm),theory(equality)],[107,211]),
[iquote('0:SpR:107.0,211.0')] ).
cnf(749,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(inverse(multiply(y,inverse(multiply(multiply(multiply(inverse(z),z),inverse(multiply(inverse(multiply(inverse(multiply(x1,w)),inverse(z))),u))),z)))),multiply(y,multiply(x1,x)))),
inference(spr,[status(thm),theory(equality)],[1,275]),
[iquote('0:SpR:1.0,275.0')] ).
cnf(784,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(inverse(u),multiply(inverse(multiply(y,w)),multiply(y,x)))),
inference(rew,[status(thm),theory(equality)],[223,749]),
[iquote('0:Rew:223.0,749.0')] ).
cnf(851,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),inverse(u))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(w),w),inverse(x))),multiply(inverse(multiply(y,z)),multiply(y,x1))))),x)))),u)),multiply(v,inverse(multiply(multiply(inverse(multiply(x2,z)),multiply(x2,x1)),w)))),
inference(spr,[status(thm),theory(equality)],[784,29]),
[iquote('0:SpR:784.0,29.0')] ).
cnf(975,plain,
equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(u,multiply(inverse(multiply(y,w)),multiply(y,x)))),
inference(spr,[status(thm),theory(equality)],[107,784]),
[iquote('0:SpR:107.0,784.0')] ).
cnf(991,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(v,w)),multiply(v,x)),y))),multiply(u,inverse(multiply(multiply(inverse(multiply(z,w)),multiply(z,x)),y)))),
inference(rew,[status(thm),theory(equality)],[29,851]),
[iquote('0:Rew:29.0,851.0')] ).
cnf(1750,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,inverse(u))),multiply(v,inverse(multiply(multiply(inverse(multiply(w,x)),multiply(w,y)),z)))))),u)),inverse(multiply(multiply(inverse(multiply(x1,x)),multiply(x1,y)),z))),
inference(spr,[status(thm),theory(equality)],[991,107]),
[iquote('0:SpR:991.0,107.0')] ).
cnf(1897,plain,
equal(inverse(multiply(multiply(inverse(multiply(u,v)),multiply(u,w)),x)),inverse(multiply(multiply(inverse(multiply(y,v)),multiply(y,w)),x))),
inference(rew,[status(thm),theory(equality)],[107,1750]),
[iquote('0:Rew:107.0,1750.0')] ).
cnf(2740,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,w)),multiply(v,w)))),u)),multiply(x,inverse(multiply(multiply(multiply(inverse(y),y),inverse(multiply(inverse(multiply(x,inverse(y))),inverse(u)))),y)))),
inference(spr,[status(thm),theory(equality)],[297,29]),
[iquote('0:SpR:297.0,29.0')] ).
cnf(2923,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,w)),multiply(v,w)))),u)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1,2740]),
[iquote('0:Rew:1.0,2740.0')] ).
cnf(2986,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[24,2923]),
[iquote('0:SpR:24.0,2923.0')] ).
cnf(3117,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(v))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[2986,24]),
[iquote('0:SpR:2986.0,24.0')] ).
cnf(3145,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),multiply(multiply(multiply(inverse(w),w),inverse(multiply(inverse(x),x))),w)),
inference(spr,[status(thm),theory(equality)],[2986,24]),
[iquote('0:SpR:2986.0,24.0')] ).
cnf(3203,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),u),u),
inference(rew,[status(thm),theory(equality)],[24,3145]),
[iquote('0:Rew:24.0,3145.0')] ).
cnf(3482,plain,
equal(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),inverse(multiply(inverse(w),w))),inverse(u))),inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),v),
inference(spr,[status(thm),theory(equality)],[3203,24]),
[iquote('0:SpR:3203.0,24.0')] ).
cnf(3489,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),w))),inverse(u))),v))),u)),v),
inference(spr,[status(thm),theory(equality)],[3203,107]),
[iquote('0:SpR:3203.0,107.0')] ).
cnf(3506,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,v)),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[3203,297]),
[iquote('0:SpR:3203.0,297.0')] ).
cnf(3702,plain,
equal(multiply(inverse(inverse(u)),inverse(u)),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[3506,3117]),
[iquote('0:Rew:3506.0,3117.0')] ).
cnf(3715,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(x),y))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))))),y),
inference(rew,[status(thm),theory(equality)],[3506,88]),
[iquote('0:Rew:3506.0,88.0')] ).
cnf(3729,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,v)))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x))),
inference(rew,[status(thm),theory(equality)],[3506,62]),
[iquote('0:Rew:3506.0,62.0')] ).
cnf(3820,plain,
equal(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),y))),v))))),x),
inference(rew,[status(thm),theory(equality)],[3506,3715]),
[iquote('0:Rew:3506.0,3715.0')] ).
cnf(3838,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),inverse(w)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[3702,3203]),
[iquote('0:SpR:3702.0,3203.0')] ).
cnf(3842,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(inverse(v)),inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),w),
inference(spr,[status(thm),theory(equality)],[3702,24]),
[iquote('0:SpR:3702.0,24.0')] ).
cnf(3849,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[3702]),
[iquote('0:SpR:3702.0,3702.0')] ).
cnf(3911,plain,
equal(inverse(multiply(multiply(inverse(multiply(u,v)),multiply(u,v)),w)),inverse(multiply(multiply(inverse(inverse(x)),inverse(x)),w))),
inference(spr,[status(thm),theory(equality)],[3702,1897]),
[iquote('0:SpR:3702.0,1897.0')] ).
cnf(3917,plain,
equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,w))),multiply(u,multiply(inverse(inverse(x)),inverse(x)))),
inference(spr,[status(thm),theory(equality)],[3702,975]),
[iquote('0:SpR:3702.0,975.0')] ).
cnf(3925,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(inverse(w)),inverse(w)),inverse(x)),v)))),x),
inference(spr,[status(thm),theory(equality)],[3702,24]),
[iquote('0:SpR:3702.0,24.0')] ).
cnf(3975,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(u))),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[3702,211]),
[iquote('0:SpR:3702.0,211.0')] ).
cnf(4034,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),v),
inference(rew,[status(thm),theory(equality)],[3838,3482]),
[iquote('0:Rew:3838.0,3482.0')] ).
cnf(4035,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(u)),v))),u)),v),
inference(rew,[status(thm),theory(equality)],[3838,3489]),
[iquote('0:Rew:3838.0,3489.0')] ).
cnf(4045,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[4034,3842]),
[iquote('0:Rew:4034.0,3842.0')] ).
cnf(4047,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[4045,3975]),
[iquote('0:Rew:4045.0,3975.0')] ).
cnf(4398,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(inverse(w)),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[4047,3917]),
[iquote('0:Rew:4047.0,3917.0')] ).
cnf(4704,plain,
equal(inverse(multiply(multiply(inverse(u),u),v)),inverse(multiply(multiply(inverse(inverse(w)),inverse(w)),v))),
inference(rew,[status(thm),theory(equality)],[4047,3911]),
[iquote('0:Rew:4047.0,3911.0')] ).
cnf(4757,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(multiply(multiply(inverse(inverse(v)),inverse(v)),inverse(w)),u))),w),
inference(rew,[status(thm),theory(equality)],[4047,3925]),
[iquote('0:Rew:4047.0,3925.0')] ).
cnf(4811,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(u))),w))),u),multiply(inverse(inverse(v)),inverse(multiply(w,v)))),
inference(rew,[status(thm),theory(equality)],[4047,39]),
[iquote('0:Rew:4047.0,39.0')] ).
cnf(4812,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),w))),multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(multiply(inverse(x),x),inverse(u))),v))),u)),multiply(inverse(inverse(x)),inverse(multiply(w,x)))),
inference(rew,[status(thm),theory(equality)],[4047,3729]),
[iquote('0:Rew:4047.0,3729.0')] ).
cnf(5357,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),w))),multiply(inverse(inverse(x)),inverse(multiply(v,x)))),multiply(inverse(inverse(x)),inverse(multiply(w,x)))),
inference(rew,[status(thm),theory(equality)],[4811,4812]),
[iquote('0:Rew:4811.0,4812.0')] ).
cnf(6148,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),w),w),
inference(spr,[status(thm),theory(equality)],[3849,3203]),
[iquote('0:SpR:3849.0,3203.0')] ).
cnf(6167,plain,
~ equal(multiply(multiply(inverse(u),u),a2),a2),
inference(spl,[status(thm),theory(equality)],[3849,2]),
[iquote('0:SpL:3849.0,2.0')] ).
cnf(6374,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[4398]),
[iquote('0:SpR:4398.0,4398.0')] ).
cnf(6629,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(v)),w))),v)),w),
inference(spr,[status(thm),theory(equality)],[3849,4035]),
[iquote('0:SpR:3849.0,4035.0')] ).
cnf(6743,plain,
equal(inverse(multiply(multiply(inverse(u),u),v)),inverse(multiply(multiply(inverse(w),w),v))),
inference(spr,[status(thm),theory(equality)],[4704]),
[iquote('0:SpR:4704.0,4704.0')] ).
cnf(6926,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(multiply(inverse(z),z),inverse(v))),y))),v))))),x),
inference(spr,[status(thm),theory(equality)],[6743,3820]),
[iquote('0:SpR:6743.0,3820.0')] ).
cnf(7014,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(v)),inverse(multiply(w,v))))),w),
inference(rew,[status(thm),theory(equality)],[5357,6926,4811]),
[iquote('0:Rew:5357.0,6926.0,5357.0,6926.0,4811.0,6926.0')] ).
cnf(7057,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(v)),inverse(multiply(inverse(w),w))))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3849,7014]),
[iquote('0:SpR:3849.0,7014.0')] ).
cnf(7098,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(multiply(inverse(inverse(v)),inverse(v)),inverse(w)),x))),multiply(inverse(multiply(inverse(inverse(x)),u)),w)),
inference(spr,[status(thm),theory(equality)],[4757,4047]),
[iquote('0:SpR:4757.0,4047.0')] ).
cnf(7117,plain,
equal(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(multiply(multiply(inverse(inverse(v)),inverse(v)),inverse(w)),multiply(inverse(x),x)))),w),
inference(spr,[status(thm),theory(equality)],[6374,4757]),
[iquote('0:SpR:6374.0,4757.0')] ).
cnf(7122,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(v),v)))),w),w),
inference(rew,[status(thm),theory(equality)],[7098,7117]),
[iquote('0:Rew:7098.0,7117.0')] ).
cnf(7447,plain,
equal(multiply(inverse(u),u),multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(w),w)))),
inference(spr,[status(thm),theory(equality)],[7122,3849]),
[iquote('0:SpR:7122.0,3849.0')] ).
cnf(7499,plain,
~ equal(multiply(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(v),v))),a2),a2),
inference(spl,[status(thm),theory(equality)],[7122,6167]),
[iquote('0:SpL:7122.0,6167.0')] ).
cnf(7696,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),inverse(multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[7447,7014]),
[iquote('0:SpR:7447.0,7014.0')] ).
cnf(9642,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),inverse(multiply(inverse(w),w))))),v),
inference(spr,[status(thm),theory(equality)],[6629,7057]),
[iquote('0:SpR:6629.0,7057.0')] ).
cnf(9765,plain,
equal(multiply(multiply(inverse(u),u),inverse(inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[4045,9642]),
[iquote('0:SpR:4045.0,9642.0')] ).
cnf(10338,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(inverse(inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(w),w))))),multiply(inverse(x),x)),
inference(spr,[status(thm),theory(equality)],[9765,7014]),
[iquote('0:SpR:9765.0,7014.0')] ).
cnf(10474,plain,
equal(inverse(inverse(inverse(multiply(inverse(u),u)))),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[9642,10338]),
[iquote('0:Rew:9642.0,10338.0')] ).
cnf(10533,plain,
equal(multiply(multiply(inverse(u),u),inverse(multiply(multiply(inverse(v),v),inverse(multiply(w,inverse(multiply(inverse(x),x))))))),w),
inference(spr,[status(thm),theory(equality)],[10474,7014]),
[iquote('0:SpR:10474.0,7014.0')] ).
cnf(10620,plain,
equal(inverse(inverse(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[7696,10474]),
[iquote('0:SpR:7696.0,10474.0')] ).
cnf(16932,plain,
equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(multiply(inverse(v),v),inverse(multiply(multiply(inverse(w),w),inverse(multiply(inverse(x),x))))))),y),y),
inference(spr,[status(thm),theory(equality)],[10620,6148]),
[iquote('0:SpR:10620.0,6148.0')] ).
cnf(17276,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[10533,16932]),
[iquote('0:Rew:10533.0,16932.0')] ).
cnf(17277,plain,
$false,
inference(unc,[status(thm)],[17276,7499]),
[iquote('0:UnC:17276.0,7499.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP413-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 21:01:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 29.52/29.69
% 29.52/29.69 SPASS V 3.9
% 29.52/29.69 SPASS beiseite: Proof found.
% 29.52/29.69 % SZS status Theorem
% 29.52/29.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.52/29.69 SPASS derived 12337 clauses, backtracked 0 clauses, performed 0 splits and kept 3140 clauses.
% 29.52/29.69 SPASS allocated 121949 KBytes.
% 29.52/29.69 SPASS spent 0:0:29.33 on the problem.
% 29.52/29.69 0:00:00.04 for the input.
% 29.52/29.69 0:00:00.00 for the FLOTTER CNF translation.
% 29.52/29.69 0:00:00.19 for inferences.
% 29.52/29.69 0:00:00.00 for the backtracking.
% 29.52/29.69 0:0:29.08 for the reduction.
% 29.52/29.69
% 29.52/29.69
% 29.52/29.69 Here is a proof with depth 18, length 77 :
% 29.52/29.69 % SZS output start Refutation
% See solution above
% 29.90/30.09 Formulae used in the proof : single_axiom prove_these_axioms_2
% 29.90/30.09
%------------------------------------------------------------------------------