TSTP Solution File: GRP080-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP080-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:45:12 EDT 2022
% Result : Unsatisfiable 0.17s 0.45s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of clauses : 81 ( 75 unt; 0 nHn; 81 RR)
% Number of literals : 91 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(identity,double_divide(u,double_divide(v,identity))),double_divide(double_divide(v,double_divide(w,u)),identity)),w),
file('GRP080-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP080-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP080-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP080-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP080-1.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(identity,double_divide(u,inverse(v))),multiply(double_divide(w,u),v)),w),
inference(rew,[status(thm),theory(equality)],[3,1,6]),
[iquote('0:Rew:3.0,1.0,6.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(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:12.0,5.1')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ 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(18,plain,
equal(multiply(multiply(double_divide(u,v),w),double_divide(identity,double_divide(v,inverse(w)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(21,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),inverse(v))),multiply(identity,v)),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(24,plain,
equal(double_divide(double_divide(identity,identity),multiply(double_divide(u,v),v)),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(25,plain,
equal(double_divide(inverse(identity),multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,24]),
[iquote('0:Rew:3.0,24.0')] ).
cnf(26,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),inverse(v))),inverse(inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[13,21]),
[iquote('0:Rew:13.0,21.0')] ).
cnf(31,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(39,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[31,15]),
[iquote('0:Rew:31.0,15.1')] ).
cnf(41,plain,
equal(double_divide(identity,multiply(double_divide(u,v),v)),u),
inference(rew,[status(thm),theory(equality)],[31,25]),
[iquote('0:Rew:31.0,25.0')] ).
cnf(52,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[39]),
[iquote('0:Obv:39.1')] ).
cnf(87,plain,
equal(double_divide(identity,multiply(identity,inverse(u))),u),
inference(spr,[status(thm),theory(equality)],[4,41]),
[iquote('0:SpR:4.0,41.0')] ).
cnf(88,plain,
equal(double_divide(identity,multiply(inverse(u),identity)),u),
inference(spr,[status(thm),theory(equality)],[3,41]),
[iquote('0:SpR:3.0,41.0')] ).
cnf(90,plain,
equal(double_divide(identity,multiply(identity,multiply(u,v))),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[10,41]),
[iquote('0:SpR:10.0,41.0')] ).
cnf(91,plain,
equal(double_divide(identity,inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[13,87]),
[iquote('0:Rew:13.0,87.0')] ).
cnf(94,plain,
equal(double_divide(identity,inverse(inverse(multiply(u,v)))),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[13,90]),
[iquote('0:Rew:13.0,90.0')] ).
cnf(125,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,double_divide(identity,double_divide(inverse(u),inverse(w)))),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[26,7]),
[iquote('0:SpR:26.0,7.0')] ).
cnf(126,plain,
equal(multiply(inverse(inverse(u)),double_divide(identity,double_divide(inverse(v),inverse(u)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[26,6]),
[iquote('0:SpR:26.0,6.0')] ).
cnf(128,plain,
equal(double_divide(identity,double_divide(inverse(u),inverse(v))),double_divide(identity,multiply(u,inverse(inverse(v))))),
inference(spr,[status(thm),theory(equality)],[26,41]),
[iquote('0:SpR:26.0,41.0')] ).
cnf(133,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(137,plain,
equal(double_divide(double_divide(identity,double_divide(identity,inverse(u))),inverse(inverse(u))),identity),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(140,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[6,133,3,31]),
[iquote('0:Rew:6.0,133.0,3.0,133.0,3.0,133.0,31.0,133.0')] ).
cnf(144,plain,
equal(multiply(inverse(inverse(u)),double_divide(identity,multiply(v,inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[128,126]),
[iquote('0:Rew:128.0,126.0')] ).
cnf(147,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,double_divide(identity,multiply(u,inverse(inverse(w))))),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[128,125]),
[iquote('0:Rew:128.0,125.0')] ).
cnf(150,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),u),identity),
inference(spr,[status(thm),theory(equality)],[140,10]),
[iquote('0:SpR:140.0,10.0')] ).
cnf(152,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[140,88]),
[iquote('0:SpR:140.0,88.0')] ).
cnf(158,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[152,91]),
[iquote('0:Rew:152.0,91.0')] ).
cnf(159,plain,
equal(double_divide(inverse(double_divide(u,inverse(v))),multiply(double_divide(w,u),v)),w),
inference(rew,[status(thm),theory(equality)],[152,7]),
[iquote('0:Rew:152.0,7.0')] ).
cnf(162,plain,
equal(double_divide(identity,multiply(u,inverse(inverse(v)))),inverse(double_divide(inverse(u),inverse(v)))),
inference(rew,[status(thm),theory(equality)],[152,128]),
[iquote('0:Rew:152.0,128.0')] ).
cnf(166,plain,
equal(multiply(multiply(double_divide(u,v),w),inverse(double_divide(v,inverse(w)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[152,18]),
[iquote('0:Rew:152.0,18.0')] ).
cnf(169,plain,
equal(double_divide(inverse(double_divide(identity,inverse(u))),inverse(inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[152,137]),
[iquote('0:Rew:152.0,137.0')] ).
cnf(170,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[152,94]),
[iquote('0:Rew:152.0,94.0')] ).
cnf(173,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,inverse(multiply(u,inverse(inverse(w))))),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[152,147]),
[iquote('0:Rew:152.0,147.0')] ).
cnf(174,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[152,144]),
[iquote('0:Rew:152.0,144.0')] ).
cnf(180,plain,
equal(double_divide(inverse(inverse(inverse(u))),u),identity),
inference(rew,[status(thm),theory(equality)],[152,150]),
[iquote('0:Rew:152.0,150.0')] ).
cnf(183,plain,
equal(double_divide(multiply(inverse(u),identity),inverse(inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[6,169]),
[iquote('0:Rew:6.0,169.0')] ).
cnf(185,plain,
equal(double_divide(multiply(inverse(u),v),multiply(double_divide(w,v),u)),w),
inference(rew,[status(thm),theory(equality)],[6,159]),
[iquote('0:Rew:6.0,159.0')] ).
cnf(187,plain,
equal(double_divide(identity,multiply(u,inverse(inverse(v)))),multiply(inverse(v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,162]),
[iquote('0:Rew:6.0,162.0')] ).
cnf(188,plain,
equal(inverse(multiply(u,inverse(inverse(v)))),multiply(inverse(v),inverse(u))),
inference(rew,[status(thm),theory(equality)],[152,187]),
[iquote('0:Rew:152.0,187.0')] ).
cnf(189,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[188,174]),
[iquote('0:Rew:188.0,174.0')] ).
cnf(192,plain,
equal(multiply(multiply(double_divide(u,v),w),multiply(inverse(w),v)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[6,166]),
[iquote('0:Rew:6.0,166.0')] ).
cnf(197,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,multiply(inverse(w),inverse(u))),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[152,173,188]),
[iquote('0:Rew:152.0,173.0,188.0,173.0')] ).
cnf(204,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[152,6]),
[iquote('0:SpR:152.0,6.0')] ).
cnf(218,plain,
equal(double_divide(inverse(inverse(inverse(u))),inverse(inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[204,183]),
[iquote('0:Rew:204.0,183.0')] ).
cnf(273,plain,
equal(double_divide(multiply(inverse(u),v),multiply(identity,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[180,185]),
[iquote('0:SpR:180.0,185.0')] ).
cnf(286,plain,
equal(double_divide(multiply(inverse(u),v),inverse(inverse(u))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[13,273]),
[iquote('0:Rew:13.0,273.0')] ).
cnf(336,plain,
equal(double_divide(multiply(inverse(u),inverse(inverse(v))),multiply(identity,u)),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[218,185]),
[iquote('0:SpR:218.0,185.0')] ).
cnf(341,plain,
equal(double_divide(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[158,218]),
[iquote('0:SpR:158.0,218.0')] ).
cnf(353,plain,
equal(double_divide(multiply(inverse(u),inverse(inverse(v))),inverse(inverse(u))),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[13,336]),
[iquote('0:Rew:13.0,336.0')] ).
cnf(354,plain,
equal(inverse(inverse(inverse(inverse(inverse(u))))),inverse(inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[286,353]),
[iquote('0:Rew:286.0,353.0')] ).
cnf(355,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[158,354]),
[iquote('0:Rew:158.0,354.0')] ).
cnf(356,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[355,158]),
[iquote('0:Rew:355.0,158.0')] ).
cnf(360,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[355,170]),
[iquote('0:Rew:355.0,170.0')] ).
cnf(366,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[356,52]),
[iquote('0:Rew:356.0,52.0')] ).
cnf(367,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[356,13]),
[iquote('0:Rew:356.0,13.0')] ).
cnf(369,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[356,188]),
[iquote('0:Rew:356.0,188.0')] ).
cnf(374,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[356,189]),
[iquote('0:Rew:356.0,189.0')] ).
cnf(379,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(u,v)),
inference(rew,[status(thm),theory(equality)],[360,369]),
[iquote('0:Rew:360.0,369.0')] ).
cnf(380,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,u)),inverse(w))),v),
inference(rew,[status(thm),theory(equality)],[379,197]),
[iquote('0:Rew:379.0,197.0')] ).
cnf(381,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[379,374]),
[iquote('0:Rew:379.0,374.0')] ).
cnf(387,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[366]),
[iquote('0:Obv:366.0')] ).
cnf(514,plain,
equal(multiply(multiply(identity,u),multiply(inverse(u),v)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[341,192]),
[iquote('0:SpR:341.0,192.0')] ).
cnf(528,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[367,514,356]),
[iquote('0:Rew:367.0,514.0,356.0,514.0')] ).
cnf(590,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[381,528]),
[iquote('0:SpR:381.0,528.0')] ).
cnf(597,plain,
equal(multiply(u,inverse(multiply(double_divide(v,double_divide(w,u)),inverse(w)))),v),
inference(rew,[status(thm),theory(equality)],[590,380]),
[iquote('0:Rew:590.0,380.0')] ).
cnf(601,plain,
equal(multiply(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),w),
inference(rew,[status(thm),theory(equality)],[360,597]),
[iquote('0:Rew:360.0,597.0')] ).
cnf(602,plain,
equal(multiply(u,multiply(v,inverse(double_divide(w,double_divide(v,u))))),w),
inference(rew,[status(thm),theory(equality)],[590,601]),
[iquote('0:Rew:590.0,601.0')] ).
cnf(603,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,602]),
[iquote('0:Rew:6.0,602.0')] ).
cnf(1098,plain,
equal(multiply(inverse(double_divide(u,v)),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[528,603]),
[iquote('0:SpR:528.0,603.0')] ).
cnf(1115,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1098]),
[iquote('0:Rew:6.0,1098.0')] ).
cnf(1116,plain,
$false,
inference(unc,[status(thm)],[1115,387]),
[iquote('0:UnC:1115.0,387.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP080-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n020.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jun 13 11:59:05 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.45
% 0.17/0.45 SPASS V 3.9
% 0.17/0.45 SPASS beiseite: Proof found.
% 0.17/0.45 % SZS status Theorem
% 0.17/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 SPASS derived 675 clauses, backtracked 0 clauses, performed 0 splits and kept 166 clauses.
% 0.17/0.45 SPASS allocated 64046 KBytes.
% 0.17/0.45 SPASS spent 0:00:00.12 on the problem.
% 0.17/0.45 0:00:00.04 for the input.
% 0.17/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.45 0:00:00.01 for inferences.
% 0.17/0.45 0:00:00.00 for the backtracking.
% 0.17/0.45 0:00:00.06 for the reduction.
% 0.17/0.45
% 0.17/0.45
% 0.17/0.45 Here is a proof with depth 6, length 81 :
% 0.17/0.45 % SZS output start Refutation
% See solution above
% 0.17/0.46 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.17/0.46
%------------------------------------------------------------------------------