TSTP Solution File: GRP501-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP501-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:47:46 EDT 2022
% Result : Unsatisfiable 4.08s 4.29s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 3
% Syntax : Number of clauses : 108 ( 108 unt; 0 nHn; 108 RR)
% Number of literals : 108 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(inverse(u),inverse(double_divide(inverse(double_divide(u,double_divide(v,w))),double_divide(x,double_divide(v,x))))),w),
file('GRP501-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP501-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP501-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,v)),multiply(double_divide(w,x),u))),x),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),inverse(x)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(inverse(w),v)),multiply(x,u))),multiply(double_divide(y,double_divide(z,y)),multiply(double_divide(z,x),w))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(10,plain,
equal(double_divide(multiply(u,v),multiply(double_divide(w,double_divide(x,w)),multiply(double_divide(x,y),double_divide(v,u)))),y),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(12,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),double_divide(x,y))),multiply(y,x)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(80,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,double_divide(inverse(w),x)),w)),x),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(85,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),multiply(double_divide(y,double_divide(z,y)),multiply(double_divide(z,w),x))),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(89,plain,
equal(double_divide(inverse(multiply(double_divide(u,v),w)),multiply(double_divide(x,double_divide(y,x)),double_divide(inverse(z),multiply(double_divide(x1,double_divide(inverse(w),x1)),multiply(v,z))))),double_divide(u,y)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(90,plain,
equal(double_divide(inverse(multiply(double_divide(u,v),w)),multiply(double_divide(x,double_divide(inverse(y),x)),double_divide(inverse(z),multiply(double_divide(x1,double_divide(inverse(w),x1)),multiply(v,z))))),multiply(double_divide(x2,double_divide(x3,x2)),multiply(double_divide(x3,double_divide(x4,double_divide(u,x4))),y))),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(91,plain,
equal(double_divide(inverse(u),double_divide(inverse(v),multiply(double_divide(w,double_divide(inverse(u),w)),multiply(x,v)))),x),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(94,plain,
equal(multiply(double_divide(inverse(u),multiply(double_divide(v,double_divide(inverse(w),v)),multiply(x,u))),inverse(w)),inverse(x)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(95,plain,
equal(double_divide(multiply(u,v),double_divide(inverse(w),multiply(double_divide(x,double_divide(inverse(double_divide(v,u)),x)),multiply(y,w)))),y),
inference(spr,[status(thm),theory(equality)],[7,10]),
[iquote('0:SpR:7.0,10.0')] ).
cnf(116,plain,
equal(double_divide(multiply(u,v),double_divide(inverse(w),multiply(double_divide(x,double_divide(multiply(u,v),x)),multiply(y,w)))),y),
inference(rew,[status(thm),theory(equality)],[2,95]),
[iquote('0:Rew:2.0,95.0')] ).
cnf(120,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,double_divide(w,double_divide(x,w))),y)),double_divide(x,inverse(y))),
inference(rew,[status(thm),theory(equality)],[89,90]),
[iquote('0:Rew:89.0,90.0')] ).
cnf(121,plain,
equal(double_divide(inverse(multiply(double_divide(u,double_divide(inverse(v),w)),v)),multiply(double_divide(x,double_divide(y,x)),w)),double_divide(u,y)),
inference(spr,[status(thm),theory(equality)],[80,4]),
[iquote('0:SpR:80.0,4.0')] ).
cnf(171,plain,
equal(double_divide(inverse(u),double_divide(inverse(multiply(double_divide(v,double_divide(inverse(w),x)),w)),multiply(double_divide(y,double_divide(inverse(u),y)),x))),double_divide(z,double_divide(v,z))),
inference(spr,[status(thm),theory(equality)],[80,91]),
[iquote('0:SpR:80.0,91.0')] ).
cnf(186,plain,
equal(double_divide(inverse(u),double_divide(v,inverse(u))),double_divide(w,double_divide(v,w))),
inference(rew,[status(thm),theory(equality)],[121,171]),
[iquote('0:Rew:121.0,171.0')] ).
cnf(219,plain,
equal(double_divide(u,double_divide(v,u)),double_divide(w,double_divide(v,w))),
inference(spr,[status(thm),theory(equality)],[186]),
[iquote('0:SpR:186.0,186.0')] ).
cnf(271,plain,
equal(inverse(double_divide(u,double_divide(v,u))),multiply(double_divide(v,w),w)),
inference(spr,[status(thm),theory(equality)],[219,2]),
[iquote('0:SpR:219.0,2.0')] ).
cnf(286,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(w,double_divide(inverse(x),w)),x)),v),
inference(spr,[status(thm),theory(equality)],[219,80]),
[iquote('0:SpR:219.0,80.0')] ).
cnf(289,plain,
equal(double_divide(u,double_divide(v,u)),double_divide(double_divide(w,v),double_divide(x,double_divide(w,x)))),
inference(spr,[status(thm),theory(equality)],[219]),
[iquote('0:SpR:219.0,219.0')] ).
cnf(349,plain,
equal(multiply(double_divide(u,v),v),multiply(double_divide(u,w),w)),
inference(rew,[status(thm),theory(equality)],[2,271]),
[iquote('0:Rew:2.0,271.0')] ).
cnf(355,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,v)),multiply(double_divide(w,x),x))),u),
inference(spr,[status(thm),theory(equality)],[349,4]),
[iquote('0:SpR:349.0,4.0')] ).
cnf(383,plain,
equal(multiply(double_divide(u,double_divide(v,u)),double_divide(v,w)),multiply(double_divide(w,x),x)),
inference(spr,[status(thm),theory(equality)],[219,349]),
[iquote('0:SpR:219.0,349.0')] ).
cnf(461,plain,
equal(multiply(double_divide(u,double_divide(double_divide(v,w),u)),multiply(double_divide(x,double_divide(w,x)),y)),double_divide(v,inverse(y))),
inference(spr,[status(thm),theory(equality)],[289,80]),
[iquote('0:SpR:289.0,80.0')] ).
cnf(532,plain,
equal(multiply(double_divide(inverse(multiply(u,v)),multiply(double_divide(w,double_divide(inverse(x),w)),inverse(y))),inverse(x)),inverse(multiply(double_divide(z,double_divide(x1,z)),multiply(double_divide(x1,y),double_divide(v,u))))),
inference(spr,[status(thm),theory(equality)],[12,94]),
[iquote('0:SpR:12.0,94.0')] ).
cnf(715,plain,
equal(double_divide(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),w)),x),double_divide(y,double_divide(inverse(x),y))),
inference(spr,[status(thm),theory(equality)],[355,219]),
[iquote('0:SpR:355.0,219.0')] ).
cnf(744,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(double_divide(w,x),v)),multiply(double_divide(y,double_divide(x,y)),double_divide(z,double_divide(w,z))))),u),
inference(spr,[status(thm),theory(equality)],[289,355]),
[iquote('0:SpR:289.0,355.0')] ).
cnf(764,plain,
equal(double_divide(inverse(u),double_divide(v,inverse(double_divide(w,double_divide(v,w))))),u),
inference(rew,[status(thm),theory(equality)],[461,744]),
[iquote('0:Rew:461.0,744.0')] ).
cnf(765,plain,
equal(double_divide(inverse(u),double_divide(v,multiply(double_divide(v,w),w))),u),
inference(rew,[status(thm),theory(equality)],[2,764]),
[iquote('0:Rew:2.0,764.0')] ).
cnf(769,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),v)),inverse(w)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[765,2]),
[iquote('0:SpR:765.0,2.0')] ).
cnf(770,plain,
equal(multiply(u,double_divide(v,multiply(double_divide(v,w),w))),multiply(double_divide(inverse(u),x),x)),
inference(spr,[status(thm),theory(equality)],[765,349]),
[iquote('0:SpR:765.0,349.0')] ).
cnf(784,plain,
equal(double_divide(u,double_divide(inverse(v),u)),double_divide(double_divide(w,multiply(double_divide(w,x),x)),v)),
inference(spr,[status(thm),theory(equality)],[765,219]),
[iquote('0:SpR:765.0,219.0')] ).
cnf(821,plain,
equal(double_divide(multiply(u,v),double_divide(w,multiply(double_divide(w,x),x))),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,765]),
[iquote('0:SpR:2.0,765.0')] ).
cnf(870,plain,
equal(double_divide(u,double_divide(inverse(v),multiply(double_divide(w,double_divide(u,w)),multiply(x,v)))),x),
inference(spr,[status(thm),theory(equality)],[80,116]),
[iquote('0:SpR:80.0,116.0')] ).
cnf(924,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),v)),multiply(w,x)),multiply(w,x)),
inference(spr,[status(thm),theory(equality)],[2,769]),
[iquote('0:SpR:2.0,769.0')] ).
cnf(943,plain,
equal(multiply(double_divide(u,v),double_divide(w,multiply(double_divide(w,x),x))),multiply(double_divide(multiply(v,u),y),y)),
inference(spr,[status(thm),theory(equality)],[821,349]),
[iquote('0:SpR:821.0,349.0')] ).
cnf(1054,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),v)),w),w),
inference(spr,[status(thm),theory(equality)],[80,924]),
[iquote('0:SpR:80.0,924.0')] ).
cnf(1086,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,v)),u)),multiply(double_divide(w,x),x)),
inference(spr,[status(thm),theory(equality)],[1054,4]),
[iquote('0:SpR:1054.0,4.0')] ).
cnf(1107,plain,
equal(multiply(double_divide(u,multiply(double_divide(v,double_divide(w,v)),double_divide(w,u))),x),x),
inference(spr,[status(thm),theory(equality)],[219,1054]),
[iquote('0:SpR:219.0,1054.0')] ).
cnf(1169,plain,
equal(multiply(double_divide(u,double_divide(double_divide(v,w),u)),multiply(double_divide(x,y),y)),double_divide(v,inverse(double_divide(w,x)))),
inference(spr,[status(thm),theory(equality)],[383,120]),
[iquote('0:SpR:383.0,120.0')] ).
cnf(1193,plain,
equal(multiply(double_divide(u,double_divide(double_divide(v,w),u)),multiply(double_divide(x,y),y)),double_divide(v,multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[2,1169]),
[iquote('0:Rew:2.0,1169.0')] ).
cnf(1778,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,double_divide(w,x)),y)),multiply(double_divide(z,double_divide(x,z)),multiply(double_divide(x1,double_divide(w,x1)),y))),
inference(spr,[status(thm),theory(equality)],[219,85]),
[iquote('0:SpR:219.0,85.0')] ).
cnf(2082,plain,
equal(double_divide(inverse(double_divide(u,v)),multiply(double_divide(v,w),w)),multiply(double_divide(u,x),x)),
inference(spr,[status(thm),theory(equality)],[349,1086]),
[iquote('0:SpR:349.0,1086.0')] ).
cnf(2104,plain,
equal(double_divide(multiply(u,v),multiply(double_divide(u,w),w)),multiply(double_divide(v,x),x)),
inference(rew,[status(thm),theory(equality)],[2,2082]),
[iquote('0:Rew:2.0,2082.0')] ).
cnf(2115,plain,
equal(inverse(multiply(double_divide(u,v),v)),multiply(multiply(double_divide(w,x),x),multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[2104,2]),
[iquote('0:SpR:2104.0,2.0')] ).
cnf(2175,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,u),multiply(double_divide(v,w),w))),x),x),
inference(spr,[status(thm),theory(equality)],[2104,1107]),
[iquote('0:SpR:2104.0,1107.0')] ).
cnf(2288,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,multiply(double_divide(v,w),w)),u)),x),x),
inference(spr,[status(thm),theory(equality)],[2175,1107]),
[iquote('0:SpR:2175.0,1107.0')] ).
cnf(2604,plain,
equal(multiply(double_divide(double_divide(inverse(u),multiply(double_divide(v,double_divide(multiply(w,multiply(double_divide(w,x),x)),v)),multiply(y,u))),y),z),z),
inference(spr,[status(thm),theory(equality)],[870,2288]),
[iquote('0:SpR:870.0,2288.0')] ).
cnf(2613,plain,
equal(multiply(double_divide(double_divide(inverse(u),multiply(v,u)),v),w),w),
inference(rew,[status(thm),theory(equality)],[2288,2604]),
[iquote('0:Rew:2288.0,2604.0')] ).
cnf(2643,plain,
equal(multiply(double_divide(double_divide(inverse(u),multiply(v,u)),w),w),v),
inference(spr,[status(thm),theory(equality)],[2613,349]),
[iquote('0:SpR:2613.0,349.0')] ).
cnf(2681,plain,
equal(multiply(double_divide(u,double_divide(inverse(double_divide(inverse(v),v)),u)),w),w),
inference(spr,[status(thm),theory(equality)],[784,2613]),
[iquote('0:SpR:784.0,2613.0')] ).
cnf(2682,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,inverse(v)),u)),w),w),
inference(rew,[status(thm),theory(equality)],[2,2681]),
[iquote('0:Rew:2.0,2681.0')] ).
cnf(2736,plain,
equal(multiply(double_divide(double_divide(inverse(u),multiply(v,double_divide(w,multiply(double_divide(w,x),x)))),y),y),double_divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[770,2643]),
[iquote('0:SpR:770.0,2643.0')] ).
cnf(2753,plain,
equal(multiply(double_divide(multiply(double_divide(u,v),v),w),w),double_divide(x,double_divide(u,x))),
inference(spr,[status(thm),theory(equality)],[355,2643]),
[iquote('0:SpR:355.0,2643.0')] ).
cnf(2809,plain,
equal(multiply(double_divide(u,v),v),double_divide(multiply(w,inverse(w)),u)),
inference(spr,[status(thm),theory(equality)],[2682,349]),
[iquote('0:SpR:2682.0,349.0')] ).
cnf(3103,plain,
equal(inverse(multiply(double_divide(u,v),v)),multiply(u,multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[2809,2]),
[iquote('0:SpR:2809.0,2.0')] ).
cnf(3149,plain,
equal(multiply(double_divide(u,double_divide(multiply(v,inverse(v)),u)),multiply(multiply(double_divide(double_divide(inverse(w),x),y),y),w)),x),
inference(spr,[status(thm),theory(equality)],[2809,80]),
[iquote('0:SpR:2809.0,80.0')] ).
cnf(3175,plain,
equal(multiply(double_divide(multiply(double_divide(u,v),v),w),w),multiply(double_divide(inverse(u),x),x)),
inference(spr,[status(thm),theory(equality)],[2809,2104]),
[iquote('0:SpR:2809.0,2104.0')] ).
cnf(3189,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),multiply(double_divide(y,double_divide(multiply(z,inverse(z)),y)),multiply(multiply(double_divide(w,x1),x1),x))),
inference(spr,[status(thm),theory(equality)],[2809,85]),
[iquote('0:SpR:2809.0,85.0')] ).
cnf(3195,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(multiply(double_divide(double_divide(inverse(w),multiply(x,inverse(x))),y),y),w)),v),
inference(spr,[status(thm),theory(equality)],[2809,286]),
[iquote('0:SpR:2809.0,286.0')] ).
cnf(3225,plain,
equal(multiply(double_divide(u,v),v),double_divide(inverse(double_divide(w,multiply(double_divide(w,x),x))),u)),
inference(spr,[status(thm),theory(equality)],[1054,2809]),
[iquote('0:SpR:1054.0,2809.0')] ).
cnf(3231,plain,
equal(multiply(double_divide(u,v),v),double_divide(multiply(multiply(double_divide(w,x),x),w),u)),
inference(rew,[status(thm),theory(equality)],[2,3225]),
[iquote('0:Rew:2.0,3225.0')] ).
cnf(3249,plain,
equal(multiply(multiply(double_divide(double_divide(inverse(u),v),w),w),u),v),
inference(rew,[status(thm),theory(equality)],[2682,3149]),
[iquote('0:Rew:2682.0,3149.0')] ).
cnf(3250,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(w,inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[3249,3195]),
[iquote('0:Rew:3249.0,3195.0')] ).
cnf(3270,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),multiply(multiply(double_divide(w,y),y),x)),
inference(rew,[status(thm),theory(equality)],[2682,3189]),
[iquote('0:Rew:2682.0,3189.0')] ).
cnf(3338,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),double_divide(inverse(inverse(w)),inverse(x))),
inference(spr,[status(thm),theory(equality)],[3250,7]),
[iquote('0:SpR:3250.0,7.0')] ).
cnf(3344,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),inverse(double_divide(x,w)))),x),
inference(spr,[status(thm),theory(equality)],[3250,85]),
[iquote('0:SpR:3250.0,85.0')] ).
cnf(3351,plain,
equal(double_divide(u,double_divide(inverse(inverse(v)),u)),v),
inference(spr,[status(thm),theory(equality)],[3250,870]),
[iquote('0:SpR:3250.0,870.0')] ).
cnf(3410,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),multiply(w,x))),x),
inference(rew,[status(thm),theory(equality)],[2,3344]),
[iquote('0:Rew:2.0,3344.0')] ).
cnf(3484,plain,
equal(double_divide(inverse(inverse(u)),inverse(multiply(u,v))),v),
inference(rew,[status(thm),theory(equality)],[3338,3410]),
[iquote('0:Rew:3338.0,3410.0')] ).
cnf(3533,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(w,double_divide(x,w)),y)),double_divide(inverse(inverse(double_divide(x,v))),inverse(y))),
inference(rew,[status(thm),theory(equality)],[3338,1778]),
[iquote('0:Rew:3338.0,1778.0')] ).
cnf(3546,plain,
equal(double_divide(double_divide(inverse(inverse(u)),inverse(u)),v),double_divide(w,double_divide(inverse(v),w))),
inference(rew,[status(thm),theory(equality)],[3338,715]),
[iquote('0:Rew:3338.0,715.0')] ).
cnf(3683,plain,
equal(multiply(double_divide(inverse(multiply(u,v)),multiply(double_divide(w,double_divide(inverse(x),w)),inverse(y))),inverse(x)),inverse(double_divide(inverse(inverse(y)),inverse(double_divide(v,u))))),
inference(rew,[status(thm),theory(equality)],[3338,532]),
[iquote('0:Rew:3338.0,532.0')] ).
cnf(3870,plain,
equal(multiply(multiply(double_divide(u,v),v),w),double_divide(inverse(inverse(u)),inverse(w))),
inference(rew,[status(thm),theory(equality)],[3338,3270]),
[iquote('0:Rew:3338.0,3270.0')] ).
cnf(4027,plain,
equal(multiply(double_divide(u,v),v),double_divide(double_divide(inverse(inverse(w)),inverse(w)),u)),
inference(rew,[status(thm),theory(equality)],[3870,3231]),
[iquote('0:Rew:3870.0,3231.0')] ).
cnf(4061,plain,
equal(inverse(multiply(double_divide(u,v),v)),double_divide(inverse(inverse(w)),inverse(multiply(w,u)))),
inference(rew,[status(thm),theory(equality)],[3870,2115]),
[iquote('0:Rew:3870.0,2115.0')] ).
cnf(4138,plain,
equal(inverse(multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[3484,4061]),
[iquote('0:Rew:3484.0,4061.0')] ).
cnf(4146,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[4138,3103]),
[iquote('0:Rew:4138.0,3103.0')] ).
cnf(4148,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[4146,3250]),
[iquote('0:Rew:4146.0,3250.0')] ).
cnf(4163,plain,
equal(multiply(u,double_divide(u,v)),multiply(double_divide(v,w),w)),
inference(rew,[status(thm),theory(equality)],[4148,383]),
[iquote('0:Rew:4148.0,383.0')] ).
cnf(4166,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[4148,3351]),
[iquote('0:Rew:4148.0,3351.0')] ).
cnf(4228,plain,
equal(multiply(double_divide(u,v),multiply(double_divide(w,x),x)),double_divide(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[4148,1193]),
[iquote('0:Rew:4148.0,1193.0')] ).
cnf(4426,plain,
equal(double_divide(double_divide(inverse(inverse(u)),inverse(u)),v),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4148,3546]),
[iquote('0:Rew:4148.0,3546.0')] ).
cnf(4555,plain,
equal(multiply(double_divide(multiply(double_divide(u,v),v),w),w),u),
inference(rew,[status(thm),theory(equality)],[4148,2753]),
[iquote('0:Rew:4148.0,2753.0')] ).
cnf(4830,plain,
equal(multiply(double_divide(u,v),v),double_divide(double_divide(w,inverse(w)),u)),
inference(rew,[status(thm),theory(equality)],[4166,4027]),
[iquote('0:Rew:4166.0,4027.0')] ).
cnf(4851,plain,
equal(double_divide(double_divide(u,inverse(u)),v),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4166,4426]),
[iquote('0:Rew:4166.0,4426.0')] ).
cnf(4855,plain,
equal(multiply(double_divide(inverse(u),v),v),u),
inference(rew,[status(thm),theory(equality)],[4555,3175]),
[iquote('0:Rew:4555.0,3175.0')] ).
cnf(4861,plain,
equal(multiply(u,double_divide(v,multiply(double_divide(v,w),w))),u),
inference(rew,[status(thm),theory(equality)],[4855,770]),
[iquote('0:Rew:4855.0,770.0')] ).
cnf(4879,plain,
equal(multiply(double_divide(multiply(u,v),w),w),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[4861,943]),
[iquote('0:Rew:4861.0,943.0')] ).
cnf(4885,plain,
equal(multiply(double_divide(double_divide(inverse(u),v),w),w),double_divide(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[4861,2736]),
[iquote('0:Rew:4861.0,2736.0')] ).
cnf(4966,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4851,4830]),
[iquote('0:Rew:4851.0,4830.0')] ).
cnf(4981,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[4966,4879]),
[iquote('0:Rew:4966.0,4879.0')] ).
cnf(5006,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4966,4163]),
[iquote('0:Rew:4966.0,4163.0')] ).
cnf(5163,plain,
equal(inverse(double_divide(inverse(u),v)),double_divide(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[4966,4885]),
[iquote('0:Rew:4966.0,4885.0')] ).
cnf(5164,plain,
equal(multiply(u,inverse(v)),double_divide(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[2,5163]),
[iquote('0:Rew:2.0,5163.0')] ).
cnf(5238,plain,
equal(double_divide(inverse(double_divide(u,v)),w),double_divide(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[5164,4228,4966]),
[iquote('0:Rew:5164.0,4228.0,4966.0,4228.0')] ).
cnf(5239,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[2,5238]),
[iquote('0:Rew:2.0,5238.0')] ).
cnf(6193,plain,
equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(w,double_divide(x,w)),y)),double_divide(inverse(multiply(v,x)),inverse(y))),
inference(rew,[status(thm),theory(equality)],[2,3533]),
[iquote('0:Rew:2.0,3533.0')] ).
cnf(6194,plain,
equal(double_divide(double_divide(u,v),inverse(w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[4148,6193,4981]),
[iquote('0:Rew:4148.0,6193.0,4148.0,6193.0,4981.0,6193.0')] ).
cnf(6869,plain,
equal(multiply(double_divide(inverse(multiply(u,v)),multiply(double_divide(w,double_divide(inverse(x),w)),inverse(y))),inverse(x)),multiply(multiply(u,v),inverse(inverse(y)))),
inference(rew,[status(thm),theory(equality)],[2,3683]),
[iquote('0:Rew:2.0,3683.0,2.0,3683.0')] ).
cnf(6870,plain,
equal(double_divide(inverse(double_divide(double_divide(u,v),double_divide(w,x))),w),multiply(multiply(v,u),x)),
inference(rew,[status(thm),theory(equality)],[5164,6869,4981,4166,4148]),
[iquote('0:Rew:5164.0,6869.0,4981.0,6869.0,4166.0,6869.0,5164.0,6869.0,4148.0,6869.0,4166.0,6869.0')] ).
cnf(6871,plain,
equal(double_divide(multiply(double_divide(u,v),double_divide(w,x)),u),multiply(multiply(x,w),v)),
inference(rew,[status(thm),theory(equality)],[2,6870]),
[iquote('0:Rew:2.0,6870.0')] ).
cnf(6872,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6194,6871,5006,5239]),
[iquote('0:Rew:6194.0,6871.0,5006.0,6871.0,5239.0,6871.0')] ).
cnf(6873,plain,
$false,
inference(unc,[status(thm)],[6872,3]),
[iquote('0:UnC:6872.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP501-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 00:11:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.08/4.29
% 4.08/4.29 SPASS V 3.9
% 4.08/4.29 SPASS beiseite: Proof found.
% 4.08/4.29 % SZS status Theorem
% 4.08/4.29 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/4.29 SPASS derived 4698 clauses, backtracked 0 clauses, performed 0 splits and kept 1937 clauses.
% 4.08/4.29 SPASS allocated 76396 KBytes.
% 4.08/4.29 SPASS spent 0:00:03.94 on the problem.
% 4.08/4.29 0:00:00.03 for the input.
% 4.08/4.29 0:00:00.00 for the FLOTTER CNF translation.
% 4.08/4.29 0:00:00.04 for inferences.
% 4.08/4.29 0:00:00.00 for the backtracking.
% 4.08/4.29 0:00:03.85 for the reduction.
% 4.08/4.29
% 4.08/4.29
% 4.08/4.29 Here is a proof with depth 19, length 108 :
% 4.08/4.29 % SZS output start Refutation
% See solution above
% 4.15/4.36 Formulae used in the proof : single_axiom multiply prove_these_axioms_3
% 4.15/4.36
%------------------------------------------------------------------------------