TSTP Solution File: GRP059-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP059-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:45:05 EDT 2022
% Result : Unsatisfiable 1.72s 1.97s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of clauses : 62 ( 58 unt; 0 nHn; 62 RR)
% Number of literals : 68 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),v),multiply(x,inverse(x)))),w),
file('GRP059-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP059-1.p',unknown),
[] ).
cnf(4,plain,
equal(inverse(multiply(multiply(multiply(u,multiply(inverse(multiply(multiply(v,w),u)),v)),w),multiply(x,inverse(x)))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(10,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(35,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,inverse(u)),v)),w),inverse(w)),multiply(x,inverse(x)))),v),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(37,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),v),w),multiply(x,inverse(x)))),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(68,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w)))),inverse(multiply(inverse(inverse(multiply(x,inverse(x)))),v))),
inference(spr,[status(thm),theory(equality)],[10,37]),
[iquote('0:SpR:10.0,37.0')] ).
cnf(79,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[35,37]),
[iquote('0:SpR:35.0,37.0')] ).
cnf(123,plain,
equal(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[79,10]),
[iquote('0:SpR:79.0,10.0')] ).
cnf(147,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,inverse(u)),v)),multiply(w,inverse(w))),inverse(multiply(x,inverse(x)))),multiply(y,inverse(y)))),v),
inference(spr,[status(thm),theory(equality)],[79,35]),
[iquote('0:SpR:79.0,35.0')] ).
cnf(184,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),inverse(inverse(inverse(multiply(multiply(w,inverse(w)),x))))),multiply(y,inverse(y)))),x),
inference(spr,[status(thm),theory(equality)],[123,35]),
[iquote('0:SpR:123.0,35.0')] ).
cnf(185,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),multiply(x,inverse(x)))),inverse(multiply(inverse(inverse(multiply(y,inverse(y)))),w))),
inference(spr,[status(thm),theory(equality)],[123,37]),
[iquote('0:SpR:123.0,37.0')] ).
cnf(204,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),multiply(inverse(multiply(v,inverse(v))),w)),inverse(w)),multiply(x,inverse(x)))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[123,4]),
[iquote('0:SpR:123.0,4.0')] ).
cnf(236,plain,
equal(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),multiply(w,inverse(w))),
inference(rew,[status(thm),theory(equality)],[37,204]),
[iquote('0:Rew:37.0,204.0')] ).
cnf(242,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),multiply(x,inverse(x)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[236,1]),
[iquote('0:SpR:236.0,1.0')] ).
cnf(315,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(u,inverse(u)),v))))),v),
inference(rew,[status(thm),theory(equality)],[242,184]),
[iquote('0:Rew:242.0,184.0')] ).
cnf(316,plain,
equal(inverse(multiply(inverse(inverse(multiply(u,inverse(u)))),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[242,185]),
[iquote('0:Rew:242.0,185.0')] ).
cnf(318,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w)))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[316,68]),
[iquote('0:Rew:316.0,68.0')] ).
cnf(412,plain,
equal(multiply(u,inverse(u)),multiply(inverse(inverse(inverse(multiply(multiply(v,inverse(v)),w)))),w)),
inference(spr,[status(thm),theory(equality)],[315,10]),
[iquote('0:SpR:315.0,10.0')] ).
cnf(421,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(u,inverse(u)),v)))),v),w))))),w),
inference(spr,[status(thm),theory(equality)],[315]),
[iquote('0:SpR:315.0,315.0')] ).
cnf(433,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w))))),w),
inference(spr,[status(thm),theory(equality)],[79,315]),
[iquote('0:SpR:79.0,315.0')] ).
cnf(438,plain,
equal(inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),w))))),w),
inference(spr,[status(thm),theory(equality)],[236,315]),
[iquote('0:SpR:236.0,315.0')] ).
cnf(460,plain,
equal(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u))))))),v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[316]),
[iquote('0:SpR:316.0,316.0')] ).
cnf(983,plain,
equal(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u))))))),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[318,315]),
[iquote('0:SpR:318.0,315.0')] ).
cnf(1034,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[123,318]),
[iquote('0:SpR:123.0,318.0')] ).
cnf(1250,plain,
equal(inverse(multiply(multiply(u,inverse(u)),v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[983,460]),
[iquote('0:SpR:983.0,460.0')] ).
cnf(1362,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),v),inverse(v)),multiply(w,inverse(w)))),u),
inference(rew,[status(thm),theory(equality)],[1250,35]),
[iquote('0:Rew:1250.0,35.0')] ).
cnf(1363,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[1250,315]),
[iquote('0:Rew:1250.0,315.0')] ).
cnf(1423,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),multiply(v,inverse(v))),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x)))),u),
inference(rew,[status(thm),theory(equality)],[1250,147]),
[iquote('0:Rew:1250.0,147.0')] ).
cnf(1428,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(u))),u),v))))),v),
inference(rew,[status(thm),theory(equality)],[1250,421]),
[iquote('0:Rew:1250.0,421.0')] ).
cnf(1474,plain,
equal(multiply(u,inverse(u)),multiply(inverse(inverse(inverse(v))),v)),
inference(rew,[status(thm),theory(equality)],[1250,412]),
[iquote('0:Rew:1250.0,412.0')] ).
cnf(1566,plain,
equal(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),w),w),
inference(rew,[status(thm),theory(equality)],[1363,438]),
[iquote('0:Rew:1363.0,438.0')] ).
cnf(1570,plain,
equal(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),w),
inference(rew,[status(thm),theory(equality)],[1363,433]),
[iquote('0:Rew:1363.0,433.0')] ).
cnf(1643,plain,
equal(multiply(multiply(inverse(inverse(inverse(u))),u),v),v),
inference(rew,[status(thm),theory(equality)],[1363,1428]),
[iquote('0:Rew:1363.0,1428.0')] ).
cnf(1654,plain,
equal(inverse(multiply(u,multiply(v,inverse(v)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1570,242]),
[iquote('0:Rew:1570.0,242.0')] ).
cnf(1658,plain,
equal(inverse(multiply(multiply(u,multiply(inverse(multiply(multiply(v,w),u)),v)),w)),multiply(x,inverse(x))),
inference(rew,[status(thm),theory(equality)],[1654,4]),
[iquote('0:Rew:1654.0,4.0')] ).
cnf(1660,plain,
equal(inverse(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),v)),w),
inference(rew,[status(thm),theory(equality)],[1654,1]),
[iquote('0:Rew:1654.0,1.0')] ).
cnf(1823,plain,
equal(inverse(multiply(multiply(inverse(u),v),inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[1654,1362]),
[iquote('0:Rew:1654.0,1362.0')] ).
cnf(1869,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[1823,1566]),
[iquote('0:Rew:1823.0,1566.0')] ).
cnf(1885,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(w,inverse(w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1869,1034]),
[iquote('0:Rew:1869.0,1034.0')] ).
cnf(2017,plain,
equal(inverse(multiply(u,inverse(multiply(v,inverse(v))))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1869,1885]),
[iquote('0:Rew:1869.0,1885.0')] ).
cnf(2168,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[1654,1423,2017]),
[iquote('0:Rew:1654.0,1423.0,2017.0,1423.0,1654.0,1423.0')] ).
cnf(2171,plain,
equal(multiply(u,inverse(u)),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[2168,1474]),
[iquote('0:Rew:2168.0,1474.0')] ).
cnf(2178,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[2168,1643]),
[iquote('0:Rew:2168.0,1643.0')] ).
cnf(2201,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[2178,2]),
[iquote('0:Rew:2178.0,2.2')] ).
cnf(2414,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[2201]),
[iquote('0:Obv:2201.2')] ).
cnf(2677,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(multiply(v,w),u))),v)),w),
inference(spr,[status(thm),theory(equality)],[1660]),
[iquote('0:SpR:1660.0,1660.0')] ).
cnf(2824,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[2171]),
[iquote('0:SpR:2171.0,2171.0')] ).
cnf(2985,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(v,u))),multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[1869,2677]),
[iquote('0:SpR:1869.0,2677.0')] ).
cnf(3008,plain,
equal(inverse(multiply(u,inverse(multiply(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[1654,2985]),
[iquote('0:Rew:1654.0,2985.0')] ).
cnf(3049,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3008,2168]),
[iquote('0:SpR:3008.0,2168.0')] ).
cnf(3067,plain,
equal(inverse(inverse(multiply(u,multiply(v,inverse(v))))),u),
inference(spr,[status(thm),theory(equality)],[1869,3008]),
[iquote('0:SpR:1869.0,3008.0')] ).
cnf(3078,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[2168,3067]),
[iquote('0:Rew:2168.0,3067.0')] ).
cnf(3301,plain,
equal(inverse(multiply(multiply(u,multiply(multiply(v,inverse(v)),w)),multiply(inverse(multiply(multiply(x,u),w)),x))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1658]),
[iquote('0:SpR:1658.0,1658.0')] ).
cnf(3456,plain,
equal(inverse(multiply(multiply(u,v),multiply(inverse(multiply(multiply(w,u),v)),w))),multiply(x,inverse(x))),
inference(rew,[status(thm),theory(equality)],[1869,3301]),
[iquote('0:Rew:1869.0,3301.0')] ).
cnf(3768,plain,
equal(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),multiply(x,inverse(x))),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[3456,3049]),
[iquote('0:SpR:3456.0,3049.0')] ).
cnf(3868,plain,
equal(multiply(inverse(multiply(multiply(u,v),w)),u),inverse(multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[3078,3768]),
[iquote('0:Rew:3078.0,3768.0')] ).
cnf(4525,plain,
equal(multiply(u,inverse(inverse(multiply(v,w)))),inverse(inverse(multiply(multiply(u,v),w)))),
inference(spr,[status(thm),theory(equality)],[3868,3049]),
[iquote('0:SpR:3868.0,3049.0')] ).
cnf(4601,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2168,4525]),
[iquote('0:Rew:2168.0,4525.0,2168.0,4525.0')] ).
cnf(4602,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[4601,2414]),
[iquote('0:Rew:4601.0,2414.1')] ).
cnf(4706,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[4602]),
[iquote('0:Obv:4602.1')] ).
cnf(4707,plain,
$false,
inference(unc,[status(thm)],[4706,2824]),
[iquote('0:UnC:4706.0,2824.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP059-1 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 12:09:07 EDT 2022
% 0.20/0.35 % CPUTime :
% 1.72/1.97
% 1.72/1.97 SPASS V 3.9
% 1.72/1.97 SPASS beiseite: Proof found.
% 1.72/1.97 % SZS status Theorem
% 1.72/1.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.72/1.97 SPASS derived 3110 clauses, backtracked 0 clauses, performed 0 splits and kept 914 clauses.
% 1.72/1.97 SPASS allocated 69827 KBytes.
% 1.72/1.97 SPASS spent 0:00:01.61 on the problem.
% 1.72/1.97 0:00:00.03 for the input.
% 1.72/1.97 0:00:00.00 for the FLOTTER CNF translation.
% 1.72/1.97 0:00:00.03 for inferences.
% 1.72/1.97 0:00:00.00 for the backtracking.
% 1.72/1.97 0:00:01.53 for the reduction.
% 1.72/1.97
% 1.72/1.97
% 1.72/1.97 Here is a proof with depth 11, length 62 :
% 1.72/1.97 % SZS output start Refutation
% See solution above
% 1.78/2.01 Formulae used in the proof : single_axiom prove_these_axioms
% 1.78/2.01
%------------------------------------------------------------------------------