%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP176-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:46:07 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Refutation 0.12s
% 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; 2 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(multiply(c,multiply(least_upper_bound(a,b),d)),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))),
file('GRP176-2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP176-2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP176-2.p',unknown),
[] ).
cnf(18,plain,
~ equal(least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d)))),
inference(rew,[status(thm),theory(equality)],[14,2,16]),
[iquote('0:Rew:14.0,2.0,16.0,2.0')] ).
cnf(19,plain,
$false,
inference(obv,[status(thm),theory(equality)],[18]),
[iquote('0:Obv:18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP176-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 17:22:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.40
% 0.12/0.40 SPASS V 3.9
% 0.12/0.40 SPASS beiseite: Proof found.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.40 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.12/0.40 SPASS allocated 63108 KBytes.
% 0.12/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.40 0:00:00.03 for the input.
% 0.12/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.40 0:00:00.00 for inferences.
% 0.12/0.40 0:00:00.00 for the backtracking.
% 0.12/0.40 0:00:00.00 for the reduction.
% 0.12/0.40
% 0.12/0.40
% 0.12/0.40 Here is a proof with depth 0, length 5 :
% 0.12/0.40 % SZS output start Refutation
% See solution above
% 0.12/0.40 Formulae used in the proof : prove_p07 monotony_lub1 monotony_lub2
% 0.12/0.40
%------------------------------------------------------------------------------