TSTP Solution File: GRP168-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP168-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:46:02 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% 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(least_upper_bound(a,b),b),
file('GRP168-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c))),
file('GRP168-1.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP168-1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP168-1.p',unknown),
[] ).
cnf(423,plain,
equal(least_upper_bound(multiply(a,u),multiply(b,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[1,16]),
[iquote('0:SpR:1.0,16.0')] ).
cnf(1326,plain,
equal(least_upper_bound(multiply(u,multiply(a,v)),multiply(u,multiply(b,v))),multiply(u,multiply(b,v))),
inference(spr,[status(thm),theory(equality)],[423,14]),
[iquote('0:SpR:423.0,14.0')] ).
cnf(1350,plain,
$false,
inference(unc,[status(thm)],[1326,2]),
[iquote('0:UnC:1326.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP168-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 00:19:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 923 clauses, backtracked 0 clauses, performed 0 splits and kept 216 clauses.
% 0.19/0.50 SPASS allocated 64500 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.04 for the input.
% 0.19/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.09 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 2, length 7 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : p01a_1 prove_p01a monotony_lub1 monotony_lub2
% 0.19/0.50
%------------------------------------------------------------------------------