TSTP Solution File: GRP002-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:44:41 EDT 2022
% Result : Unsatisfiable 0.55s 0.73s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 6
% Syntax : Number of clauses : 98 ( 98 unt; 0 nHn; 98 RR)
% Number of literals : 98 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(v,multiply(inverse(u),inverse(v)))),commutator(u,v)),
file('GRP002-3.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(u,multiply(u,u)),identity),
file('GRP002-3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(commutator(commutator(a,b),b),identity),
file('GRP002-3.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(identity,u),u),
file('GRP002-3.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP002-3.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP002-3.p',unknown),
[] ).
cnf(17,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(19,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[4,17]),
[iquote('0:Rew:4.0,17.0')] ).
cnf(25,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[19]),
[iquote('0:SpR:19.0,19.0')] ).
cnf(28,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[5,19]),
[iquote('0:SpR:5.0,19.0')] ).
cnf(29,plain,
equal(multiply(inverse(u),identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[2,19]),
[iquote('0:SpR:2.0,19.0')] ).
cnf(31,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[25,28]),
[iquote('0:Rew:25.0,28.0')] ).
cnf(32,plain,
equal(multiply(u,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[31,29]),
[iquote('0:Rew:31.0,29.0')] ).
cnf(33,plain,
equal(multiply(u,inverse(u)),identity),
inference(rew,[status(thm),theory(equality)],[32,2]),
[iquote('0:Rew:32.0,2.0')] ).
cnf(49,plain,
equal(multiply(u,multiply(inverse(u),v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[33,6]),
[iquote('0:SpR:33.0,6.0')] ).
cnf(52,plain,
equal(multiply(u,multiply(v,inverse(multiply(u,v)))),identity),
inference(spr,[status(thm),theory(equality)],[33,6]),
[iquote('0:SpR:33.0,6.0')] ).
cnf(54,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[4,49]),
[iquote('0:Rew:4.0,49.0')] ).
cnf(57,plain,
equal(multiply(u,multiply(multiply(v,multiply(inverse(u),inverse(v))),w)),multiply(commutator(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(59,plain,
equal(multiply(u,multiply(v,multiply(w,multiply(inverse(multiply(u,v)),inverse(w))))),commutator(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(75,plain,
equal(multiply(u,multiply(v,multiply(inverse(u),multiply(inverse(v),w)))),multiply(commutator(u,v),w)),
inference(rew,[status(thm),theory(equality)],[6,57]),
[iquote('0:Rew:6.0,57.0,6.0,57.0')] ).
cnf(97,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[33,54]),
[iquote('0:SpR:33.0,54.0')] ).
cnf(101,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[31,97]),
[iquote('0:Rew:31.0,97.0')] ).
cnf(114,plain,
equal(multiply(inverse(u),multiply(v,multiply(u,inverse(v)))),commutator(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[101,1]),
[iquote('0:SpR:101.0,1.0')] ).
cnf(119,plain,
equal(multiply(u,multiply(inverse(v),multiply(inverse(u),v))),commutator(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[101,1]),
[iquote('0:SpR:101.0,1.0')] ).
cnf(126,plain,
equal(multiply(u,multiply(u,v)),multiply(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(142,plain,
equal(multiply(u,inverse(multiply(v,u))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[52,19]),
[iquote('0:SpR:52.0,19.0')] ).
cnf(167,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[31,142]),
[iquote('0:Rew:31.0,142.0')] ).
cnf(192,plain,
equal(multiply(u,multiply(inverse(v),multiply(inverse(u),multiply(v,w)))),multiply(commutator(u,inverse(v)),w)),
inference(spr,[status(thm),theory(equality)],[101,75]),
[iquote('0:SpR:101.0,75.0')] ).
cnf(238,plain,
equal(multiply(inverse(multiply(u,v)),inverse(inverse(u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[167]),
[iquote('0:SpR:167.0,167.0')] ).
cnf(240,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[167,19]),
[iquote('0:SpR:167.0,19.0')] ).
cnf(244,plain,
equal(multiply(u,multiply(multiply(v,inverse(u)),inverse(v))),commutator(u,multiply(v,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[167,1]),
[iquote('0:SpR:167.0,1.0')] ).
cnf(245,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[167,54]),
[iquote('0:SpR:167.0,54.0')] ).
cnf(261,plain,
equal(multiply(u,multiply(v,inverse(multiply(v,u)))),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[240,1]),
[iquote('0:Rew:240.0,1.0')] ).
cnf(264,plain,
equal(multiply(u,multiply(v,multiply(w,inverse(multiply(w,multiply(u,v)))))),commutator(multiply(u,v),w)),
inference(rew,[status(thm),theory(equality)],[240,59]),
[iquote('0:Rew:240.0,59.0')] ).
cnf(267,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[101,238]),
[iquote('0:Rew:101.0,238.0')] ).
cnf(274,plain,
equal(multiply(u,multiply(v,multiply(inverse(u),inverse(v)))),commutator(u,multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[6,244]),
[iquote('0:Rew:6.0,244.0')] ).
cnf(275,plain,
equal(commutator(u,multiply(v,inverse(u))),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[261,274,240]),
[iquote('0:Rew:261.0,274.0,240.0,274.0')] ).
cnf(293,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[54,267]),
[iquote('0:SpR:54.0,267.0')] ).
cnf(318,plain,
equal(multiply(inverse(u),multiply(inverse(v),w)),multiply(inverse(multiply(v,u)),w)),
inference(spr,[status(thm),theory(equality)],[240,6]),
[iquote('0:SpR:240.0,6.0')] ).
cnf(341,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(v,u)),w))),multiply(commutator(u,v),w)),
inference(rew,[status(thm),theory(equality)],[318,75]),
[iquote('0:Rew:318.0,75.0')] ).
cnf(342,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),multiply(v,w))),multiply(commutator(u,inverse(v)),w)),
inference(rew,[status(thm),theory(equality)],[318,192]),
[iquote('0:Rew:318.0,192.0')] ).
cnf(343,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),v)),commutator(u,inverse(v))),
inference(rew,[status(thm),theory(equality)],[318,119]),
[iquote('0:Rew:318.0,119.0')] ).
cnf(358,plain,
equal(multiply(inverse(u),multiply(v,inverse(w))),inverse(multiply(multiply(w,inverse(v)),u))),
inference(spr,[status(thm),theory(equality)],[245,240]),
[iquote('0:SpR:245.0,240.0')] ).
cnf(371,plain,
equal(inverse(multiply(u,multiply(v,inverse(w)))),multiply(w,inverse(multiply(u,v)))),
inference(spr,[status(thm),theory(equality)],[6,245]),
[iquote('0:SpR:6.0,245.0')] ).
cnf(387,plain,
equal(multiply(inverse(u),multiply(v,inverse(w))),inverse(multiply(w,multiply(inverse(v),u)))),
inference(rew,[status(thm),theory(equality)],[6,358]),
[iquote('0:Rew:6.0,358.0')] ).
cnf(391,plain,
equal(multiply(multiply(u,inverse(multiply(u,v))),multiply(v,inverse(commutator(v,u)))),commutator(multiply(u,inverse(multiply(u,v))),v)),
inference(spr,[status(thm),theory(equality)],[261]),
[iquote('0:SpR:261.0,261.0')] ).
cnf(409,plain,
equal(multiply(multiply(u,v),multiply(inverse(u),inverse(v))),commutator(multiply(u,v),inverse(u))),
inference(spr,[status(thm),theory(equality)],[19,261]),
[iquote('0:SpR:19.0,261.0')] ).
cnf(436,plain,
equal(commutator(multiply(u,v),inverse(u)),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[261,409,6,240]),
[iquote('0:Rew:261.0,409.0,6.0,409.0,240.0,409.0')] ).
cnf(445,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),multiply(v,inverse(commutator(v,u))))),commutator(multiply(u,inverse(multiply(u,v))),v)),
inference(rew,[status(thm),theory(equality)],[6,391]),
[iquote('0:Rew:6.0,391.0')] ).
cnf(446,plain,
equal(multiply(u,inverse(multiply(commutator(v,u),multiply(inverse(v),multiply(u,v))))),commutator(multiply(u,inverse(multiply(u,v))),v)),
inference(rew,[status(thm),theory(equality)],[387,445]),
[iquote('0:Rew:387.0,445.0')] ).
cnf(468,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(u,inverse(v))))),v),inverse(commutator(inverse(v),u))),
inference(spr,[status(thm),theory(equality)],[261,293]),
[iquote('0:SpR:261.0,293.0')] ).
cnf(498,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(u)))),v),inverse(commutator(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[245,468]),
[iquote('0:Rew:245.0,468.0')] ).
cnf(499,plain,
equal(multiply(multiply(u,inverse(multiply(u,v))),v),inverse(commutator(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[371,498]),
[iquote('0:Rew:371.0,498.0')] ).
cnf(500,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),v)),inverse(commutator(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[6,499]),
[iquote('0:Rew:6.0,499.0')] ).
cnf(501,plain,
equal(inverse(commutator(inverse(u),v)),commutator(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[343,500]),
[iquote('0:Rew:343.0,500.0')] ).
cnf(516,plain,
equal(inverse(commutator(u,v)),commutator(v,u)),
inference(spr,[status(thm),theory(equality)],[101,501]),
[iquote('0:SpR:101.0,501.0')] ).
cnf(530,plain,
equal(multiply(commutator(u,v),commutator(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[516,5]),
[iquote('0:SpR:516.0,5.0')] ).
cnf(531,plain,
equal(multiply(commutator(u,v),multiply(commutator(v,u),w)),w),
inference(spr,[status(thm),theory(equality)],[516,19]),
[iquote('0:SpR:516.0,19.0')] ).
cnf(716,plain,
equal(multiply(u,multiply(v,multiply(inverse(inverse(multiply(v,u))),w))),multiply(commutator(u,v),multiply(inverse(multiply(v,u)),w))),
inference(spr,[status(thm),theory(equality)],[126,341]),
[iquote('0:SpR:126.0,341.0')] ).
cnf(762,plain,
equal(multiply(commutator(u,v),multiply(inverse(multiply(v,u)),w)),multiply(u,multiply(inverse(v),multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[126,716,6,101]),
[iquote('0:Rew:126.0,716.0,6.0,716.0,101.0,716.0')] ).
cnf(779,plain,
equal(commutator(multiply(u,v),inverse(u)),commutator(multiply(u,v),v)),
inference(spr,[status(thm),theory(equality)],[167,275]),
[iquote('0:SpR:167.0,275.0')] ).
cnf(794,plain,
equal(commutator(multiply(u,v),v),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[436,779]),
[iquote('0:Rew:436.0,779.0')] ).
cnf(796,plain,
equal(commutator(u,multiply(v,u)),inverse(commutator(v,u))),
inference(spr,[status(thm),theory(equality)],[794,516]),
[iquote('0:SpR:794.0,516.0')] ).
cnf(804,plain,
equal(commutator(inverse(multiply(u,v)),u),commutator(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[267,794]),
[iquote('0:SpR:267.0,794.0')] ).
cnf(814,plain,
equal(commutator(u,multiply(v,u)),commutator(inverse(v),multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[19,794]),
[iquote('0:SpR:19.0,794.0')] ).
cnf(821,plain,
equal(commutator(u,multiply(v,u)),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[516,796]),
[iquote('0:Rew:516.0,796.0')] ).
cnf(826,plain,
equal(commutator(inverse(u),multiply(u,v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[821,814]),
[iquote('0:Rew:821.0,814.0')] ).
cnf(1007,plain,
equal(commutator(multiply(inverse(u),v),inverse(u)),commutator(u,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[126,436]),
[iquote('0:SpR:126.0,436.0')] ).
cnf(1082,plain,
equal(commutator(multiply(u,inverse(multiply(u,v))),v),commutator(inverse(v),commutator(v,u))),
inference(spr,[status(thm),theory(equality)],[261,826]),
[iquote('0:SpR:261.0,826.0')] ).
cnf(1099,plain,
equal(commutator(commutator(u,v),multiply(commutator(v,u),w)),commutator(w,commutator(v,u))),
inference(spr,[status(thm),theory(equality)],[516,826]),
[iquote('0:SpR:516.0,826.0')] ).
cnf(1117,plain,
equal(multiply(u,inverse(multiply(commutator(v,u),multiply(inverse(v),multiply(u,v))))),commutator(inverse(v),commutator(v,u))),
inference(rew,[status(thm),theory(equality)],[1082,446]),
[iquote('0:Rew:1082.0,446.0')] ).
cnf(1174,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),multiply(v,inverse(commutator(v,u))))),commutator(multiply(u,inverse(multiply(u,v))),v)),
inference(spr,[status(thm),theory(equality)],[261,264]),
[iquote('0:SpR:261.0,264.0')] ).
cnf(1238,plain,
equal(multiply(u,multiply(inverse(multiply(u,v)),multiply(v,commutator(u,v)))),commutator(multiply(u,inverse(multiply(u,v))),v)),
inference(rew,[status(thm),theory(equality)],[516,1174]),
[iquote('0:Rew:516.0,1174.0')] ).
cnf(1239,plain,
equal(multiply(commutator(u,inverse(v)),commutator(u,v)),commutator(inverse(v),commutator(v,u))),
inference(rew,[status(thm),theory(equality)],[342,1238,1082]),
[iquote('0:Rew:342.0,1238.0,1082.0,1238.0')] ).
cnf(1556,plain,
equal(multiply(multiply(commutator(u,v),multiply(inverse(u),multiply(v,u))),inverse(v)),inverse(commutator(inverse(u),commutator(u,v)))),
inference(spr,[status(thm),theory(equality)],[1117,245]),
[iquote('0:SpR:1117.0,245.0')] ).
cnf(1577,plain,
equal(multiply(u,inverse(multiply(commutator(multiply(u,v),u),multiply(inverse(multiply(u,v)),multiply(inverse(u),v))))),commutator(inverse(multiply(u,v)),commutator(multiply(u,v),u))),
inference(spr,[status(thm),theory(equality)],[126,1117]),
[iquote('0:SpR:126.0,1117.0')] ).
cnf(1623,plain,
equal(multiply(commutator(u,v),multiply(inverse(u),multiply(v,multiply(u,inverse(v))))),commutator(commutator(u,v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,1556,516]),
[iquote('0:Rew:6.0,1556.0,6.0,1556.0,6.0,1556.0,516.0,1556.0')] ).
cnf(1624,plain,
equal(multiply(commutator(u,v),commutator(inverse(u),v)),commutator(commutator(u,v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[114,1623]),
[iquote('0:Rew:114.0,1623.0')] ).
cnf(1687,plain,
equal(multiply(u,inverse(multiply(multiply(u,v),multiply(inverse(u),multiply(multiply(u,v),v))))),commutator(inverse(multiply(u,v)),commutator(multiply(u,v),u))),
inference(rew,[status(thm),theory(equality)],[762,1577,318]),
[iquote('0:Rew:762.0,1577.0,318.0,1577.0')] ).
cnf(1688,plain,
equal(commutator(inverse(multiply(u,v)),commutator(multiply(u,v),u)),identity),
inference(rew,[status(thm),theory(equality)],[33,1687,31,6,19,32]),
[iquote('0:Rew:33.0,1687.0,31.0,1687.0,33.0,1687.0,6.0,1687.0,19.0,1687.0,32.0,1687.0,6.0,1687.0')] ).
cnf(2098,plain,
equal(commutator(inverse(multiply(commutator(u,v),w)),commutator(v,u)),commutator(inverse(w),commutator(v,u))),
inference(spr,[status(thm),theory(equality)],[531,804]),
[iquote('0:SpR:531.0,804.0')] ).
cnf(2397,plain,
equal(commutator(inverse(u),commutator(u,v)),identity),
inference(spr,[status(thm),theory(equality)],[54,1688]),
[iquote('0:SpR:54.0,1688.0')] ).
cnf(2450,plain,
equal(multiply(commutator(u,inverse(v)),commutator(u,v)),identity),
inference(rew,[status(thm),theory(equality)],[2397,1239]),
[iquote('0:Rew:2397.0,1239.0')] ).
cnf(2500,plain,
equal(multiply(commutator(inverse(u),v),identity),commutator(v,u)),
inference(spr,[status(thm),theory(equality)],[2450,531]),
[iquote('0:SpR:2450.0,531.0')] ).
cnf(2552,plain,
equal(commutator(inverse(u),v),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[31,2500]),
[iquote('0:Rew:31.0,2500.0')] ).
cnf(2557,plain,
equal(commutator(multiply(u,v),u),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[2552,826]),
[iquote('0:Rew:2552.0,826.0')] ).
cnf(2558,plain,
equal(commutator(u,multiply(u,v)),commutator(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[2552,804]),
[iquote('0:Rew:2552.0,804.0')] ).
cnf(2566,plain,
equal(commutator(inverse(multiply(commutator(u,v),w)),commutator(v,u)),commutator(commutator(v,u),w)),
inference(rew,[status(thm),theory(equality)],[2552,2098]),
[iquote('0:Rew:2552.0,2098.0')] ).
cnf(2628,plain,
equal(multiply(commutator(u,v),commutator(v,u)),commutator(commutator(u,v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[2552,1624]),
[iquote('0:Rew:2552.0,1624.0')] ).
cnf(2639,plain,
equal(commutator(u,multiply(u,v)),commutator(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[2557,1007]),
[iquote('0:Rew:2557.0,1007.0')] ).
cnf(2641,plain,
equal(commutator(u,multiply(u,v)),commutator(u,v)),
inference(rew,[status(thm),theory(equality)],[2552,2558]),
[iquote('0:Rew:2552.0,2558.0')] ).
cnf(2647,plain,
equal(commutator(u,inverse(v)),commutator(v,u)),
inference(rew,[status(thm),theory(equality)],[2641,2639]),
[iquote('0:Rew:2641.0,2639.0')] ).
cnf(2761,plain,
equal(commutator(commutator(u,v),inverse(u)),identity),
inference(rew,[status(thm),theory(equality)],[530,2628]),
[iquote('0:Rew:530.0,2628.0')] ).
cnf(2762,plain,
equal(commutator(u,commutator(u,v)),identity),
inference(rew,[status(thm),theory(equality)],[2647,2761]),
[iquote('0:Rew:2647.0,2761.0')] ).
cnf(2800,plain,
equal(commutator(u,commutator(v,w)),commutator(commutator(w,v),u)),
inference(rew,[status(thm),theory(equality)],[1099,2566,2552]),
[iquote('0:Rew:1099.0,2566.0,2552.0,2566.0')] ).
cnf(2801,plain,
~ equal(commutator(b,commutator(b,a)),identity),
inference(rew,[status(thm),theory(equality)],[2800,3]),
[iquote('0:Rew:2800.0,3.0')] ).
cnf(2817,plain,
~ equal(identity,identity),
inference(rew,[status(thm),theory(equality)],[2762,2801]),
[iquote('0:Rew:2762.0,2801.0')] ).
cnf(2818,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2817]),
[iquote('0:Obv:2817.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 00:55:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.73
% 0.55/0.73 SPASS V 3.9
% 0.55/0.73 SPASS beiseite: Proof found.
% 0.55/0.73 % SZS status Theorem
% 0.55/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.73 SPASS derived 1552 clauses, backtracked 0 clauses, performed 0 splits and kept 471 clauses.
% 0.55/0.73 SPASS allocated 67026 KBytes.
% 0.55/0.73 SPASS spent 0:00:00.38 on the problem.
% 0.55/0.73 0:00:00.03 for the input.
% 0.55/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.73 0:00:00.01 for inferences.
% 0.55/0.73 0:00:00.00 for the backtracking.
% 0.55/0.73 0:00:00.31 for the reduction.
% 0.55/0.73
% 0.55/0.73
% 0.55/0.73 Here is a proof with depth 8, length 98 :
% 0.55/0.73 % SZS output start Refutation
% See solution above
% 0.55/0.75 Formulae used in the proof : commutator x_cubed_is_identity prove_commutator left_identity left_inverse associativity
% 0.55/0.75
%------------------------------------------------------------------------------