TSTP Solution File: GRP087-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:45:14 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of clauses : 22 ( 15 unt; 0 nHn; 22 RR)
% Number of literals : 37 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(multiply(inverse(multiply(u,v)),w),v)),w),
file('GRP087-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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('GRP087-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,multiply(multiply(inverse(v),w),multiply(multiply(inverse(multiply(u,x)),v),x))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(multiply(inverse(multiply(inverse(multiply(u,v)),w)),x),w),multiply(u,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(15,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(22,plain,
equal(multiply(multiply(inverse(multiply(inverse(u),v)),w),v),multiply(w,u)),
inference(spr,[status(thm),theory(equality)],[1,15]),
[iquote('0:SpR:1.0,15.0')] ).
cnf(23,plain,
equal(multiply(multiply(inverse(u),v),multiply(multiply(inverse(multiply(inverse(w),x)),u),x)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[3,15]),
[iquote('0:SpR:3.0,15.0')] ).
cnf(26,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[22,4]),
[iquote('0:Rew:22.0,4.0')] ).
cnf(28,plain,
equal(multiply(u,multiply(multiply(inverse(u),v),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[26,23,22]),
[iquote('0:Rew:26.0,23.0,22.0,23.0')] ).
cnf(70,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[15,28]),
[iquote('0:SpR:15.0,28.0')] ).
cnf(72,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
inference(rew,[status(thm),theory(equality)],[70,2]),
[iquote('0:Rew:70.0,2.2')] ).
cnf(73,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[70,15]),
[iquote('0:Rew:70.0,15.0')] ).
cnf(104,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
inference(rew,[status(thm),theory(equality)],[26,72]),
[iquote('0:Rew:26.0,72.2')] ).
cnf(105,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(a2,multiply(b2,inverse(b2))),a2) ),
inference(rew,[status(thm),theory(equality)],[70,104]),
[iquote('0:Rew:70.0,104.3,70.0,104.3,70.0,104.2,70.0,104.1,70.0,104.1,70.0,104.0')] ).
cnf(106,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(a2,multiply(b2,inverse(b2))),a2) ),
inference(obv,[status(thm),theory(equality)],[105]),
[iquote('0:Obv:105.2')] ).
cnf(107,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(multiply(b2,multiply(a2,inverse(b2))),a2) ),
inference(rew,[status(thm),theory(equality)],[26,106]),
[iquote('0:Rew:26.0,106.1')] ).
cnf(130,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[70,73]),
[iquote('0:SpR:70.0,73.0')] ).
cnf(133,plain,
( ~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[130,107]),
[iquote('0:Rew:130.0,107.1')] ).
cnf(135,plain,
~ equal(multiply(b1,inverse(b1)),multiply(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[133]),
[iquote('0:Obv:133.1')] ).
cnf(136,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[130,26]),
[iquote('0:SpR:130.0,26.0')] ).
cnf(154,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[136,73]),
[iquote('0:SpR:136.0,73.0')] ).
cnf(159,plain,
$false,
inference(unc,[status(thm)],[154,135]),
[iquote('0:UnC:154.0,135.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 08:06:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 124 clauses, backtracked 0 clauses, performed 0 splits and kept 55 clauses.
% 0.19/0.43 SPASS allocated 63331 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.02 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 7, length 22 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : single_axiom prove_these_axioms
% 0.19/0.43
%------------------------------------------------------------------------------