TSTP Solution File: GRP057-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP057-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:45:04 EDT 2022
% Result : Unsatisfiable 23.94s 24.16s
% Output : Refutation 24.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 2
% Syntax : Number of clauses : 194 ( 190 unt; 0 nHn; 194 RR)
% Number of literals : 200 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 23 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 17 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('GRP057-1.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('GRP057-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(u),w))),inverse(multiply(multiply(inverse(multiply(inverse(x),multiply(inverse(v),y))),z),inverse(multiply(x,z))))),inverse(y)))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
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(42,plain,
equal(multiply(u,inverse(multiply(v,inverse(multiply(w,multiply(multiply(inverse(w),multiply(inverse(u),x)),inverse(multiply(multiply(inverse(multiply(inverse(y),v)),z),inverse(multiply(y,z)))))))))),x),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
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(105,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(inverse(inverse(multiply(inverse(w),multiply(inverse(u),x))))),multiply(inverse(w),y)))),z),inverse(multiply(v,z)))),inverse(y)))),x),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
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(650,plain,
equal(inverse(multiply(multiply(inverse(u),multiply(u,v)),inverse(multiply(w,multiply(multiply(inverse(w),multiply(inverse(x),multiply(x,y))),v))))),y),
inference(spr,[status(thm),theory(equality)],[244,178]),
[iquote('0:SpR:244.0,178.0')] ).
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(786,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(w,multiply(multiply(multiply(inverse(multiply(inverse(x),multiply(x,multiply(y,w)))),z),inverse(multiply(inverse(y),z))),v))),
inference(spr,[status(thm),theory(equality)],[562,244]),
[iquote('0:SpR:562.0,244.0')] ).
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(2432,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(v,w))),inverse(multiply(x,y))),z)))),multiply(multiply(inverse(multiply(inverse(x),multiply(inverse(x1),multiply(x1,z)))),y),w)),
inference(spr,[status(thm),theory(equality)],[178,315]),
[iquote('0:SpR:178.0,315.0')] ).
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(2449,plain,
equal(multiply(inverse(u),multiply(u,inverse(multiply(multiply(inverse(multiply(inverse(v),w)),x),inverse(multiply(y,x)))))),multiply(y,inverse(multiply(z,inverse(multiply(x1,multiply(multiply(inverse(x1),multiply(inverse(v),w)),inverse(multiply(multiply(inverse(multiply(inverse(x2),z)),x3),inverse(multiply(x2,x3))))))))))),
inference(spr,[status(thm),theory(equality)],[42,315]),
[iquote('0:SpR:42.0,315.0')] ).
cnf(2488,plain,
equal(multiply(inverse(u),multiply(u,inverse(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(inverse(multiply(inverse(multiply(inverse(w),multiply(w,x))),inverse(multiply(y,z))))),x1))),x2),inverse(multiply(v,x2))))))),multiply(multiply(inverse(multiply(inverse(y),x1)),z),x)),
inference(spr,[status(thm),theory(equality)],[4,315]),
[iquote('0:SpR:4.0,315.0')] ).
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(3836,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(inverse(v),w))),x),inverse(multiply(u,x)))),inverse(multiply(multiply(inverse(y),multiply(y,z)),inverse(multiply(inverse(v),multiply(multiply(inverse(x1),multiply(x1,w)),z)))))),
inference(spr,[status(thm),theory(equality)],[736,178]),
[iquote('0:SpR:736.0,178.0')] ).
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(4313,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(inverse(inverse(w))),multiply(inverse(inverse(u)),x)))),y),inverse(multiply(v,y)))),inverse(x)))),inverse(multiply(multiply(inverse(z),multiply(z,x1)),inverse(multiply(x2,multiply(multiply(inverse(x2),w),x1)))))),
inference(spr,[status(thm),theory(equality)],[311,105]),
[iquote('0:SpR:311.0,105.0')] ).
cnf(4364,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(w),multiply(inverse(inverse(inverse(multiply(inverse(x),multiply(inverse(u),y))))),multiply(inverse(x),multiply(multiply(inverse(multiply(inverse(z),x1)),x2),inverse(multiply(z,x2))))))),x3),inverse(multiply(w,x3)))))),x1))),x4),inverse(multiply(v,x4)))))),y),
inference(spr,[status(thm),theory(equality)],[4,105]),
[iquote('0:SpR:4.0,105.0')] ).
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(4672,plain,
equal(multiply(inverse(multiply(inverse(u),multiply(u,v))),v),multiply(inverse(multiply(w,multiply(multiply(multiply(inverse(multiply(inverse(x),multiply(inverse(y),multiply(y,w)))),z),inverse(multiply(x,z))),x1))),x1)),
inference(spr,[status(thm),theory(equality)],[178,4058]),
[iquote('0:SpR:178.0,4058.0')] ).
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(4700,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)],[4700,3975]),
[iquote('0:SpR:4700.0,3975.0')] ).
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)],[4700,238]),
[iquote('0:SpR:4700.0,238.0')] ).
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)],[4700,311]),
[iquote('0:SpR:4700.0,311.0')] ).
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)],[4700,244]),
[iquote('0:SpR:4700.0,244.0')] ).
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)],[4700,1492]),
[iquote('0:SpR:4700.0,1492.0')] ).
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(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(6039,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(multiply(inverse(multiply(inverse(x),multiply(x,multiply(y,u)))),z),inverse(multiply(inverse(y),z)))),
inference(spr,[status(thm),theory(equality)],[562,4694]),
[iquote('0:SpR:562.0,4694.0')] ).
cnf(6040,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(multiply(inverse(x),multiply(x,y)),inverse(multiply(z,multiply(multiply(inverse(z),multiply(inverse(x1),multiply(x1,u))),y))))),
inference(spr,[status(thm),theory(equality)],[650,4694]),
[iquote('0:SpR:650.0,4694.0')] ).
cnf(6227,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(6401,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)],[6298,244]),
[iquote('0:SpR:6298.0,244.0')] ).
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(6650,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)],[6650,6660]),
[iquote('0:Rew:6650.0,6660.0')] ).
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(6820,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(6844,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),v)),w),inverse(multiply(x,w)))))),multiply(x,inverse(multiply(y,inverse(multiply(z,multiply(multiply(inverse(z),multiply(inverse(u),v)),inverse(multiply(multiply(inverse(multiply(inverse(x1),y)),x2),inverse(multiply(x1,x2))))))))))),
inference(rew,[status(thm),theory(equality)],[6816,2449]),
[iquote('0:Rew:6816.0,2449.0')] ).
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(7027,plain,
equal(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(u,v))),inverse(multiply(w,x))),y)))),multiply(multiply(inverse(multiply(inverse(w),multiply(inverse(z),multiply(z,y)))),x),v)),
inference(rew,[status(thm),theory(equality)],[6816,2432]),
[iquote('0:Rew:6816.0,2432.0')] ).
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(7032,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),multiply(v,w))),inverse(multiply(x,y))))),z))),x1),inverse(multiply(u,x1))))))),multiply(multiply(inverse(multiply(inverse(x),z)),y),w)),
inference(rew,[status(thm),theory(equality)],[6816,2488]),
[iquote('0:Rew:6816.0,2488.0')] ).
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(7066,plain,
equal(multiply(u,inverse(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(multiply(inverse(inverse(inverse(multiply(inverse(w),multiply(inverse(u),x))))),multiply(inverse(w),multiply(multiply(inverse(multiply(inverse(y),z)),x1),inverse(multiply(y,x1))))),z))),x2),inverse(multiply(v,x2)))))),x),
inference(rew,[status(thm),theory(equality)],[6819,4364]),
[iquote('0:Rew:6819.0,4364.0')] ).
cnf(7078,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(7082,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(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(7136,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(multiply(inverse(inverse(inverse(multiply(x,u)))),y),inverse(multiply(inverse(x),y)))),
inference(rew,[status(thm),theory(equality)],[7089,6039]),
[iquote('0:Rew:7089.0,6039.0')] ).
cnf(7267,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),inverse(inverse(w))),
inference(rew,[status(thm),theory(equality)],[7089,6401]),
[iquote('0:Rew:7089.0,6401.0')] ).
cnf(7331,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(7412,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(v),multiply(v,w))),w)),multiply(multiply(inverse(x),multiply(x,y)),inverse(multiply(z,multiply(multiply(inverse(z),inverse(inverse(u))),y))))),
inference(rew,[status(thm),theory(equality)],[7089,6040]),
[iquote('0:Rew:7089.0,6040.0')] ).
cnf(7429,plain,
equal(inverse(multiply(multiply(inverse(multiply(inverse(u),multiply(inverse(v),w))),x),inverse(multiply(u,x)))),inverse(multiply(multiply(inverse(y),multiply(y,z)),inverse(multiply(inverse(v),multiply(inverse(inverse(w)),z)))))),
inference(rew,[status(thm),theory(equality)],[7089,3836]),
[iquote('0:Rew:7089.0,3836.0')] ).
cnf(7605,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(7674,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(v),multiply(inverse(inverse(inverse(w))),multiply(inverse(inverse(u)),x)))),y),inverse(multiply(v,y)))),inverse(x)))),inverse(multiply(inverse(inverse(z)),inverse(multiply(x1,multiply(multiply(inverse(x1),w),z)))))),
inference(rew,[status(thm),theory(equality)],[7089,4313]),
[iquote('0:Rew:7089.0,4313.0')] ).
cnf(7770,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(7872,plain,
equal(multiply(inverse(multiply(inverse(u),multiply(u,v))),v),multiply(inverse(multiply(w,multiply(multiply(multiply(inverse(multiply(inverse(x),inverse(inverse(w)))),y),inverse(multiply(x,y))),z))),z)),
inference(rew,[status(thm),theory(equality)],[7089,4672]),
[iquote('0:Rew:7089.0,4672.0')] ).
cnf(7888,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(w,multiply(multiply(multiply(inverse(inverse(inverse(multiply(x,w)))),y),inverse(multiply(inverse(x),y))),v))),
inference(rew,[status(thm),theory(equality)],[7089,786]),
[iquote('0:Rew:7089.0,786.0')] ).
cnf(7996,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(8062,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(8119,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(8186,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(8259,plain,
equal(multiply(inverse(inverse(u)),inverse(inverse(v))),inverse(inverse(multiply(u,v)))),
inference(rew,[status(thm),theory(equality)],[7089,7078]),
[iquote('0:Rew:7089.0,7078.0')] ).
cnf(8302,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[6650,6831,8259,7082]),
[iquote('0:Rew:6650.0,6831.0,8259.0,6831.0,7082.0,6831.0')] ).
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)],[7089,6820]),
[iquote('0:Rew:7089.0,6820.0')] ).
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)],[8302,8062]),
[iquote('0:Rew:8302.0,8062.0')] ).
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(8447,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(8448,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(8882,plain,
equal(multiply(u,inverse(inverse(multiply(v,inverse(v))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8448,6666]),
[iquote('0:Rew:8448.0,6666.0')] ).
cnf(8913,plain,
equal(multiply(inverse(inverse(u)),inverse(inverse(inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8448,8119]),
[iquote('0:Rew:8448.0,8119.0')] ).
cnf(8919,plain,
equal(inverse(inverse(multiply(u,inverse(multiply(inverse(inverse(inverse(v))),v))))),u),
inference(rew,[status(thm),theory(equality)],[8259,8913]),
[iquote('0:Rew:8259.0,8913.0')] ).
cnf(8925,plain,
equal(multiply(u,inverse(multiply(multiply(v,w),inverse(multiply(inverse(u),w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[8302,6774,6650]),
[iquote('0:Rew:8302.0,6774.0,6650.0,6774.0')] ).
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(multiply(u,inverse(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8930,6227]),
[iquote('0:Rew:8930.0,6227.0')] ).
cnf(8945,plain,
equal(inverse(inverse(multiply(inverse(inverse(u)),v))),multiply(u,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[8930,8447]),
[iquote('0:Rew:8930.0,8447.0')] ).
cnf(9033,plain,
equal(multiply(u,inverse(inverse(inverse(multiply(v,inverse(v)))))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[8930,8933]),
[iquote('0:Rew:8930.0,8933.0')] ).
cnf(9034,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(9084,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)],[8930,7996]),
[iquote('0:Rew:8930.0,7996.0')] ).
cnf(9204,plain,
equal(multiply(u,multiply(multiply(multiply(inverse(inverse(inverse(multiply(v,u)))),w),inverse(multiply(inverse(v),w))),x)),inverse(inverse(x))),
inference(rew,[status(thm),theory(equality)],[7089,7888]),
[iquote('0:Rew:7089.0,7888.0')] ).
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)],[7089,6775,8302,6650]),
[iquote('0:Rew:7089.0,6775.0,8302.0,6775.0,6650.0,6775.0')] ).
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)],[8945,6917,7089,8930]),
[iquote('0:Rew:8945.0,6917.0,7089.0,6917.0,8930.0,6917.0')] ).
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(9326,plain,
equal(multiply(multiply(inverse(inverse(inverse(multiply(u,v)))),w),inverse(multiply(inverse(u),w))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[9034,7136,7089]),
[iquote('0:Rew:9034.0,7136.0,7089.0,7136.0')] ).
cnf(9334,plain,
equal(multiply(u,multiply(inverse(inverse(inverse(u))),v)),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[9326,9204]),
[iquote('0:Rew:9326.0,9204.0')] ).
cnf(9347,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)],[9034,7331,7089]),
[iquote('0:Rew:9034.0,7331.0,7089.0,7331.0')] ).
cnf(9426,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)],[8930,7605,7089]),
[iquote('0:Rew:8930.0,7605.0,7089.0,7605.0')] ).
cnf(9603,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),u)))),inverse(inverse(inverse(w)))),
inference(rew,[status(thm),theory(equality)],[9034,7412,7089]),
[iquote('0:Rew:9034.0,7412.0,7089.0,7412.0,7089.0,7412.0')] ).
cnf(9621,plain,
equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[9301,7770,7089,9347]),
[iquote('0:Rew:9301.0,7770.0,9301.0,7770.0,7089.0,7770.0,9347.0,7770.0,7089.0,7770.0')] ).
cnf(9623,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)],[9621,9084]),
[iquote('0:Rew:9621.0,9084.0')] ).
cnf(9624,plain,
equal(inverse(multiply(inverse(u),inverse(inverse(v)))),multiply(inverse(inverse(inverse(v))),u)),
inference(rew,[status(thm),theory(equality)],[9621,9301]),
[iquote('0:Rew:9621.0,9301.0')] ).
cnf(9625,plain,
equal(multiply(u,multiply(inverse(u),inverse(inverse(v)))),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[9621,9334]),
[iquote('0:Rew:9621.0,9334.0')] ).
cnf(9657,plain,
equal(inverse(multiply(inverse(u),inverse(inverse(v)))),multiply(inverse(v),inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[9621,9624]),
[iquote('0:Rew:9621.0,9624.0')] ).
cnf(9662,plain,
equal(multiply(multiply(multiply(inverse(u),inverse(inverse(v))),w),inverse(multiply(v,w))),inverse(inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[9657,9347]),
[iquote('0:Rew:9657.0,9347.0')] ).
cnf(9668,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)],[9657,8186]),
[iquote('0:Rew:9657.0,8186.0')] ).
cnf(9682,plain,
equal(inverse(inverse(multiply(multiply(u,inverse(u)),v))),v),
inference(rew,[status(thm),theory(equality)],[9623,9668,9621,8882]),
[iquote('0:Rew:9623.0,9668.0,9621.0,9668.0,8882.0,9668.0')] ).
cnf(9686,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[9682,9047]),
[iquote('0:Rew:9682.0,9047.0')] ).
cnf(9703,plain,
equal(multiply(inverse(multiply(u,inverse(u))),multiply(multiply(v,inverse(v)),w)),w),
inference(rew,[status(thm),theory(equality)],[9686,7267]),
[iquote('0:Rew:9686.0,7267.0')] ).
cnf(9705,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,multiply(multiply(inverse(v),w),u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[9686,9603]),
[iquote('0:Rew:9686.0,9603.0')] ).
cnf(9709,plain,
equal(inverse(multiply(u,inverse(inverse(inverse(multiply(v,multiply(w,u))))))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[9686,9255]),
[iquote('0:Rew:9686.0,9255.0')] ).
cnf(9723,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)],[9686,9426]),
[iquote('0:Rew:9686.0,9426.0')] ).
cnf(9729,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[9686,7089]),
[iquote('0:Rew:9686.0,7089.0')] ).
cnf(9739,plain,
equal(multiply(inverse(u),inverse(inverse(v))),inverse(multiply(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[9686,9657]),
[iquote('0:Rew:9686.0,9657.0')] ).
cnf(9741,plain,
equal(multiply(multiply(multiply(inverse(u),v),w),inverse(multiply(v,w))),inverse(inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[9686,9662]),
[iquote('0:Rew:9686.0,9662.0')] ).
cnf(9750,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[9686,9625]),
[iquote('0:Rew:9686.0,9625.0')] ).
cnf(9753,plain,
equal(inverse(multiply(multiply(u,v),inverse(multiply(w,v)))),multiply(w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[9686,9230]),
[iquote('0:Rew:9686.0,9230.0')] ).
cnf(9759,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[9686,9682]),
[iquote('0:Rew:9686.0,9682.0')] ).
cnf(9770,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[9686,6650]),
[iquote('0:Rew:9686.0,6650.0')] ).
cnf(9785,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[9686,9739]),
[iquote('0:Rew:9686.0,9739.0')] ).
cnf(9795,plain,
equal(multiply(inverse(multiply(u,inverse(u))),v),v),
inference(rew,[status(thm),theory(equality)],[9759,9703]),
[iquote('0:Rew:9759.0,9703.0')] ).
cnf(9800,plain,
equal(inverse(multiply(u,inverse(multiply(v,multiply(w,u))))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[9686,9709]),
[iquote('0:Rew:9686.0,9709.0')] ).
cnf(9811,plain,
equal(multiply(u,inverse(multiply(v,multiply(multiply(inverse(v),w),u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[9686,9705]),
[iquote('0:Rew:9686.0,9705.0')] ).
cnf(9821,plain,
equal(multiply(multiply(multiply(inverse(u),v),w),inverse(multiply(v,w))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[9686,9741]),
[iquote('0:Rew:9686.0,9741.0')] ).
cnf(9836,plain,
equal(inverse(multiply(u,multiply(inverse(multiply(v,u)),w))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[9686,9723,9785]),
[iquote('0:Rew:9686.0,9723.0,9785.0,9723.0,9785.0,9723.0,9785.0,9723.0')] ).
cnf(9878,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[9729,7872,9750,9821,9785,9686]),
[iquote('0:Rew:9729.0,7872.0,9750.0,7872.0,9821.0,7872.0,9785.0,7872.0,9686.0,7872.0')] ).
cnf(9899,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,w))),x)),multiply(multiply(multiply(inverse(x),v),w),u)),
inference(rew,[status(thm),theory(equality)],[9686,7027,9729,9785]),
[iquote('0:Rew:9686.0,7027.0,9729.0,7027.0,9785.0,7027.0,9729.0,7027.0')] ).
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)],[9686,7028,9729,9785]),
[iquote('0:Rew:9686.0,7028.0,9729.0,7028.0,9785.0,7028.0,9729.0,7028.0')] ).
cnf(10076,plain,
equal(multiply(u,inverse(multiply(multiply(inverse(v),w),u))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[9753,7429,9785,9836,9729,9686]),
[iquote('0:Rew:9753.0,7429.0,9785.0,7429.0,9785.0,7429.0,9836.0,7429.0,9729.0,7429.0,9785.0,7429.0,9686.0,7429.0')] ).
cnf(10440,plain,
equal(multiply(u,multiply(inverse(multiply(v,u)),w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[9800,8927,9900,9753,9836,9785,9686]),
[iquote('0:Rew:9800.0,8927.0,9900.0,8927.0,9753.0,8927.0,9836.0,8927.0,9785.0,8927.0,9686.0,8927.0,9785.0,8927.0,9785.0,8927.0,9785.0,8927.0,9785.0,8927.0')] ).
cnf(10548,plain,
equal(multiply(multiply(multiply(inverse(u),v),w),x),multiply(inverse(u),multiply(multiply(v,w),x))),
inference(rew,[status(thm),theory(equality)],[9785,7032,10076,9753,9686,9729]),
[iquote('0:Rew:9785.0,7032.0,9785.0,7032.0,9785.0,7032.0,10076.0,7032.0,9753.0,7032.0,9785.0,7032.0,9785.0,7032.0,9686.0,7032.0,9785.0,7032.0,9729.0,7032.0,9785.0,7032.0')] ).
cnf(10554,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,w))),x)),multiply(inverse(x),multiply(multiply(v,w),u))),
inference(rew,[status(thm),theory(equality)],[10548,9899]),
[iquote('0:Rew:10548.0,9899.0')] ).
cnf(10705,plain,
equal(multiply(u,multiply(v,multiply(multiply(inverse(multiply(u,v)),multiply(multiply(w,x),y)),inverse(multiply(x,y))))),w),
inference(rew,[status(thm),theory(equality)],[9686,7674,9785,10548,9811]),
[iquote('0:Rew:9686.0,7674.0,9785.0,7674.0,10548.0,7674.0,9785.0,7674.0,9785.0,7674.0,9686.0,7674.0,9686.0,7674.0,9811.0,7674.0,9686.0,7674.0')] ).
cnf(10796,plain,
equal(multiply(multiply(u,inverse(v)),w),multiply(u,multiply(inverse(v),w))),
inference(rew,[status(thm),theory(equality)],[9686,6844,9753,9785,10548,9811,9770]),
[iquote('0:Rew:9686.0,6844.0,9753.0,6844.0,9785.0,6844.0,10548.0,6844.0,9785.0,6844.0,9785.0,6844.0,9811.0,6844.0,9686.0,6844.0,9770.0,6844.0,10548.0,6844.0,9785.0,6844.0')] ).
cnf(10801,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(multiply(v,w)),x))),multiply(inverse(x),multiply(multiply(v,w),u))),
inference(rew,[status(thm),theory(equality)],[10796,10554]),
[iquote('0:Rew:10796.0,10554.0')] ).
cnf(10802,plain,
equal(multiply(multiply(inverse(u),multiply(v,w)),x),multiply(inverse(u),multiply(multiply(v,w),x))),
inference(rew,[status(thm),theory(equality)],[9785,10801]),
[iquote('0:Rew:9785.0,10801.0,9785.0,10801.0')] ).
cnf(10812,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(u,v)),multiply(multiply(multiply(w,x),y),inverse(multiply(x,y)))))),w),
inference(rew,[status(thm),theory(equality)],[10802,10705]),
[iquote('0:Rew:10802.0,10705.0')] ).
cnf(10832,plain,
equal(multiply(multiply(multiply(u,v),w),inverse(multiply(v,w))),u),
inference(rew,[status(thm),theory(equality)],[9750,10812,10440]),
[iquote('0:Rew:9750.0,10812.0,10440.0,10812.0')] ).
cnf(10865,plain,
equal(multiply(u,multiply(inverse(multiply(multiply(multiply(u,v),multiply(inverse(v),inverse(w))),w)),x)),x),
inference(rew,[status(thm),theory(equality)],[9785,7066,10832,10802,10548,9686]),
[iquote('0:Rew:9785.0,7066.0,9785.0,7066.0,10832.0,7066.0,10802.0,7066.0,10548.0,7066.0,9785.0,7066.0,9785.0,7066.0,10802.0,7066.0,10548.0,7066.0,9686.0,7066.0,9785.0,7066.0,9785.0,7066.0,10832.0,7066.0,9785.0,7066.0')] ).
cnf(11683,plain,
equal(multiply(inverse(multiply(multiply(multiply(inverse(u),v),multiply(inverse(v),inverse(w))),w)),x),multiply(u,x)),
inference(spr,[status(thm),theory(equality)],[10865,9750]),
[iquote('0:SpR:10865.0,9750.0')] ).
cnf(11714,plain,
equal(multiply(multiply(inverse(multiply(multiply(u,multiply(inverse(u),inverse(v))),v)),w),x),multiply(w,x)),
inference(rew,[status(thm),theory(equality)],[9785,11683,10548]),
[iquote('0:Rew:9785.0,11683.0,10548.0,11683.0')] ).
cnf(11715,plain,
equal(multiply(multiply(inverse(multiply(inverse(u),u)),v),w),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[9750,11714]),
[iquote('0:Rew:9750.0,11714.0')] ).
cnf(11716,plain,
equal(multiply(inverse(u),multiply(multiply(u,v),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[10548,11715,9785]),
[iquote('0:Rew:10548.0,11715.0,9785.0,11715.0')] ).
cnf(11818,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(spr,[status(thm),theory(equality)],[9686,9795]),
[iquote('0:SpR:9686.0,9795.0')] ).
cnf(11826,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[9785,11818]),
[iquote('0:Rew:9785.0,11818.0')] ).
cnf(11827,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[11826,2]),
[iquote('0:Rew:11826.0,2.2')] ).
cnf(11844,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[11827]),
[iquote('0:Obv:11827.2')] ).
cnf(12749,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[11716,9750]),
[iquote('0:SpR:11716.0,9750.0')] ).
cnf(12785,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12749,11844]),
[iquote('0:Rew:12749.0,11844.1')] ).
cnf(12886,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[12785]),
[iquote('0:Obv:12785.1')] ).
cnf(12887,plain,
$false,
inference(unc,[status(thm)],[12886,9878]),
[iquote('0:UnC:12886.0,9878.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP057-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n029.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 04:17:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 23.94/24.16
% 23.94/24.16 SPASS V 3.9
% 23.94/24.16 SPASS beiseite: Proof found.
% 23.94/24.16 % SZS status Theorem
% 23.94/24.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.94/24.16 SPASS derived 8827 clauses, backtracked 0 clauses, performed 0 splits and kept 2706 clauses.
% 23.94/24.16 SPASS allocated 104283 KBytes.
% 23.94/24.16 SPASS spent 0:0:23.80 on the problem.
% 23.94/24.16 0:00:00.03 for the input.
% 23.94/24.16 0:00:00.00 for the FLOTTER CNF translation.
% 23.94/24.16 0:00:00.10 for inferences.
% 23.94/24.16 0:00:00.00 for the backtracking.
% 23.94/24.16 0:0:23.64 for the reduction.
% 23.94/24.16
% 23.94/24.16
% 23.94/24.16 Here is a proof with depth 12, length 194 :
% 23.94/24.16 % SZS output start Refutation
% See solution above
% 24.24/24.46 Formulae used in the proof : single_axiom prove_these_axioms
% 24.24/24.46
%------------------------------------------------------------------------------