TSTP Solution File: GRP609-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:48:16 EDT 2022
% Result : Unsatisfiable 0.46s 0.66s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of clauses : 148 ( 148 unt; 0 nHn; 148 RR)
% Number of literals : 148 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 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('GRP609-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP609-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP609-1.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(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(22,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),double_divide(multiply(v,x),double_divide(x,y))),y),double_divide(w,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(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(65,plain,
equal(multiply(multiply(double_divide(inverse(u),v),multiply(double_divide(multiply(w,x),u),w)),x),inverse(v)),
inference(spr,[status(thm),theory(equality)],[32]),
[iquote('0:SpR:32.0,32.0')] ).
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(114,plain,
equal(multiply(double_divide(double_divide(multiply(u,v),double_divide(v,w)),x),multiply(x,y)),double_divide(w,double_divide(u,y))),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
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(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(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(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(212,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,x)),double_divide(multiply(multiply(double_divide(y,x),v),y),u)),
inference(spr,[status(thm),theory(equality)],[190,6]),
[iquote('0:SpR:190.0,6.0')] ).
cnf(217,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(x,double_divide(multiply(multiply(double_divide(y,u),x),y),w))),
inference(spr,[status(thm),theory(equality)],[190,9]),
[iquote('0:SpR:190.0,9.0')] ).
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(288,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(x,u)),double_divide(v,multiply(w,inverse(x)))),
inference(spr,[status(thm),theory(equality)],[159,6]),
[iquote('0:SpR:159.0,6.0')] ).
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(292,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(multiply(u,multiply(multiply(x,inverse(w)),y)),double_divide(y,x))),
inference(spr,[status(thm),theory(equality)],[159,9]),
[iquote('0:SpR:159.0,9.0')] ).
cnf(364,plain,
equal(double_divide(multiply(multiply(inverse(u),v),w),double_divide(w,multiply(x,v))),multiply(u,x)),
inference(spr,[status(thm),theory(equality)],[195,42]),
[iquote('0:SpR:195.0,42.0')] ).
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(381,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,x)),double_divide(multiply(v,y),double_divide(multiply(inverse(u),y),x))),
inference(spr,[status(thm),theory(equality)],[195,9]),
[iquote('0:SpR:195.0,9.0')] ).
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(408,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(multiply(double_divide(inverse(w),x),u),v)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,65]),
[iquote('0:Rew:397.0,65.0')] ).
cnf(409,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)],[397,409]),
[iquote('0:Rew:397.0,409.0')] ).
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(420,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(450,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(spr,[status(thm),theory(equality)],[419,190]),
[iquote('0:SpR:419.0,190.0')] ).
cnf(451,plain,
equal(multiply(double_divide(double_divide(u,v),w),multiply(w,x)),double_divide(inverse(v),double_divide(u,x))),
inference(spr,[status(thm),theory(equality)],[419,9]),
[iquote('0:SpR:419.0,9.0')] ).
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(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(500,plain,
equal(double_divide(u,multiply(double_divide(u,multiply(v,w)),multiply(inverse(x),w))),multiply(x,v)),
inference(rew,[status(thm),theory(equality)],[460,364]),
[iquote('0:Rew:460.0,364.0')] ).
cnf(513,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,x)),double_divide(y,multiply(double_divide(multiply(inverse(u),y),x),v))),
inference(rew,[status(thm),theory(equality)],[460,381]),
[iquote('0:Rew:460.0,381.0')] ).
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(534,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(multiply(multiply(x,inverse(w)),y),multiply(double_divide(y,x),u))),
inference(rew,[status(thm),theory(equality)],[460,292]),
[iquote('0:Rew:460.0,292.0')] ).
cnf(548,plain,
equal(multiply(double_divide(multiply(u,v),multiply(double_divide(multiply(u,w),double_divide(w,x)),y)),x),double_divide(v,y)),
inference(rew,[status(thm),theory(equality)],[460,22]),
[iquote('0:Rew:460.0,22.0')] ).
cnf(555,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(x,double_divide(y,multiply(w,multiply(double_divide(y,u),x))))),
inference(rew,[status(thm),theory(equality)],[460,217]),
[iquote('0:Rew:460.0,217.0')] ).
cnf(571,plain,
equal(multiply(double_divide(multiply(u,v),w),multiply(w,x)),double_divide(y,multiply(u,multiply(double_divide(y,x),v)))),
inference(rew,[status(thm),theory(equality)],[460,212]),
[iquote('0:Rew:460.0,212.0')] ).
cnf(604,plain,
equal(multiply(double_divide(double_divide(u,multiply(double_divide(u,v),w)),x),multiply(x,y)),double_divide(v,double_divide(w,y))),
inference(rew,[status(thm),theory(equality)],[460,114]),
[iquote('0:Rew:460.0,114.0')] ).
cnf(619,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(x,w)),double_divide(u,multiply(v,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[460,288]),
[iquote('0:Rew:460.0,288.0')] ).
cnf(620,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(multiply(double_divide(inverse(v),x),w),u)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[460,408]),
[iquote('0:Rew:460.0,408.0')] ).
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(633,plain,
equal(multiply(u,multiply(double_divide(v,u),inverse(w))),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[470,434]),
[iquote('0:Rew:470.0,434.0')] ).
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(671,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(673,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[671,420]),
[iquote('0:Rew:671.0,420.0')] ).
cnf(691,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(692,plain,
equal(multiply(u,inverse(inverse(v))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[671,691]),
[iquote('0:Rew:671.0,691.0')] ).
cnf(695,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(701,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(702,plain,
equal(inverse(multiply(u,double_divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[673,468,621,460]),
[iquote('0:Rew:673.0,468.0,621.0,468.0,460.0,468.0')] ).
cnf(706,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(739,plain,
equal(multiply(u,multiply(double_divide(double_divide(v,w),u),x)),double_divide(inverse(w),double_divide(v,x))),
inference(rew,[status(thm),theory(equality)],[470,451]),
[iquote('0:Rew:470.0,451.0')] ).
cnf(743,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(750,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[643,529,701,646,460]),
[iquote('0:Rew:643.0,529.0,701.0,529.0,646.0,529.0,646.0,529.0,460.0,529.0,646.0,529.0,460.0,529.0,646.0,529.0')] ).
cnf(751,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[750,692]),
[iquote('0:Rew:750.0,692.0')] ).
cnf(752,plain,
~ equal(multiply(inverse(a1),a1),multiply(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[751,3]),
[iquote('0:Rew:751.0,3.0')] ).
cnf(753,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[751,419]),
[iquote('0:Rew:751.0,419.0')] ).
cnf(768,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(rew,[status(thm),theory(equality)],[751,752]),
[iquote('0:Rew:751.0,752.0')] ).
cnf(793,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(x,w)),double_divide(u,double_divide(inverse(v),x))),
inference(rew,[status(thm),theory(equality)],[695,619]),
[iquote('0:Rew:695.0,619.0')] ).
cnf(794,plain,
equal(double_divide(u,double_divide(u,double_divide(inverse(v),inverse(w)))),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[793,500]),
[iquote('0:Rew:793.0,500.0')] ).
cnf(795,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[462,794]),
[iquote('0:Rew:462.0,794.0')] ).
cnf(820,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(double_divide(inverse(v),x),multiply(w,u))),inverse(x)),
inference(rew,[status(thm),theory(equality)],[646,620]),
[iquote('0:Rew:646.0,620.0')] ).
cnf(861,plain,
equal(multiply(u,double_divide(v,multiply(w,multiply(double_divide(x,multiply(double_divide(x,u),w)),y)))),double_divide(v,y)),
inference(rew,[status(thm),theory(equality)],[751,548,460]),
[iquote('0:Rew:751.0,548.0,751.0,548.0,460.0,548.0,460.0,548.0')] ).
cnf(862,plain,
equal(multiply(u,multiply(double_divide(v,u),w)),double_divide(x,double_divide(y,multiply(w,multiply(double_divide(y,v),x))))),
inference(rew,[status(thm),theory(equality)],[470,555]),
[iquote('0:Rew:470.0,555.0')] ).
cnf(867,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(u,w),x))),double_divide(x,double_divide(inverse(v),w))),
inference(rew,[status(thm),theory(equality)],[743,571,470,460]),
[iquote('0:Rew:743.0,571.0,470.0,571.0,460.0,571.0')] ).
cnf(868,plain,
equal(multiply(u,multiply(double_divide(v,u),w)),double_divide(x,double_divide(x,double_divide(inverse(w),v)))),
inference(rew,[status(thm),theory(equality)],[867,862]),
[iquote('0:Rew:867.0,862.0')] ).
cnf(876,plain,
equal(multiply(u,multiply(double_divide(v,u),w)),double_divide(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[462,868]),
[iquote('0:Rew:462.0,868.0')] ).
cnf(879,plain,
equal(double_divide(inverse(u),double_divide(v,w)),double_divide(inverse(w),double_divide(v,u))),
inference(rew,[status(thm),theory(equality)],[876,739]),
[iquote('0:Rew:876.0,739.0')] ).
cnf(880,plain,
equal(double_divide(inverse(inverse(u)),v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[876,633]),
[iquote('0:Rew:876.0,633.0')] ).
cnf(881,plain,
equal(double_divide(u,multiply(double_divide(u,v),w)),double_divide(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[876,706]),
[iquote('0:Rew:876.0,706.0')] ).
cnf(892,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[750,880]),
[iquote('0:Rew:750.0,880.0')] ).
cnf(900,plain,
equal(multiply(u,double_divide(v,multiply(w,multiply(double_divide(inverse(u),w),x)))),double_divide(v,x)),
inference(rew,[status(thm),theory(equality)],[881,861]),
[iquote('0:Rew:881.0,861.0')] ).
cnf(938,plain,
equal(multiply(u,double_divide(v,multiply(u,w))),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[795,900,876]),
[iquote('0:Rew:795.0,900.0,876.0,900.0')] ).
cnf(958,plain,
equal(double_divide(inverse(u),double_divide(inverse(v),w)),double_divide(v,double_divide(w,u))),
inference(rew,[status(thm),theory(equality)],[876,604,470,881]),
[iquote('0:Rew:876.0,604.0,470.0,604.0,881.0,604.0')] ).
cnf(976,plain,
equal(double_divide(inverse(double_divide(inverse(u),v)),w),double_divide(w,double_divide(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[743,513,470,460,881,695]),
[iquote('0:Rew:743.0,513.0,470.0,513.0,460.0,513.0,881.0,513.0,695.0,513.0,460.0,513.0')] ).
cnf(977,plain,
equal(double_divide(multiply(u,inverse(v)),w),double_divide(w,double_divide(inverse(u),v))),
inference(rew,[status(thm),theory(equality)],[2,976]),
[iquote('0:Rew:2.0,976.0')] ).
cnf(978,plain,
equal(double_divide(inverse(u),multiply(v,w)),double_divide(v,double_divide(inverse(w),u))),
inference(rew,[status(thm),theory(equality)],[460,977]),
[iquote('0:Rew:460.0,977.0')] ).
cnf(981,plain,
equal(double_divide(inverse(u),multiply(inverse(v),multiply(u,w))),double_divide(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[876,534,470,646,978,751,460]),
[iquote('0:Rew:876.0,534.0,470.0,534.0,646.0,534.0,978.0,534.0,876.0,534.0,751.0,534.0,460.0,534.0,646.0,534.0')] ).
cnf(1016,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,750]),
[iquote('0:SpR:2.0,750.0')] ).
cnf(1023,plain,
equal(multiply(u,multiply(v,double_divide(u,w))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[1016,701]),
[iquote('0:Rew:1016.0,701.0')] ).
cnf(1026,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[1016,702]),
[iquote('0:Rew:1016.0,702.0')] ).
cnf(1033,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[892,1026]),
[iquote('0:Rew:892.0,1026.0')] ).
cnf(1079,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1033,2]),
[iquote('0:SpR:1033.0,2.0')] ).
cnf(1089,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[751,1079]),
[iquote('0:Rew:751.0,1079.0')] ).
cnf(1100,plain,
equal(double_divide(u,multiply(inverse(v),w)),multiply(v,double_divide(u,w))),
inference(spr,[status(thm),theory(equality)],[938,450]),
[iquote('0:SpR:938.0,450.0')] ).
cnf(1101,plain,
equal(multiply(u,double_divide(v,double_divide(w,x))),double_divide(v,double_divide(w,multiply(u,x)))),
inference(spr,[status(thm),theory(equality)],[938]),
[iquote('0:SpR:938.0,938.0')] ).
cnf(1110,plain,
equal(multiply(u,double_divide(inverse(v),multiply(v,w))),double_divide(inverse(u),w)),
inference(rew,[status(thm),theory(equality)],[1100,981]),
[iquote('0:Rew:1100.0,981.0')] ).
cnf(1112,plain,
equal(multiply(u,double_divide(v,double_divide(inverse(w),v))),double_divide(inverse(u),w)),
inference(rew,[status(thm),theory(equality)],[978,1110]),
[iquote('0:Rew:978.0,1110.0')] ).
cnf(1113,plain,
equal(multiply(u,inverse(v)),double_divide(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[1033,1112]),
[iquote('0:Rew:1033.0,1112.0')] ).
cnf(1114,plain,
~ equal(multiply(a1,inverse(a1)),double_divide(inverse(b1),b1)),
inference(rew,[status(thm),theory(equality)],[1113,768]),
[iquote('0:Rew:1113.0,768.0')] ).
cnf(1124,plain,
~ equal(multiply(a1,inverse(a1)),double_divide(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[892,1114]),
[iquote('0:Rew:892.0,1114.0')] ).
cnf(1125,plain,
~ equal(double_divide(inverse(a1),a1),double_divide(b1,inverse(b1))),
inference(rew,[status(thm),theory(equality)],[1113,1124]),
[iquote('0:Rew:1113.0,1124.0')] ).
cnf(1126,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(rew,[status(thm),theory(equality)],[892,1125]),
[iquote('0:Rew:892.0,1125.0')] ).
cnf(1157,plain,
equal(multiply(u,double_divide(v,inverse(w))),double_divide(v,double_divide(u,w))),
inference(spr,[status(thm),theory(equality)],[753,938]),
[iquote('0:SpR:753.0,938.0')] ).
cnf(1186,plain,
equal(multiply(u,double_divide(v,inverse(w))),double_divide(v,double_divide(w,u))),
inference(spr,[status(thm),theory(equality)],[1089,938]),
[iquote('0:SpR:1089.0,938.0')] ).
cnf(1197,plain,
equal(double_divide(u,double_divide(v,w)),double_divide(u,double_divide(w,v))),
inference(rew,[status(thm),theory(equality)],[1157,1186]),
[iquote('0:Rew:1157.0,1186.0')] ).
cnf(1206,plain,
equal(double_divide(inverse(u),multiply(v,w)),multiply(double_divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[2,795]),
[iquote('0:SpR:2.0,795.0')] ).
cnf(1207,plain,
equal(multiply(inverse(u),v),double_divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[750,795]),
[iquote('0:SpR:750.0,795.0')] ).
cnf(1208,plain,
equal(double_divide(inverse(u),double_divide(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[1016,795]),
[iquote('0:SpR:1016.0,795.0')] ).
cnf(1222,plain,
equal(multiply(u,multiply(v,double_divide(u,w))),double_divide(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[1207,1023]),
[iquote('0:Rew:1207.0,1023.0')] ).
cnf(1246,plain,
equal(double_divide(inverse(u),double_divide(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[646,1208]),
[iquote('0:Rew:646.0,1208.0')] ).
cnf(1247,plain,
equal(multiply(u,multiply(inverse(v),w)),double_divide(v,double_divide(u,w))),
inference(rew,[status(thm),theory(equality)],[1246,958]),
[iquote('0:Rew:1246.0,958.0')] ).
cnf(1249,plain,
equal(double_divide(inverse(u),double_divide(v,w)),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[1246,879]),
[iquote('0:Rew:1246.0,879.0')] ).
cnf(1269,plain,
equal(multiply(u,double_divide(inverse(v),w)),double_divide(w,double_divide(u,v))),
inference(rew,[status(thm),theory(equality)],[1207,1247]),
[iquote('0:Rew:1207.0,1247.0')] ).
cnf(1278,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[1246,1249]),
[iquote('0:Rew:1246.0,1249.0')] ).
cnf(1281,plain,
equal(multiply(multiply(u,v),multiply(double_divide(inverse(w),x),double_divide(v,multiply(w,u)))),inverse(x)),
inference(rew,[status(thm),theory(equality)],[1278,820]),
[iquote('0:Rew:1278.0,820.0')] ).
cnf(1312,plain,
equal(double_divide(u,double_divide(v,multiply(w,double_divide(w,v)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1101,1281,1197,1269,1206,1222,646]),
[iquote('0:Rew:1101.0,1281.0,1197.0,1281.0,1269.0,1281.0,1206.0,1281.0,1222.0,1281.0,646.0,1281.0')] ).
cnf(1313,plain,
equal(double_divide(u,double_divide(v,inverse(v))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[753,1312]),
[iquote('0:Rew:753.0,1312.0')] ).
cnf(1364,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[1313,462]),
[iquote('0:SpR:1313.0,462.0')] ).
cnf(1377,plain,
$false,
inference(unc,[status(thm)],[1364,1126]),
[iquote('0:UnC:1364.0,1126.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 13:06:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.66
% 0.46/0.66 SPASS V 3.9
% 0.46/0.66 SPASS beiseite: Proof found.
% 0.46/0.66 % SZS status Theorem
% 0.46/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.66 SPASS derived 883 clauses, backtracked 0 clauses, performed 0 splits and kept 504 clauses.
% 0.46/0.66 SPASS allocated 65269 KBytes.
% 0.46/0.66 SPASS spent 0:00:00.31 on the problem.
% 0.46/0.66 0:00:00.03 for the input.
% 0.46/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.66 0:00:00.01 for inferences.
% 0.46/0.66 0:00:00.00 for the backtracking.
% 0.46/0.66 0:00:00.25 for the reduction.
% 0.46/0.66
% 0.46/0.66
% 0.46/0.66 Here is a proof with depth 7, length 148 :
% 0.46/0.66 % SZS output start Refutation
% See solution above
% 0.51/0.68 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.51/0.68
%------------------------------------------------------------------------------