TSTP Solution File: GRP158-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP158-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:45:58 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 5 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(greatest_lower_bound(a,b),a),
file('GRP158-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(greatest_lower_bound(multiply(c,a),multiply(c,b)),multiply(c,a)),
file('GRP158-1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP158-1.p',unknown),
[] ).
cnf(583,plain,
equal(greatest_lower_bound(multiply(u,a),multiply(u,b)),multiply(u,a)),
inference(spr,[status(thm),theory(equality)],[1,15]),
[iquote('0:SpR:1.0,15.0')] ).
cnf(600,plain,
$false,
inference(unc,[status(thm)],[583,2]),
[iquote('0:UnC:583.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP158-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Mon Jun 13 08:19:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 449 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.19/0.45 SPASS allocated 63716 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.01 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.04 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 1, length 5 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : ax_mono2b_1 prove_ax_mono2b monotony_glb1
% 0.19/0.45
%------------------------------------------------------------------------------