TSTP Solution File: GRP014-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:44:46 EDT 2022
% Result : Unsatisfiable 22.59s 22.78s
% Output : Refutation 22.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 2
% Syntax : Number of clauses : 139 ( 139 unt; 0 nHn; 139 RR)
% Number of literals : 139 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 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('GRP014-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(a,b),c),multiply(a,multiply(b,c))),
file('GRP014-1.p',unknown),
[] ).
cnf(4,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(5,plain,
equal(multiply(u,inverse(multiply(v,inverse(multiply(w,inverse(multiply(multiply(inverse(multiply(inverse(x),multiply(inverse(inverse(multiply(inverse(w),multiply(inverse(u),y)))),v))),z),inverse(multiply(x,z))))))))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(33,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)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(34,plain,
equal(multiply(u,inverse(multiply(v,inverse(inverse(multiply(multiply(inverse(multiply(inverse(w),multiply(inverse(inverse(x)),multiply(inverse(inverse(multiply(inverse(x),multiply(inverse(u),y)))),v)))),z),inverse(multiply(w,z)))))))),y),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(41,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)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(43,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)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(164,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(inverse(inverse(w)),multiply(inverse(w),v))),
inference(spr,[status(thm),theory(equality)],[33,41]),
[iquote('0:SpR:33.0,41.0')] ).
cnf(178,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)],[33]),
[iquote('0:SpR:33.0,33.0')] ).
cnf(238,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)],[164,1]),
[iquote('0:SpR:164.0,1.0')] ).
cnf(244,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(inverse(w),multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[164]),
[iquote('0:SpR:164.0,164.0')] ).
cnf(294,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)],[244]),
[iquote('0:SpR:244.0,244.0')] ).
cnf(311,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)],[244,41]),
[iquote('0:SpR:244.0,41.0')] ).
cnf(315,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)],[244,41]),
[iquote('0:SpR:244.0,41.0')] ).
cnf(512,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(u),w))),x),inverse(multiply(v,x))))),inverse(multiply(multiply(inverse(multiply(inverse(y),multiply(y,multiply(z,w)))),x1),inverse(multiply(inverse(z),x1))))),
inference(spr,[status(thm),theory(equality)],[294,4]),
[iquote('0:SpR:294.0,4.0')] ).
cnf(542,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)],[244,294]),
[iquote('0:SpR:244.0,294.0')] ).
cnf(562,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(u,multiply(v,w)))),x),inverse(multiply(inverse(v),x)))),w),
inference(rew,[status(thm),theory(equality)],[1,512]),
[iquote('0:Rew:1.0,512.0')] ).
cnf(608,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)],[178,294]),
[iquote('0:SpR:178.0,294.0')] ).
cnf(736,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)],[244,238]),
[iquote('0:SpR:244.0,238.0')] ).
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)],[178,542]),
[iquote('0:SpR:178.0,542.0')] ).
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)],[178,1082]),
[iquote('0:SpR:178.0,1082.0')] ).
cnf(1492,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)],[1304,244]),
[iquote('0:SpR:1304.0,244.0')] ).
cnf(2434,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),inverse(multiply(inverse(x),y))),z)))),multiply(multiply(inverse(multiply(inverse(x1),multiply(x1,multiply(x,z)))),y),w)),
inference(spr,[status(thm),theory(equality)],[562,315]),
[iquote('0:SpR:562.0,315.0')] ).
cnf(3137,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(inverse(u),x))))),inverse(multiply(y,inverse(inverse(multiply(multiply(inverse(multiply(inverse(z),multiply(inverse(inverse(x1)),multiply(inverse(inverse(multiply(inverse(x1),multiply(inverse(v),w)))),y)))),x2),inverse(multiply(z,x2)))))))),
inference(spr,[status(thm),theory(equality)],[34,238]),
[iquote('0:SpR:34.0,238.0')] ).
cnf(3918,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)],[41,736]),
[iquote('0:SpR:41.0,736.0')] ).
cnf(3975,plain,
equal(multiply(multiply(inverse(u),multiply(u,v)),inverse(multiply(w,inverse(w)))),v),
inference(rew,[status(thm),theory(equality)],[41,3918]),
[iquote('0:Rew:41.0,3918.0')] ).
cnf(4040,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)],[3975,294]),
[iquote('0:SpR:3975.0,294.0')] ).
cnf(4047,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)],[3975,1304]),
[iquote('0:SpR:3975.0,1304.0')] ).
cnf(4049,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)],[3975,311]),
[iquote('0:SpR:3975.0,311.0')] ).
cnf(4058,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)],[3975,315]),
[iquote('0:SpR:3975.0,315.0')] ).
cnf(4069,plain,
equal(multiply(multiply(inverse(inverse(u)),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)],[41,3975]),
[iquote('0:SpR:41.0,3975.0')] ).
cnf(4085,plain,
equal(multiply(multiply(inverse(u),v),inverse(multiply(w,inverse(w)))),inverse(multiply(multiply(inverse(x),multiply(x,y)),inverse(multiply(inverse(u),multiply(multiply(inverse(z),multiply(z,v)),y)))))),
inference(spr,[status(thm),theory(equality)],[736,3975]),
[iquote('0:SpR:736.0,3975.0')] ).
cnf(4109,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)],[315,3975]),
[iquote('0:SpR:315.0,3975.0')] ).
cnf(4535,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)],[4058,315]),
[iquote('0:SpR:4058.0,315.0')] ).
cnf(4546,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)],[4058,41]),
[iquote('0:SpR:4058.0,41.0')] ).
cnf(4691,plain,
equal(multiply(u,multiply(multiply(inverse(u),v),inverse(multiply(w,inverse(w))))),v),
inference(rew,[status(thm),theory(equality)],[4535,4049]),
[iquote('0:Rew:4535.0,4049.0')] ).
cnf(4694,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),u),
inference(rew,[status(thm),theory(equality)],[41,4546]),
[iquote('0:Rew:41.0,4546.0')] ).
cnf(4705,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,inverse(multiply(w,inverse(w)))))),v),
inference(rew,[status(thm),theory(equality)],[4694,4040]),
[iquote('0:Rew:4694.0,4040.0')] ).
cnf(4852,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)],[41,4691]),
[iquote('0:SpR:41.0,4691.0')] ).
cnf(4937,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),multiply(u,inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[4705,3975]),
[iquote('0:SpR:4705.0,3975.0')] ).
cnf(4942,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)],[4705,238]),
[iquote('0:SpR:4705.0,238.0')] ).
cnf(4972,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(v),multiply(v,w)),inverse(multiply(x,multiply(y,w))))))),multiply(x,multiply(y,inverse(multiply(z,inverse(z)))))),
inference(spr,[status(thm),theory(equality)],[4705,311]),
[iquote('0:SpR:4705.0,311.0')] ).
cnf(4983,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)],[4705,244]),
[iquote('0:SpR:4705.0,244.0')] ).
cnf(5010,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)],[4705,1492]),
[iquote('0:SpR:4705.0,1492.0')] ).
cnf(5055,plain,
equal(multiply(inverse(inverse(inverse(u))),u),multiply(inverse(inverse(inverse(v))),v)),
inference(rew,[status(thm),theory(equality)],[4983,5010]),
[iquote('0:Rew:4983.0,5010.0')] ).
cnf(5120,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)],[5055,244]),
[iquote('0:SpR:5055.0,244.0')] ).
cnf(5170,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)],[5055,315]),
[iquote('0:SpR:5055.0,315.0')] ).
cnf(5180,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)],[5055,1]),
[iquote('0:SpR:5055.0,1.0')] ).
cnf(5185,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)],[5055,178]),
[iquote('0:SpR:5055.0,178.0')] ).
cnf(5193,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)],[5055,43]),
[iquote('0:SpR:5055.0,43.0')] ).
cnf(5198,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)],[5055,41]),
[iquote('0:SpR:5055.0,41.0')] ).
cnf(5211,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)],[5055,3975]),
[iquote('0:SpR:5055.0,3975.0')] ).
cnf(5216,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)],[5055,294]),
[iquote('0:SpR:5055.0,294.0')] ).
cnf(5246,plain,
equal(multiply(inverse(inverse(multiply(multiply(inverse(u),multiply(u,v)),w))),inverse(multiply(multiply(inverse(x),multiply(x,w)),inverse(multiply(inverse(inverse(inverse(y))),y))))),v),
inference(spr,[status(thm),theory(equality)],[5055,736]),
[iquote('0:SpR:5055.0,736.0')] ).
cnf(5981,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)],[3975,4694]),
[iquote('0:SpR:3975.0,4694.0')] ).
cnf(6036,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)],[178,4694]),
[iquote('0:SpR:178.0,4694.0')] ).
cnf(6233,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)],[4937]),
[iquote('0:SpR:4937.0,4937.0')] ).
cnf(6250,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)],[4937,4691]),
[iquote('0:SpR:4937.0,4691.0')] ).
cnf(6270,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)],[4937,4694]),
[iquote('0:SpR:4937.0,4694.0')] ).
cnf(6298,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[4691,6250]),
[iquote('0:Rew:4691.0,6250.0')] ).
cnf(6506,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)],[6298,4694]),
[iquote('0:SpR:6298.0,4694.0')] ).
cnf(6514,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)],[6298,178]),
[iquote('0:SpR:6298.0,178.0')] ).
cnf(6594,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[4694,6506]),
[iquote('0:Rew:4694.0,6506.0')] ).
cnf(6641,plain,
equal(multiply(u,multiply(v,inverse(v))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6594,4691]),
[iquote('0:SpR:6594.0,4691.0')] ).
cnf(6660,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),multiply(inverse(v),multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[6594,244]),
[iquote('0:SpR:6594.0,244.0')] ).
cnf(6666,plain,
equal(multiply(u,multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6594,4691]),
[iquote('0:SpR:6594.0,4691.0')] ).
cnf(6718,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)],[6594,41]),
[iquote('0:SpR:6594.0,41.0')] ).
cnf(6774,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)],[6594,238]),
[iquote('0:SpR:6594.0,238.0')] ).
cnf(6775,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(w,inverse(w)))),x),inverse(multiply(y,x)))))),multiply(y,inverse(v))),
inference(spr,[status(thm),theory(equality)],[6594,315]),
[iquote('0:SpR:6594.0,315.0')] ).
cnf(6816,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[6641,6660]),
[iquote('0:Rew:6641.0,6660.0')] ).
cnf(6819,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),v)),w),inverse(multiply(u,w)))))),v),
inference(rew,[status(thm),theory(equality)],[6816,41]),
[iquote('0:Rew:6816.0,41.0')] ).
cnf(6822,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)],[6816,4047]),
[iquote('0:Rew:6816.0,4047.0')] ).
cnf(6831,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)],[6816,6270]),
[iquote('0:Rew:6816.0,6270.0')] ).
cnf(6852,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)],[6816,5170]),
[iquote('0:Rew:6816.0,5170.0')] ).
cnf(6917,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(u),multiply(u,v)),inverse(multiply(w,multiply(x,v))))))),multiply(w,multiply(x,inverse(multiply(y,inverse(y)))))),
inference(rew,[status(thm),theory(equality)],[6816,4972]),
[iquote('0:Rew:6816.0,4972.0')] ).
cnf(7028,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(u,v))),inverse(multiply(inverse(w),x))),y)))),multiply(multiply(inverse(multiply(inverse(z),multiply(z,multiply(w,y)))),x),v)),
inference(rew,[status(thm),theory(equality)],[6816,2434]),
[iquote('0:Rew:6816.0,2434.0')] ).
cnf(7063,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(inverse(inverse(v))),v)),u),
inference(rew,[status(thm),theory(equality)],[6819,5198]),
[iquote('0:Rew:6819.0,5198.0')] ).
cnf(7070,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[7063,5211]),
[iquote('0:Rew:7063.0,5211.0')] ).
cnf(7084,plain,
equal(multiply(inverse(u),multiply(u,multiply(v,w))),multiply(inverse(inverse(v)),inverse(inverse(w)))),
inference(rew,[status(thm),theory(equality)],[7063,5216]),
[iquote('0:Rew:7063.0,5216.0')] ).
cnf(7089,plain,
equal(multiply(inverse(u),multiply(u,v)),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[7063,5120]),
[iquote('0:Rew:7063.0,5120.0')] ).
cnf(7493,plain,
equal(multiply(multiply(inverse(u),v),inverse(multiply(w,inverse(w)))),inverse(multiply(multiply(inverse(x),multiply(x,y)),inverse(multiply(inverse(u),multiply(inverse(inverse(v)),y)))))),
inference(rew,[status(thm),theory(equality)],[7089,4085]),
[iquote('0:Rew:7089.0,4085.0')] ).
cnf(7682,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)],[7089,608]),
[iquote('0:Rew:7089.0,608.0')] ).
cnf(7709,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)],[7089,6036]),
[iquote('0:Rew:7089.0,6036.0')] ).
cnf(7864,plain,
equal(multiply(inverse(inverse(multiply(multiply(inverse(u),multiply(u,v)),w))),inverse(multiply(inverse(inverse(w)),inverse(multiply(inverse(inverse(inverse(x))),x))))),v),
inference(rew,[status(thm),theory(equality)],[7089,5246]),
[iquote('0:Rew:7089.0,5246.0')] ).
cnf(7974,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)],[7089,4109]),
[iquote('0:Rew:7089.0,4109.0')] ).
cnf(8043,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)],[7089,5185]),
[iquote('0:Rew:7089.0,5185.0')] ).
cnf(8104,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)],[7089,5981]),
[iquote('0:Rew:7089.0,5981.0')] ).
cnf(8171,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)],[7089,6514]),
[iquote('0:Rew:7089.0,6514.0')] ).
cnf(8260,plain,
equal(multiply(inverse(inverse(u)),inverse(inverse(v))),inverse(inverse(multiply(u,v)))),
inference(rew,[status(thm),theory(equality)],[7089,7084]),
[iquote('0:Rew:7089.0,7084.0')] ).
cnf(8302,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[6641,6831,8260,7070]),
[iquote('0:Rew:6641.0,6831.0,8260.0,6831.0,7070.0,6831.0')] ).
cnf(8345,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)],[7089,6822]),
[iquote('0:Rew:7089.0,6822.0')] ).
cnf(8359,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(u))),u)),v),inverse(multiply(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[8302,8043]),
[iquote('0:Rew:8302.0,8043.0')] ).
cnf(8364,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)],[8359,5193]),
[iquote('0:Rew:8359.0,5193.0')] ).
cnf(8368,plain,
equal(multiply(u,inverse(inverse(multiply(inverse(u),v)))),v),
inference(rew,[status(thm),theory(equality)],[8359,5180]),
[iquote('0:Rew:8359.0,5180.0')] ).
cnf(8532,plain,
equal(multiply(multiply(inverse(inverse(u)),v),inverse(multiply(w,inverse(w)))),multiply(u,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[8364,4069]),
[iquote('0:Rew:8364.0,4069.0')] ).
cnf(8533,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,inverse(w))))),multiply(u,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[8364,4852]),
[iquote('0:Rew:8364.0,4852.0')] ).
cnf(8889,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(v))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8533,6666]),
[iquote('0:Rew:8533.0,6666.0')] ).
cnf(8916,plain,
equal(multiply(inverse(inverse(u)),inverse(inverse(inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8533,8104]),
[iquote('0:Rew:8533.0,8104.0')] ).
cnf(8919,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8260,8916]),
[iquote('0:Rew:8260.0,8916.0')] ).
cnf(8925,plain,
equal(multiply(u,inverse(multiply(multiply(v,w),inverse(multiply(inverse(u),w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[8302,6774,6641]),
[iquote('0:Rew:8302.0,6774.0,6641.0,6774.0')] ).
cnf(8927,plain,
equal(inverse(multiply(u,inverse(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(inverse(w)),multiply(inverse(inverse(multiply(inverse(w),multiply(inverse(x),y)))),u)))),z),inverse(multiply(v,z))))))),inverse(inverse(multiply(inverse(x),y)))),
inference(rew,[status(thm),theory(equality)],[8925,3137]),
[iquote('0:Rew:8925.0,3137.0')] ).
cnf(8930,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8925,4942]),
[iquote('0:Rew:8925.0,4942.0')] ).
cnf(8933,plain,
equal(inverse(inverse(multiply(inverse(inverse(u)),v))),multiply(u,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[8930,8532]),
[iquote('0:Rew:8930.0,8532.0')] ).
cnf(8943,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),multiply(u,inverse(multiply(w,inverse(w))))),
inference(rew,[status(thm),theory(equality)],[8930,6233]),
[iquote('0:Rew:8930.0,6233.0')] ).
cnf(9033,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8930,8943]),
[iquote('0:Rew:8930.0,8943.0')] ).
cnf(9035,plain,
equal(multiply(u,multiply(inverse(inverse(inverse(v))),v)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[9033,8345]),
[iquote('0:Rew:9033.0,8345.0')] ).
cnf(9047,plain,
equal(inverse(inverse(inverse(multiply(multiply(u,inverse(u)),inverse(v))))),v),
inference(rew,[status(thm),theory(equality)],[7089,6718,8368]),
[iquote('0:Rew:7089.0,6718.0,8368.0,6718.0')] ).
cnf(9083,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)],[8930,7974]),
[iquote('0:Rew:8930.0,7974.0')] ).
cnf(9204,plain,
equal(multiply(multiply(u,inverse(inverse(v))),inverse(multiply(inverse(inverse(v)),inverse(multiply(inverse(inverse(inverse(w))),w))))),u),
inference(rew,[status(thm),theory(equality)],[8933,7864,7089]),
[iquote('0:Rew:8933.0,7864.0,7089.0,7864.0')] ).
cnf(9230,plain,
equal(inverse(inverse(inverse(multiply(multiply(u,v),inverse(multiply(w,v)))))),multiply(w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[7089,6775,8302,6641]),
[iquote('0:Rew:7089.0,6775.0,8302.0,6775.0,6641.0,6775.0')] ).
cnf(9255,plain,
equal(inverse(multiply(u,inverse(inverse(inverse(multiply(v,multiply(w,u))))))),multiply(v,inverse(inverse(w)))),
inference(rew,[status(thm),theory(equality)],[8933,6917,7089,8930]),
[iquote('0:Rew:8933.0,6917.0,7089.0,6917.0,8930.0,6917.0')] ).
cnf(9301,plain,
equal(inverse(multiply(inverse(inverse(inverse(u))),v)),multiply(inverse(inverse(inverse(v))),u)),
inference(rew,[status(thm),theory(equality)],[8919,6852,7089]),
[iquote('0:Rew:8919.0,6852.0,7089.0,6852.0')] ).
cnf(9306,plain,
equal(multiply(multiply(u,inverse(inverse(v))),inverse(multiply(inverse(inverse(v)),multiply(inverse(inverse(inverse(w))),w)))),u),
inference(rew,[status(thm),theory(equality)],[9301,9204]),
[iquote('0:Rew:9301.0,9204.0')] ).
cnf(9314,plain,
equal(multiply(multiply(u,inverse(inverse(v))),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[8302,9306,9035]),
[iquote('0:Rew:8302.0,9306.0,9035.0,9306.0')] ).
cnf(9334,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)],[9035,7709,7089]),
[iquote('0:Rew:9035.0,7709.0,7089.0,7709.0')] ).
cnf(9421,plain,
equal(inverse(multiply(inverse(inverse(u)),inverse(multiply(inverse(v),multiply(inverse(inverse(w)),u))))),inverse(inverse(multiply(inverse(v),w)))),
inference(rew,[status(thm),theory(equality)],[8930,7493,7089]),
[iquote('0:Rew:8930.0,7493.0,7089.0,7493.0')] ).
cnf(9620,plain,
equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[9301,7682,7089,9334]),
[iquote('0:Rew:9301.0,7682.0,9301.0,7682.0,7089.0,7682.0,9334.0,7682.0,7089.0,7682.0')] ).
cnf(9622,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)],[9620,9083]),
[iquote('0:Rew:9620.0,9083.0')] ).
cnf(9623,plain,
equal(inverse(multiply(inverse(u),inverse(inverse(v)))),multiply(inverse(inverse(inverse(v))),u)),
inference(rew,[status(thm),theory(equality)],[9620,9301]),
[iquote('0:Rew:9620.0,9301.0')] ).
cnf(9656,plain,
equal(inverse(multiply(inverse(u),inverse(inverse(v)))),multiply(inverse(v),inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[9620,9623]),
[iquote('0:Rew:9620.0,9623.0')] ).
cnf(9667,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)],[9656,8171]),
[iquote('0:Rew:9656.0,8171.0')] ).
cnf(9681,plain,
equal(inverse(inverse(multiply(multiply(u,inverse(u)),v))),v),
inference(rew,[status(thm),theory(equality)],[9622,9667,9620,8889]),
[iquote('0:Rew:9622.0,9667.0,9620.0,9667.0,8889.0,9667.0')] ).
cnf(9685,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[9681,9047]),
[iquote('0:Rew:9681.0,9047.0')] ).
cnf(9708,plain,
equal(inverse(multiply(u,inverse(inverse(inverse(multiply(v,multiply(w,u))))))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[9685,9255]),
[iquote('0:Rew:9685.0,9255.0')] ).
cnf(9722,plain,
equal(inverse(multiply(inverse(inverse(u)),inverse(multiply(inverse(v),multiply(w,u))))),inverse(inverse(multiply(inverse(v),w)))),
inference(rew,[status(thm),theory(equality)],[9685,9421]),
[iquote('0:Rew:9685.0,9421.0')] ).
cnf(9728,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[9685,7089]),
[iquote('0:Rew:9685.0,7089.0')] ).
cnf(9732,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[9685,9314]),
[iquote('0:Rew:9685.0,9314.0')] ).
cnf(9738,plain,
equal(multiply(inverse(u),inverse(inverse(v))),inverse(multiply(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[9685,9656]),
[iquote('0:Rew:9685.0,9656.0')] ).
cnf(9752,plain,
equal(inverse(multiply(multiply(u,v),inverse(multiply(w,v)))),multiply(w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[9685,9230]),
[iquote('0:Rew:9685.0,9230.0')] ).
cnf(9784,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[9685,9738]),
[iquote('0:Rew:9685.0,9738.0')] ).
cnf(9799,plain,
equal(inverse(multiply(u,inverse(multiply(v,multiply(w,u))))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[9685,9708]),
[iquote('0:Rew:9685.0,9708.0')] ).
cnf(9835,plain,
equal(inverse(multiply(u,multiply(inverse(multiply(v,u)),w))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[9685,9722,9784]),
[iquote('0:Rew:9685.0,9722.0,9784.0,9722.0,9784.0,9722.0,9784.0,9722.0')] ).
cnf(9900,plain,
equal(inverse(multiply(multiply(inverse(u),multiply(inverse(v),w)),x)),multiply(multiply(inverse(multiply(w,x)),v),u)),
inference(rew,[status(thm),theory(equality)],[9685,7028,9728,9784]),
[iquote('0:Rew:9685.0,7028.0,9728.0,7028.0,9784.0,7028.0,9728.0,7028.0')] ).
cnf(10440,plain,
equal(multiply(u,multiply(inverse(multiply(v,u)),w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[9799,8927,9900,9752,9835,9784,9685]),
[iquote('0:Rew:9799.0,8927.0,9900.0,8927.0,9752.0,8927.0,9835.0,8927.0,9784.0,8927.0,9685.0,8927.0,9784.0,8927.0,9784.0,8927.0,9784.0,8927.0,9784.0,8927.0')] ).
cnf(11637,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[9732,9728]),
[iquote('0:SpR:9732.0,9728.0')] ).
cnf(12687,plain,
equal(multiply(inverse(inverse(multiply(u,v))),w),multiply(u,multiply(inverse(inverse(v)),w))),
inference(spr,[status(thm),theory(equality)],[11637,10440]),
[iquote('0:SpR:11637.0,10440.0')] ).
cnf(12771,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[9685,12687]),
[iquote('0:Rew:9685.0,12687.0,9685.0,12687.0')] ).
cnf(12772,plain,
$false,
inference(unc,[status(thm)],[12771,2]),
[iquote('0:UnC:12771.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 00:08:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 22.59/22.78
% 22.59/22.78 SPASS V 3.9
% 22.59/22.78 SPASS beiseite: Proof found.
% 22.59/22.78 % SZS status Theorem
% 22.59/22.78 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.59/22.78 SPASS derived 8792 clauses, backtracked 0 clauses, performed 0 splits and kept 2702 clauses.
% 22.59/22.78 SPASS allocated 104033 KBytes.
% 22.59/22.78 SPASS spent 0:0:22.42 on the problem.
% 22.59/22.78 0:00:00.03 for the input.
% 22.59/22.78 0:00:00.00 for the FLOTTER CNF translation.
% 22.59/22.78 0:00:00.10 for inferences.
% 22.59/22.78 0:00:00.00 for the backtracking.
% 22.59/22.78 0:0:22.26 for the reduction.
% 22.59/22.78
% 22.59/22.78
% 22.59/22.78 Here is a proof with depth 13, length 139 :
% 22.59/22.78 % SZS output start Refutation
% See solution above
% 22.87/23.06 Formulae used in the proof : group_axiom prove_associativity
% 22.87/23.06
%------------------------------------------------------------------------------