TSTP Solution File: GRP110-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP110-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:45:21 EDT 2022
% Result : Unsatisfiable 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of clauses : 145 ( 142 unt; 0 nHn; 145 RR)
% Number of literals : 154 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(double_divide(inverse(double_divide(inverse(double_divide(u,v)),w)),double_divide(u,w))),v),
file('GRP110-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP110-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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('GRP110-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(w,u))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),multiply(x,v)),double_divide(w,u)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(7,plain,
equal(multiply(double_divide(multiply(u,v),double_divide(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(multiply(u,x),double_divide(x,w))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(11,plain,
equal(multiply(double_divide(u,double_divide(multiply(multiply(v,u),w),double_divide(w,x))),x),v),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(15,plain,
equal(double_divide(u,multiply(double_divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(26,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(x,double_divide(multiply(multiply(w,x),y),double_divide(y,u)))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(32,plain,
equal(multiply(multiply(double_divide(multiply(u,v),w),u),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[15,2]),
[iquote('0:SpR:15.0,2.0')] ).
cnf(37,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),u),double_divide(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[15]),
[iquote('0:SpR:15.0,15.0')] ).
cnf(42,plain,
equal(double_divide(multiply(u,v),double_divide(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[6,15]),
[iquote('0:SpR:6.0,15.0')] ).
cnf(44,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[42,2]),
[iquote('0:SpR:42.0,2.0')] ).
cnf(52,plain,
equal(double_divide(multiply(multiply(u,multiply(v,w)),x),double_divide(x,v)),double_divide(w,u)),
inference(spr,[status(thm),theory(equality)],[4,42]),
[iquote('0:SpR:4.0,42.0')] ).
cnf(59,plain,
equal(multiply(double_divide(u,v),multiply(v,inverse(w))),multiply(double_divide(multiply(x,u),w),x)),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(61,plain,
equal(multiply(double_divide(u,multiply(double_divide(multiply(v,multiply(w,u)),x),v)),inverse(x)),w),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(68,plain,
equal(multiply(double_divide(multiply(u,inverse(v)),w),multiply(w,multiply(double_divide(multiply(x,y),v),x))),double_divide(y,u)),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(76,plain,
equal(multiply(double_divide(u,double_divide(u,multiply(v,w))),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[37,61]),
[iquote('0:Rew:37.0,61.0')] ).
cnf(80,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,inverse(x))),double_divide(v,multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[44,4]),
[iquote('0:SpR:44.0,4.0')] ).
cnf(126,plain,
equal(inverse(multiply(double_divide(u,v),multiply(v,w))),multiply(double_divide(x,w),multiply(u,x))),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(130,plain,
equal(multiply(multiply(double_divide(u,v),multiply(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(137,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,w),double_divide(w,x))),x),double_divide(multiply(u,y),double_divide(y,v))),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(143,plain,
equal(multiply(u,multiply(double_divide(v,multiply(u,w)),x)),double_divide(multiply(multiply(w,v),y),double_divide(y,x))),
inference(spr,[status(thm),theory(equality)],[42,9]),
[iquote('0:SpR:42.0,9.0')] ).
cnf(144,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(double_divide(multiply(w,x),y),w))),double_divide(multiply(u,x),y)),
inference(spr,[status(thm),theory(equality)],[15,9]),
[iquote('0:SpR:15.0,9.0')] ).
cnf(145,plain,
equal(multiply(double_divide(u,v),multiply(v,double_divide(w,multiply(x,y)))),double_divide(multiply(u,multiply(y,w)),x)),
inference(spr,[status(thm),theory(equality)],[42,9]),
[iquote('0:SpR:42.0,9.0')] ).
cnf(159,plain,
equal(double_divide(multiply(multiply(u,inverse(v)),w),v),double_divide(w,u)),
inference(rew,[status(thm),theory(equality)],[144,68]),
[iquote('0:Rew:144.0,68.0')] ).
cnf(174,plain,
equal(multiply(multiply(double_divide(u,v),multiply(double_divide(w,x),multiply(x,u))),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[130,32]),
[iquote('0:SpR:130.0,32.0')] ).
cnf(178,plain,
equal(multiply(double_divide(u,multiply(double_divide(v,w),multiply(w,x))),x),double_divide(multiply(u,y),double_divide(y,v))),
inference(spr,[status(thm),theory(equality)],[130,9]),
[iquote('0:SpR:130.0,9.0')] ).
cnf(180,plain,
equal(multiply(double_divide(multiply(double_divide(u,v),multiply(v,w)),x),multiply(x,y)),double_divide(w,double_divide(u,y))),
inference(spr,[status(thm),theory(equality)],[130,9]),
[iquote('0:SpR:130.0,9.0')] ).
cnf(182,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,w)),x),u),multiply(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[4,130]),
[iquote('0:SpR:4.0,130.0')] ).
cnf(184,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,multiply(w,x))),inverse(w)),u),multiply(x,v)),
inference(spr,[status(thm),theory(equality)],[44,130]),
[iquote('0:SpR:44.0,130.0')] ).
cnf(190,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[7,130]),
[iquote('0:SpR:7.0,130.0')] ).
cnf(195,plain,
equal(multiply(multiply(u,v),multiply(inverse(u),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[182,184]),
[iquote('0:Rew:182.0,184.0')] ).
cnf(232,plain,
equal(multiply(double_divide(inverse(u),multiply(v,double_divide(w,double_divide(w,multiply(u,x))))),x),inverse(v)),
inference(spr,[status(thm),theory(equality)],[76,44]),
[iquote('0:SpR:76.0,44.0')] ).
cnf(240,plain,
equal(multiply(double_divide(u,v),multiply(inverse(w),u)),inverse(double_divide(x,double_divide(x,multiply(w,v))))),
inference(spr,[status(thm),theory(equality)],[76,44]),
[iquote('0:SpR:76.0,44.0')] ).
cnf(245,plain,
equal(multiply(double_divide(double_divide(u,double_divide(u,multiply(v,w))),x),multiply(x,y)),double_divide(w,double_divide(inverse(v),y))),
inference(spr,[status(thm),theory(equality)],[76,9]),
[iquote('0:SpR:76.0,9.0')] ).
cnf(250,plain,
equal(multiply(double_divide(u,double_divide(u,v)),inverse(double_divide(w,x))),multiply(x,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[4,76]),
[iquote('0:SpR:4.0,76.0')] ).
cnf(254,plain,
equal(multiply(double_divide(u,double_divide(u,v)),inverse(w)),multiply(multiply(double_divide(x,w),v),x)),
inference(spr,[status(thm),theory(equality)],[190,76]),
[iquote('0:SpR:190.0,76.0')] ).
cnf(255,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),inverse(multiply(double_divide(multiply(w,x),v),w))),x),
inference(spr,[status(thm),theory(equality)],[32,76]),
[iquote('0:SpR:32.0,76.0')] ).
cnf(261,plain,
equal(multiply(double_divide(u,double_divide(u,v)),multiply(w,x)),multiply(w,multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[2,250]),
[iquote('0:Rew:2.0,250.0')] ).
cnf(264,plain,
equal(multiply(double_divide(u,v),multiply(inverse(w),u)),multiply(double_divide(x,multiply(w,v)),x)),
inference(rew,[status(thm),theory(equality)],[2,240]),
[iquote('0:Rew:2.0,240.0')] ).
cnf(284,plain,
equal(double_divide(multiply(u,multiply(multiply(v,inverse(multiply(w,u))),x)),double_divide(x,v)),w),
inference(spr,[status(thm),theory(equality)],[159,42]),
[iquote('0:SpR:159.0,42.0')] ).
cnf(290,plain,
equal(double_divide(u,multiply(double_divide(u,v),multiply(v,inverse(w)))),w),
inference(spr,[status(thm),theory(equality)],[159,15]),
[iquote('0:SpR:159.0,15.0')] ).
cnf(310,plain,
equal(double_divide(multiply(u,v),double_divide(v,w)),double_divide(x,double_divide(multiply(multiply(w,x),y),double_divide(y,u)))),
inference(spr,[status(thm),theory(equality)],[11,42]),
[iquote('0:SpR:11.0,42.0')] ).
cnf(334,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,w),double_divide(w,x))),x),multiply(double_divide(u,y),multiply(y,v))),
inference(spr,[status(thm),theory(equality)],[130,11]),
[iquote('0:SpR:130.0,11.0')] ).
cnf(344,plain,
equal(multiply(double_divide(u,double_divide(inverse(v),double_divide(w,x))),x),double_divide(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[32,11]),
[iquote('0:SpR:32.0,11.0')] ).
cnf(375,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(multiply(inverse(x),w),u)),inverse(multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[195,44]),
[iquote('0:SpR:195.0,44.0')] ).
cnf(376,plain,
equal(multiply(double_divide(u,double_divide(u,multiply(v,w))),inverse(multiply(x,v))),multiply(inverse(x),w)),
inference(spr,[status(thm),theory(equality)],[195,76]),
[iquote('0:SpR:195.0,76.0')] ).
cnf(383,plain,
equal(multiply(u,multiply(multiply(double_divide(v,inverse(w)),x),v)),multiply(multiply(w,u),x)),
inference(spr,[status(thm),theory(equality)],[190,195]),
[iquote('0:SpR:190.0,195.0')] ).
cnf(386,plain,
equal(multiply(u,multiply(inverse(double_divide(v,w)),x)),multiply(multiply(w,multiply(u,v)),x)),
inference(spr,[status(thm),theory(equality)],[4,195]),
[iquote('0:SpR:4.0,195.0')] ).
cnf(397,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(v,multiply(multiply(u,w),x))),
inference(rew,[status(thm),theory(equality)],[2,386]),
[iquote('0:Rew:2.0,386.0')] ).
cnf(403,plain,
equal(double_divide(multiply(u,multiply(multiply(v,w),x)),double_divide(x,u)),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[397,52]),
[iquote('0:Rew:397.0,52.0')] ).
cnf(405,plain,
equal(multiply(double_divide(u,v),multiply(multiply(double_divide(w,x),multiply(v,w)),u)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,174]),
[iquote('0:Rew:397.0,174.0')] ).
cnf(418,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(multiply(double_divide(w,x),w),u))),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,405]),
[iquote('0:Rew:397.0,405.0')] ).
cnf(419,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4,418]),
[iquote('0:Rew:4.0,418.0')] ).
cnf(421,plain,
equal(multiply(double_divide(u,v),multiply(inverse(w),u)),inverse(multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[419,264]),
[iquote('0:Rew:419.0,264.0')] ).
cnf(434,plain,
equal(multiply(double_divide(u,v),multiply(v,inverse(w))),double_divide(u,w)),
inference(spr,[status(thm),theory(equality)],[419,4]),
[iquote('0:SpR:419.0,4.0')] ).
cnf(440,plain,
equal(double_divide(multiply(multiply(u,v),w),double_divide(w,v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[419,9]),
[iquote('0:SpR:419.0,9.0')] ).
cnf(447,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(w,u)),inverse(double_divide(w,v))),
inference(spr,[status(thm),theory(equality)],[419,44]),
[iquote('0:SpR:419.0,44.0')] ).
cnf(454,plain,
equal(double_divide(multiply(inverse(u),v),w),double_divide(v,double_divide(inverse(w),u))),
inference(spr,[status(thm),theory(equality)],[419,159]),
[iquote('0:SpR:419.0,159.0')] ).
cnf(456,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[42,419]),
[iquote('0:SpR:42.0,419.0')] ).
cnf(460,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[434,80]),
[iquote('0:Rew:434.0,80.0')] ).
cnf(461,plain,
equal(multiply(double_divide(multiply(u,v),w),u),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[434,59]),
[iquote('0:Rew:434.0,59.0')] ).
cnf(462,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[434,290]),
[iquote('0:Rew:434.0,290.0')] ).
cnf(466,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,x)),double_divide(v,double_divide(inverse(u),x))),
inference(rew,[status(thm),theory(equality)],[462,245]),
[iquote('0:Rew:462.0,245.0')] ).
cnf(467,plain,
equal(multiply(multiply(u,v),inverse(multiply(w,u))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[462,376]),
[iquote('0:Rew:462.0,376.0')] ).
cnf(468,plain,
equal(multiply(inverse(u),inverse(multiply(double_divide(multiply(v,w),u),v))),w),
inference(rew,[status(thm),theory(equality)],[462,255]),
[iquote('0:Rew:462.0,255.0')] ).
cnf(470,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[462,261]),
[iquote('0:Rew:462.0,261.0')] ).
cnf(471,plain,
equal(multiply(multiply(double_divide(u,v),w),u),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[462,254]),
[iquote('0:Rew:462.0,254.0')] ).
cnf(473,plain,
equal(multiply(double_divide(inverse(u),multiply(v,multiply(u,w))),w),inverse(v)),
inference(rew,[status(thm),theory(equality)],[462,232]),
[iquote('0:Rew:462.0,232.0')] ).
cnf(482,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(x,multiply(double_divide(x,w),u))),
inference(rew,[status(thm),theory(equality)],[460,9]),
[iquote('0:Rew:460.0,9.0')] ).
cnf(521,plain,
equal(multiply(u,multiply(double_divide(v,multiply(u,w)),x)),double_divide(y,multiply(double_divide(y,x),multiply(w,v)))),
inference(rew,[status(thm),theory(equality)],[460,143]),
[iquote('0:Rew:460.0,143.0')] ).
cnf(528,plain,
equal(double_divide(multiply(multiply(u,v),w),multiply(double_divide(w,x),x)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[460,403]),
[iquote('0:Rew:460.0,403.0')] ).
cnf(529,plain,
equal(double_divide(multiply(multiply(u,inverse(multiply(v,w))),x),multiply(double_divide(x,u),w)),v),
inference(rew,[status(thm),theory(equality)],[460,284]),
[iquote('0:Rew:460.0,284.0')] ).
cnf(537,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,w),double_divide(w,x))),x),double_divide(y,multiply(double_divide(y,v),u))),
inference(rew,[status(thm),theory(equality)],[460,137]),
[iquote('0:Rew:460.0,137.0')] ).
cnf(538,plain,
equal(multiply(double_divide(u,multiply(double_divide(v,w),multiply(w,x))),x),double_divide(y,multiply(double_divide(y,v),u))),
inference(rew,[status(thm),theory(equality)],[460,178]),
[iquote('0:Rew:460.0,178.0')] ).
cnf(541,plain,
equal(multiply(double_divide(u,double_divide(v,multiply(double_divide(v,w),x))),w),multiply(double_divide(u,y),multiply(y,x))),
inference(rew,[status(thm),theory(equality)],[460,334]),
[iquote('0:Rew:460.0,334.0')] ).
cnf(586,plain,
equal(multiply(double_divide(multiply(u,v),multiply(w,double_divide(x,u))),multiply(w,y)),double_divide(v,double_divide(x,y))),
inference(rew,[status(thm),theory(equality)],[460,180]),
[iquote('0:Rew:460.0,180.0')] ).
cnf(587,plain,
equal(multiply(double_divide(u,v),multiply(v,double_divide(w,multiply(x,y)))),double_divide(multiply(y,w),multiply(x,u))),
inference(rew,[status(thm),theory(equality)],[460,145]),
[iquote('0:Rew:460.0,145.0')] ).
cnf(606,plain,
equal(double_divide(u,multiply(double_divide(u,v),w)),double_divide(x,double_divide(multiply(multiply(v,x),y),double_divide(y,w)))),
inference(rew,[status(thm),theory(equality)],[460,310]),
[iquote('0:Rew:460.0,310.0')] ).
cnf(611,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(x,double_divide(y,multiply(double_divide(y,u),multiply(w,x))))),
inference(rew,[status(thm),theory(equality)],[460,26]),
[iquote('0:Rew:460.0,26.0')] ).
cnf(612,plain,
equal(multiply(double_divide(u,double_divide(inverse(v),double_divide(w,x))),x),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[460,344]),
[iquote('0:Rew:460.0,344.0')] ).
cnf(614,plain,
equal(multiply(double_divide(multiply(u,v),multiply(w,x)),x),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[460,37]),
[iquote('0:Rew:460.0,37.0')] ).
cnf(621,plain,
equal(multiply(double_divide(u,multiply(v,w)),w),double_divide(u,v)),
inference(rew,[status(thm),theory(equality)],[460,461]),
[iquote('0:Rew:460.0,461.0')] ).
cnf(637,plain,
equal(inverse(multiply(u,multiply(double_divide(v,u),w))),multiply(double_divide(x,w),multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[470,126]),
[iquote('0:Rew:470.0,126.0')] ).
cnf(643,plain,
equal(double_divide(u,multiply(double_divide(u,v),multiply(w,v))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[460,440]),
[iquote('0:Rew:460.0,440.0')] ).
cnf(646,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2,456]),
[iquote('0:Rew:2.0,456.0')] ).
cnf(647,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(inverse(b2),multiply(b2,a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[646,3]),
[iquote('0:Rew:646.0,3.3')] ).
cnf(651,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(inverse(x),multiply(w,u))),inverse(multiply(x,v))),
inference(rew,[status(thm),theory(equality)],[646,375]),
[iquote('0:Rew:646.0,375.0')] ).
cnf(659,plain,
equal(multiply(u,multiply(multiply(double_divide(v,inverse(w)),x),v)),multiply(w,multiply(u,x))),
inference(rew,[status(thm),theory(equality)],[646,383]),
[iquote('0:Rew:646.0,383.0')] ).
cnf(672,plain,
equal(multiply(double_divide(u,v),multiply(w,u)),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[646,471]),
[iquote('0:Rew:646.0,471.0')] ).
cnf(674,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[672,421]),
[iquote('0:Rew:672.0,421.0')] ).
cnf(692,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(w,u)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[2,447]),
[iquote('0:Rew:2.0,447.0')] ).
cnf(693,plain,
equal(multiply(u,inverse(inverse(v))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[672,692]),
[iquote('0:Rew:672.0,692.0')] ).
cnf(696,plain,
equal(double_divide(u,multiply(v,inverse(w))),double_divide(u,double_divide(inverse(v),w))),
inference(rew,[status(thm),theory(equality)],[460,454]),
[iquote('0:Rew:460.0,454.0')] ).
cnf(702,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,u)))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[646,467]),
[iquote('0:Rew:646.0,467.0')] ).
cnf(703,plain,
equal(inverse(multiply(u,double_divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[674,468,621,460]),
[iquote('0:Rew:674.0,468.0,621.0,468.0,460.0,468.0')] ).
cnf(707,plain,
equal(multiply(u,multiply(double_divide(v,u),w)),double_divide(x,multiply(double_divide(x,w),v))),
inference(rew,[status(thm),theory(equality)],[470,482]),
[iquote('0:Rew:470.0,482.0')] ).
cnf(710,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(u,v),multiply(w,x)))),double_divide(x,w)),
inference(rew,[status(thm),theory(equality)],[646,528,460,470]),
[iquote('0:Rew:646.0,528.0,646.0,528.0,460.0,528.0,470.0,528.0,646.0,528.0,460.0,528.0,646.0,528.0')] ).
cnf(723,plain,
equal(multiply(double_divide(u,multiply(v,multiply(w,x))),w),double_divide(u,multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[646,614,460]),
[iquote('0:Rew:646.0,614.0,460.0,614.0')] ).
cnf(745,plain,
equal(multiply(u,multiply(double_divide(v,multiply(u,w)),x)),double_divide(v,double_divide(inverse(w),x))),
inference(rew,[status(thm),theory(equality)],[470,466,460]),
[iquote('0:Rew:470.0,466.0,460.0,466.0')] ).
cnf(752,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[643,529,702,646,460]),
[iquote('0:Rew:643.0,529.0,702.0,529.0,646.0,529.0,646.0,529.0,460.0,529.0,646.0,529.0,460.0,529.0,646.0,529.0')] ).
cnf(753,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[752,693]),
[iquote('0:Rew:752.0,693.0')] ).
cnf(760,plain,
equal(multiply(u,double_divide(v,multiply(w,multiply(u,x)))),double_divide(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[753,723]),
[iquote('0:Rew:753.0,723.0')] ).
cnf(767,plain,
equal(multiply(u,double_divide(inverse(v),multiply(w,multiply(v,u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[753,473]),
[iquote('0:Rew:753.0,473.0')] ).
cnf(792,plain,
equal(multiply(u,double_divide(v,double_divide(inverse(w),double_divide(x,u)))),double_divide(x,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[753,612]),
[iquote('0:Rew:753.0,612.0')] ).
cnf(799,plain,
equal(inverse(multiply(u,multiply(double_divide(v,u),w))),multiply(v,inverse(w))),
inference(rew,[status(thm),theory(equality)],[672,637]),
[iquote('0:Rew:672.0,637.0')] ).
cnf(805,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[752,659,672,646]),
[iquote('0:Rew:752.0,659.0,672.0,659.0,646.0,659.0')] ).
cnf(806,plain,
equal(multiply(u,multiply(double_divide(u,v),w)),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[805,672]),
[iquote('0:Rew:805.0,672.0')] ).
cnf(807,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(u,v),w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[805,643]),
[iquote('0:Rew:805.0,643.0')] ).
cnf(810,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[807,710]),
[iquote('0:Rew:807.0,710.0')] ).
cnf(811,plain,
equal(multiply(u,multiply(v,double_divide(u,w))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[810,702]),
[iquote('0:Rew:810.0,702.0')] ).
cnf(812,plain,
equal(double_divide(multiply(double_divide(u,v),w),v),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[810,799]),
[iquote('0:Rew:810.0,799.0')] ).
cnf(813,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[810,703]),
[iquote('0:Rew:810.0,703.0')] ).
cnf(814,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[810,674]),
[iquote('0:Rew:810.0,674.0')] ).
cnf(818,plain,
equal(double_divide(u,multiply(v,double_divide(w,v))),multiply(w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[460,812]),
[iquote('0:Rew:460.0,812.0')] ).
cnf(837,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[814,651,811,810,806,646,805]),
[iquote('0:Rew:814.0,651.0,811.0,651.0,810.0,651.0,806.0,651.0,646.0,651.0,805.0,651.0,810.0,651.0')] ).
cnf(839,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[837,813]),
[iquote('0:Rew:837.0,813.0')] ).
cnf(856,plain,
equal(double_divide(u,multiply(double_divide(u,v),multiply(w,x))),double_divide(x,double_divide(inverse(w),v))),
inference(rew,[status(thm),theory(equality)],[745,521]),
[iquote('0:Rew:745.0,521.0')] ).
cnf(881,plain,
equal(multiply(u,double_divide(v,double_divide(w,multiply(double_divide(w,u),x)))),double_divide(y,multiply(double_divide(y,x),v))),
inference(rew,[status(thm),theory(equality)],[753,537,460]),
[iquote('0:Rew:753.0,537.0,460.0,537.0')] ).
cnf(882,plain,
equal(double_divide(u,multiply(double_divide(u,v),w)),multiply(v,inverse(w))),
inference(rew,[status(thm),theory(equality)],[818,538,760,753,805]),
[iquote('0:Rew:818.0,538.0,760.0,538.0,753.0,538.0,805.0,538.0')] ).
cnf(883,plain,
equal(multiply(u,double_divide(v,double_divide(w,multiply(double_divide(w,u),x)))),multiply(x,inverse(v))),
inference(rew,[status(thm),theory(equality)],[882,881]),
[iquote('0:Rew:882.0,881.0')] ).
cnf(889,plain,
equal(multiply(u,multiply(double_divide(v,u),w)),multiply(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[882,707]),
[iquote('0:Rew:882.0,707.0')] ).
cnf(892,plain,
equal(multiply(u,inverse(multiply(v,w))),double_divide(w,double_divide(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[882,856]),
[iquote('0:Rew:882.0,856.0')] ).
cnf(918,plain,
equal(double_divide(u,double_divide(inverse(v),w)),multiply(w,double_divide(u,v))),
inference(rew,[status(thm),theory(equality)],[810,892]),
[iquote('0:Rew:810.0,892.0')] ).
cnf(921,plain,
equal(multiply(u,multiply(double_divide(v,u),double_divide(w,x))),double_divide(v,multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[918,792]),
[iquote('0:Rew:918.0,792.0')] ).
cnf(924,plain,
equal(double_divide(u,multiply(v,inverse(w))),multiply(w,double_divide(u,v))),
inference(rew,[status(thm),theory(equality)],[918,696]),
[iquote('0:Rew:918.0,696.0')] ).
cnf(936,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[889,921]),
[iquote('0:Rew:889.0,921.0')] ).
cnf(941,plain,
equal(multiply(u,multiply(v,double_divide(w,u))),multiply(v,inverse(w))),
inference(rew,[status(thm),theory(equality)],[924,883,882]),
[iquote('0:Rew:924.0,883.0,882.0,883.0')] ).
cnf(953,plain,
equal(multiply(u,multiply(v,double_divide(w,v))),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[753,541,646,924,882,941,805]),
[iquote('0:Rew:753.0,541.0,646.0,541.0,924.0,541.0,882.0,541.0,941.0,541.0,805.0,541.0')] ).
cnf(967,plain,
equal(multiply(u,multiply(v,inverse(w))),double_divide(w,double_divide(u,v))),
inference(rew,[status(thm),theory(equality)],[941,586,805,646,924,953,753,460]),
[iquote('0:Rew:941.0,586.0,805.0,586.0,646.0,586.0,924.0,586.0,953.0,586.0,753.0,586.0,646.0,586.0,460.0,586.0')] ).
cnf(973,plain,
equal(double_divide(u,multiply(v,multiply(w,x))),double_divide(x,multiply(v,multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[646,587,936,941,805,460]),
[iquote('0:Rew:646.0,587.0,936.0,587.0,941.0,587.0,805.0,587.0,646.0,587.0,460.0,587.0')] ).
cnf(974,plain,
equal(multiply(u,double_divide(v,multiply(w,multiply(u,inverse(v))))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[973,767]),
[iquote('0:Rew:973.0,767.0')] ).
cnf(975,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[462,974,967]),
[iquote('0:Rew:462.0,974.0,967.0,974.0')] ).
cnf(977,plain,
equal(multiply(u,inverse(v)),double_divide(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[975,818]),
[iquote('0:Rew:975.0,818.0')] ).
cnf(986,plain,
equal(double_divide(u,multiply(double_divide(u,v),w)),double_divide(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[977,882]),
[iquote('0:Rew:977.0,882.0')] ).
cnf(987,plain,
equal(double_divide(u,double_divide(v,inverse(w))),multiply(v,double_divide(u,w))),
inference(rew,[status(thm),theory(equality)],[977,924]),
[iquote('0:Rew:977.0,924.0')] ).
cnf(988,plain,
equal(multiply(u,multiply(v,double_divide(w,u))),double_divide(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[977,941]),
[iquote('0:Rew:977.0,941.0')] ).
cnf(1007,plain,
equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
inference(rew,[status(thm),theory(equality)],[986,606,462,460,646]),
[iquote('0:Rew:986.0,606.0,462.0,606.0,460.0,606.0,986.0,606.0,646.0,606.0,460.0,606.0,460.0,606.0,646.0,606.0')] ).
cnf(1029,plain,
equal(double_divide(u,multiply(v,double_divide(u,w))),double_divide(v,inverse(w))),
inference(rew,[status(thm),theory(equality)],[988,611,805,987,1007,460,986]),
[iquote('0:Rew:988.0,611.0,805.0,611.0,987.0,611.0,1007.0,611.0,460.0,611.0,986.0,611.0')] ).
cnf(1090,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[839,647,810,1007,646,753]),
[iquote('0:Rew:839.0,647.3,810.0,647.3,1007.0,647.3,646.0,647.2,1007.0,647.1,1007.0,647.1,753.0,647.0')] ).
cnf(1091,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[1090]),
[iquote('0:Obv:1090.3')] ).
cnf(1234,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[975,1029]),
[iquote('0:SpR:975.0,1029.0')] ).
cnf(1235,plain,
$false,
inference(unc,[status(thm)],[1234,1091]),
[iquote('0:UnC:1234.0,1091.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP110-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 05:38:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 812 clauses, backtracked 0 clauses, performed 0 splits and kept 457 clauses.
% 0.47/0.64 SPASS allocated 65108 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.30 on the problem.
% 0.47/0.64 0:00:00.04 for the input.
% 0.47/0.64 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.01 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.23 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 6, length 145 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.66 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.47/0.66
%------------------------------------------------------------------------------