TSTP Solution File: GRP168-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP168-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:46:03 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 7 RR)
% Number of literals : 7 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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(greatest_lower_bound(a,b),a),
file('GRP168-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(a,c))),
file('GRP168-2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP168-2.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP168-2.p',unknown),
[] ).
cnf(218,plain,
equal(greatest_lower_bound(multiply(a,u),multiply(b,u)),multiply(a,u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(996,plain,
equal(greatest_lower_bound(multiply(u,multiply(a,v)),multiply(u,multiply(b,v))),multiply(u,multiply(a,v))),
inference(spr,[status(thm),theory(equality)],[218,15]),
[iquote('0:SpR:218.0,15.0')] ).
cnf(1020,plain,
$false,
inference(unc,[status(thm)],[996,2]),
[iquote('0:UnC:996.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP168-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 18:50:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 738 clauses, backtracked 0 clauses, performed 0 splits and kept 181 clauses.
% 0.20/0.50 SPASS allocated 64168 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.07 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 2, length 7 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : p01b_1 prove_p01b monotony_glb1 monotony_glb2
% 0.20/0.50
%------------------------------------------------------------------------------