TSTP Solution File: GRP103-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP103-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:45:19 EDT 2022
% Result : Unsatisfiable 0.39s 0.55s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of clauses : 125 ( 116 unt; 0 nHn; 125 RR)
% Number of literals : 144 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(identity,identity)),w),
file('GRP103-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP103-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP103-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP103-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP103-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.2')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(21,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,u),double_divide(v,identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(22,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),double_divide(v,inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(23,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,double_divide(inverse(identity),u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(25,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,21]),
[iquote('0:Rew:3.0,21.0')] ).
cnf(66,plain,
equal(double_divide(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,25]),
[iquote('0:SpR:4.0,25.0')] ).
cnf(67,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(inverse(identity),inverse(u))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[3,25]),
[iquote('0:SpR:3.0,25.0')] ).
cnf(68,plain,
equal(double_divide(double_divide(inverse(u),identity),inverse(identity)),double_divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,25]),
[iquote('0:SpR:4.0,25.0')] ).
cnf(69,plain,
equal(double_divide(double_divide(inverse(double_divide(double_divide(identity,u),double_divide(v,double_divide(u,identity)))),v),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[7,25]),
[iquote('0:SpR:7.0,25.0')] ).
cnf(71,plain,
equal(double_divide(inverse(inverse(u)),inverse(identity)),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[3,68]),
[iquote('0:Rew:3.0,68.0')] ).
cnf(74,plain,
equal(double_divide(double_divide(multiply(double_divide(u,inverse(v)),double_divide(identity,v)),u),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,69,3]),
[iquote('0:Rew:6.0,69.0,3.0,69.0')] ).
cnf(75,plain,
equal(multiply(inverse(identity),inverse(inverse(u))),inverse(double_divide(identity,u))),
inference(spr,[status(thm),theory(equality)],[71,6]),
[iquote('0:SpR:71.0,6.0')] ).
cnf(80,plain,
equal(double_divide(inverse(multiply(u,v)),inverse(identity)),double_divide(identity,double_divide(v,u))),
inference(spr,[status(thm),theory(equality)],[6,71]),
[iquote('0:SpR:6.0,71.0')] ).
cnf(81,plain,
equal(multiply(inverse(identity),inverse(inverse(u))),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[6,75]),
[iquote('0:Rew:6.0,75.0')] ).
cnf(87,plain,
equal(multiply(inverse(identity),inverse(multiply(u,v))),multiply(double_divide(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,81]),
[iquote('0:SpR:6.0,81.0')] ).
cnf(102,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),double_divide(v,u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[67,7]),
[iquote('0:SpR:67.0,7.0')] ).
cnf(118,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,22]),
[iquote('0:SpR:4.0,22.0')] ).
cnf(119,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(double_divide(identity,double_divide(double_divide(identity,identity),w)),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[7,22]),
[iquote('0:SpR:7.0,22.0')] ).
cnf(120,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),u)),inverse(identity)),double_divide(inverse(v),double_divide(double_divide(identity,v),inverse(u)))),
inference(spr,[status(thm),theory(equality)],[25,22]),
[iquote('0:SpR:25.0,22.0')] ).
cnf(121,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),u)),inverse(identity)),double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[66,22]),
[iquote('0:SpR:66.0,22.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),u)),inverse(identity)),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(spr,[status(thm),theory(equality)],[67,22]),
[iquote('0:SpR:67.0,22.0')] ).
cnf(123,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,u))),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[71,22]),
[iquote('0:SpR:71.0,22.0')] ).
cnf(126,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[6,118,3]),
[iquote('0:Rew:6.0,118.0,3.0,118.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),double_divide(identity,u))),inverse(identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,123]),
[iquote('0:Rew:3.0,123.0')] ).
cnf(131,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[3,121]),
[iquote('0:Rew:3.0,121.0')] ).
cnf(132,plain,
equal(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(double_divide(identity,u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[131,128]),
[iquote('0:Rew:131.0,128.0')] ).
cnf(135,plain,
equal(double_divide(inverse(inverse(identity)),double_divide(identity,multiply(u,identity))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,132]),
[iquote('0:Rew:6.0,132.0')] ).
cnf(136,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[3,122]),
[iquote('0:Rew:3.0,122.0')] ).
cnf(137,plain,
equal(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u))),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[131,136]),
[iquote('0:Rew:131.0,136.0')] ).
cnf(141,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[137,131]),
[iquote('0:Rew:137.0,131.0')] ).
cnf(142,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(v),double_divide(double_divide(identity,v),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[3,120]),
[iquote('0:Rew:3.0,120.0')] ).
cnf(143,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),double_divide(inverse(identity),double_divide(inverse(identity),inverse(v)))),
inference(rew,[status(thm),theory(equality)],[141,142]),
[iquote('0:Rew:141.0,142.0')] ).
cnf(151,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(double_divide(identity,double_divide(inverse(identity),w)),inverse(identity))),
inference(rew,[status(thm),theory(equality)],[3,119]),
[iquote('0:Rew:3.0,119.0')] ).
cnf(152,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(inverse(identity),double_divide(inverse(identity),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[141,151]),
[iquote('0:Rew:141.0,151.0')] ).
cnf(161,plain,
equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,126]),
[iquote('0:SpR:12.0,126.0')] ).
cnf(163,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,161]),
[iquote('0:Rew:4.0,161.0,4.0,161.0')] ).
cnf(166,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[163,15]),
[iquote('0:Rew:163.0,15.2')] ).
cnf(167,plain,
equal(double_divide(inverse(inverse(u)),identity),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[163,71]),
[iquote('0:Rew:163.0,71.0')] ).
cnf(170,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),identity),u),
inference(rew,[status(thm),theory(equality)],[163,126]),
[iquote('0:Rew:163.0,126.0')] ).
cnf(171,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,double_divide(identity,u)))),identity),v),
inference(rew,[status(thm),theory(equality)],[163,23]),
[iquote('0:Rew:163.0,23.0')] ).
cnf(175,plain,
equal(double_divide(double_divide(multiply(double_divide(u,inverse(v)),double_divide(identity,v)),u),identity),identity),
inference(rew,[status(thm),theory(equality)],[163,74]),
[iquote('0:Rew:163.0,74.0')] ).
cnf(176,plain,
equal(double_divide(inverse(multiply(u,v)),identity),double_divide(identity,double_divide(v,u))),
inference(rew,[status(thm),theory(equality)],[163,80]),
[iquote('0:Rew:163.0,80.0')] ).
cnf(178,plain,
equal(multiply(identity,inverse(multiply(u,v))),multiply(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[163,87]),
[iquote('0:Rew:163.0,87.0')] ).
cnf(179,plain,
equal(double_divide(inverse(identity),double_divide(identity,multiply(u,identity))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[163,135]),
[iquote('0:Rew:163.0,135.0')] ).
cnf(184,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),double_divide(v,u))),identity),v),
inference(rew,[status(thm),theory(equality)],[163,102]),
[iquote('0:Rew:163.0,102.0')] ).
cnf(188,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),identity),double_divide(identity,double_divide(identity,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[163,141]),
[iquote('0:Rew:163.0,141.0')] ).
cnf(189,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),double_divide(identity,double_divide(identity,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[163,143]),
[iquote('0:Rew:163.0,143.0')] ).
cnf(191,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(identity,double_divide(identity,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[163,152]),
[iquote('0:Rew:163.0,152.0')] ).
cnf(192,plain,
equal(inverse(inverse(inverse(u))),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[3,167]),
[iquote('0:Rew:3.0,167.0')] ).
cnf(195,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[6,170,3]),
[iquote('0:Rew:6.0,170.0,3.0,170.0')] ).
cnf(210,plain,
equal(double_divide(identity,double_divide(u,v)),inverse(inverse(multiply(v,u)))),
inference(rew,[status(thm),theory(equality)],[3,176]),
[iquote('0:Rew:3.0,176.0')] ).
cnf(212,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),multiply(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[13,178]),
[iquote('0:Rew:13.0,178.0')] ).
cnf(213,plain,
equal(double_divide(identity,multiply(u,v)),multiply(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[192,212]),
[iquote('0:Rew:192.0,212.0')] ).
cnf(214,plain,
equal(multiply(inverse(inverse(multiply(u,identity))),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[210,179,213,163]),
[iquote('0:Rew:210.0,179.0,213.0,179.0,163.0,179.0,213.0,179.0')] ).
cnf(222,plain,
equal(multiply(double_divide(identity,double_divide(u,double_divide(identity,v))),v),u),
inference(rew,[status(thm),theory(equality)],[6,171,3]),
[iquote('0:Rew:6.0,171.0,3.0,171.0')] ).
cnf(223,plain,
equal(multiply(inverse(inverse(multiply(double_divide(identity,u),v))),u),v),
inference(rew,[status(thm),theory(equality)],[210,222]),
[iquote('0:Rew:210.0,222.0')] ).
cnf(228,plain,
equal(multiply(u,multiply(double_divide(u,inverse(v)),double_divide(identity,v))),identity),
inference(rew,[status(thm),theory(equality)],[6,175,3]),
[iquote('0:Rew:6.0,175.0,3.0,175.0')] ).
cnf(232,plain,
equal(double_divide(identity,double_divide(identity,inverse(u))),multiply(double_divide(identity,u),identity)),
inference(rew,[status(thm),theory(equality)],[6,188,3]),
[iquote('0:Rew:6.0,188.0,3.0,188.0')] ).
cnf(233,plain,
equal(inverse(inverse(multiply(inverse(u),identity))),multiply(double_divide(identity,u),identity)),
inference(rew,[status(thm),theory(equality)],[210,232]),
[iquote('0:Rew:210.0,232.0')] ).
cnf(238,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),multiply(double_divide(identity,v),identity)),
inference(rew,[status(thm),theory(equality)],[233,189,210]),
[iquote('0:Rew:233.0,189.0,210.0,189.0')] ).
cnf(243,plain,
equal(multiply(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),double_divide(v,u)),identity),v),
inference(rew,[status(thm),theory(equality)],[6,184,3]),
[iquote('0:Rew:6.0,184.0,3.0,184.0')] ).
cnf(244,plain,
equal(multiply(double_divide(inverse(inverse(u)),double_divide(v,u)),identity),v),
inference(rew,[status(thm),theory(equality)],[214,243,210,213,233]),
[iquote('0:Rew:214.0,243.0,210.0,243.0,213.0,243.0,233.0,243.0,210.0,243.0')] ).
cnf(245,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),multiply(double_divide(identity,w),identity)),
inference(rew,[status(thm),theory(equality)],[233,191,210]),
[iquote('0:Rew:233.0,191.0,210.0,191.0')] ).
cnf(246,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[166]),
[iquote('0:Obv:166.2')] ).
cnf(265,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(inverse(double_divide(identity,u)))),
inference(spr,[status(thm),theory(equality)],[192]),
[iquote('0:SpR:192.0,192.0')] ).
cnf(267,plain,
equal(double_divide(identity,inverse(u)),inverse(double_divide(identity,u))),
inference(spr,[status(thm),theory(equality)],[192]),
[iquote('0:SpR:192.0,192.0')] ).
cnf(272,plain,
equal(double_divide(identity,inverse(u)),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[6,267]),
[iquote('0:Rew:6.0,267.0')] ).
cnf(275,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(multiply(u,identity))),
inference(rew,[status(thm),theory(equality)],[6,265]),
[iquote('0:Rew:6.0,265.0')] ).
cnf(276,plain,
equal(multiply(inverse(u),identity),inverse(multiply(u,identity))),
inference(rew,[status(thm),theory(equality)],[272,275]),
[iquote('0:Rew:272.0,275.0')] ).
cnf(363,plain,
equal(inverse(multiply(double_divide(u,v),identity)),multiply(multiply(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,276]),
[iquote('0:SpR:6.0,276.0')] ).
cnf(429,plain,
equal(multiply(u,multiply(identity,double_divide(identity,u))),identity),
inference(spr,[status(thm),theory(equality)],[4,228]),
[iquote('0:SpR:4.0,228.0')] ).
cnf(432,plain,
equal(multiply(u,inverse(multiply(u,identity))),identity),
inference(rew,[status(thm),theory(equality)],[6,429,13]),
[iquote('0:Rew:6.0,429.0,13.0,429.0')] ).
cnf(446,plain,
equal(inverse(multiply(double_divide(identity,u),identity)),multiply(inverse(inverse(identity)),u)),
inference(spr,[status(thm),theory(equality)],[432,223]),
[iquote('0:SpR:432.0,223.0')] ).
cnf(459,plain,
equal(inverse(multiply(double_divide(identity,u),identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,446,163]),
[iquote('0:Rew:13.0,446.0,163.0,446.0,163.0,446.0')] ).
cnf(460,plain,
equal(multiply(multiply(u,identity),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[363,459]),
[iquote('0:Rew:363.0,459.0')] ).
cnf(461,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[195,460]),
[iquote('0:Rew:195.0,460.0')] ).
cnf(462,plain,
equal(multiply(multiply(double_divide(identity,u),v),u),v),
inference(rew,[status(thm),theory(equality)],[461,223]),
[iquote('0:Rew:461.0,223.0')] ).
cnf(463,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[461,192]),
[iquote('0:Rew:461.0,192.0')] ).
cnf(464,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[461,246]),
[iquote('0:Rew:461.0,246.0')] ).
cnf(477,plain,
equal(multiply(double_divide(u,double_divide(v,u)),identity),v),
inference(rew,[status(thm),theory(equality)],[461,244]),
[iquote('0:Rew:461.0,244.0')] ).
cnf(480,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[463,272]),
[iquote('0:Rew:463.0,272.0')] ).
cnf(483,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),multiply(inverse(w),identity)),
inference(rew,[status(thm),theory(equality)],[463,245]),
[iquote('0:Rew:463.0,245.0')] ).
cnf(484,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),multiply(inverse(v),identity)),
inference(rew,[status(thm),theory(equality)],[463,238]),
[iquote('0:Rew:463.0,238.0')] ).
cnf(486,plain,
equal(multiply(double_divide(u,v),identity),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[463,213]),
[iquote('0:Rew:463.0,213.0')] ).
cnf(491,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[461,480]),
[iquote('0:Rew:461.0,480.0')] ).
cnf(501,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[463,462]),
[iquote('0:Rew:463.0,462.0')] ).
cnf(503,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[491,477]),
[iquote('0:Rew:491.0,477.0')] ).
cnf(505,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[491,486]),
[iquote('0:Rew:491.0,486.0')] ).
cnf(517,plain,
equal(double_divide(inverse(u),double_divide(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[463,484,491]),
[iquote('0:Rew:463.0,484.0,491.0,484.0')] ).
cnf(518,plain,
equal(double_divide(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[463,483,491]),
[iquote('0:Rew:463.0,483.0,491.0,483.0')] ).
cnf(519,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[464]),
[iquote('0:Obv:464.0')] ).
cnf(571,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[503]),
[iquote('0:SpR:503.0,503.0')] ).
cnf(589,plain,
equal(multiply(multiply(multiply(u,v),w),double_divide(v,u)),w),
inference(spr,[status(thm),theory(equality)],[6,501]),
[iquote('0:SpR:6.0,501.0')] ).
cnf(599,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[571,6]),
[iquote('0:SpR:571.0,6.0')] ).
cnf(680,plain,
equal(double_divide(inverse(u),inverse(v)),double_divide(inverse(v),inverse(u))),
inference(spr,[status(thm),theory(equality)],[517,571]),
[iquote('0:SpR:517.0,571.0')] ).
cnf(713,plain,
equal(double_divide(inverse(u),v),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[599,501]),
[iquote('0:SpR:599.0,501.0')] ).
cnf(726,plain,
equal(double_divide(u,multiply(inverse(double_divide(v,double_divide(w,u))),w)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[713,518]),
[iquote('0:Rew:713.0,518.0')] ).
cnf(727,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(inverse(inverse(u)),v)),
inference(rew,[status(thm),theory(equality)],[713,680]),
[iquote('0:Rew:713.0,680.0')] ).
cnf(740,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[461,727]),
[iquote('0:Rew:461.0,727.0')] ).
cnf(741,plain,
equal(multiply(inverse(inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[713,740]),
[iquote('0:Rew:713.0,740.0')] ).
cnf(742,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[461,741]),
[iquote('0:Rew:461.0,741.0')] ).
cnf(744,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[742,519]),
[iquote('0:Rew:742.0,519.1')] ).
cnf(753,plain,
equal(multiply(double_divide(u,v),multiply(multiply(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[742,589]),
[iquote('0:Rew:742.0,589.0')] ).
cnf(756,plain,
equal(double_divide(u,multiply(multiply(double_divide(v,u),w),v)),inverse(w)),
inference(rew,[status(thm),theory(equality)],[6,726]),
[iquote('0:Rew:6.0,726.0')] ).
cnf(757,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(v,u),w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[742,756]),
[iquote('0:Rew:742.0,756.0')] ).
cnf(760,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[742,744]),
[iquote('0:Rew:742.0,744.0')] ).
cnf(761,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[760]),
[iquote('0:Obv:760.0')] ).
cnf(1211,plain,
equal(inverse(multiply(multiply(u,v),w)),double_divide(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[753,757]),
[iquote('0:SpR:753.0,757.0')] ).
cnf(1230,plain,
equal(double_divide(u,multiply(v,w)),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[505,1211]),
[iquote('0:Rew:505.0,1211.0')] ).
cnf(1467,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1230,6]),
[iquote('0:SpR:1230.0,6.0')] ).
cnf(1538,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(w,u),v)),
inference(rew,[status(thm),theory(equality)],[6,1467]),
[iquote('0:Rew:6.0,1467.0')] ).
cnf(2030,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1538,742]),
[iquote('0:SpR:1538.0,742.0')] ).
cnf(2045,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[1538]),
[iquote('0:SpR:1538.0,1538.0')] ).
cnf(2158,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[2030,2045]),
[iquote('0:Rew:2030.0,2045.0,2030.0,2045.0')] ).
cnf(2159,plain,
$false,
inference(unc,[status(thm)],[2158,761]),
[iquote('0:UnC:2158.0,761.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP103-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n025.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 12:14:54 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.39/0.55
% 0.39/0.55 SPASS V 3.9
% 0.39/0.55 SPASS beiseite: Proof found.
% 0.39/0.55 % SZS status Theorem
% 0.39/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.55 SPASS derived 1211 clauses, backtracked 0 clauses, performed 0 splits and kept 260 clauses.
% 0.39/0.55 SPASS allocated 65007 KBytes.
% 0.39/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.39/0.55 0:00:00.03 for the input.
% 0.39/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.55 0:00:00.01 for inferences.
% 0.39/0.55 0:00:00.00 for the backtracking.
% 0.39/0.55 0:00:00.14 for the reduction.
% 0.39/0.55
% 0.39/0.55
% 0.39/0.55 Here is a proof with depth 6, length 125 :
% 0.39/0.55 % SZS output start Refutation
% See solution above
% 0.39/0.56 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.39/0.56
%------------------------------------------------------------------------------