TSTP Solution File: GRP170-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:46:04 EDT 2022
% Result : Unsatisfiable 6.10s 6.30s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(least_upper_bound(a,b),b),
file('GRP170-4.p',unknown),
[] ).
cnf(2,axiom,
equal(greatest_lower_bound(c,d),c),
file('GRP170-4.p',unknown),
[] ).
cnf(3,axiom,
~ equal(least_upper_bound(multiply(a,c),multiply(b,d)),multiply(b,d)),
file('GRP170-4.p',unknown),
[] ).
cnf(7,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP170-4.p',unknown),
[] ).
cnf(8,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP170-4.p',unknown),
[] ).
cnf(10,axiom,
equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
file('GRP170-4.p',unknown),
[] ).
cnf(13,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP170-4.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP170-4.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP170-4.p',unknown),
[] ).
cnf(44,plain,
equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(64,plain,
equal(least_upper_bound(d,c),d),
inference(spr,[status(thm),theory(equality)],[2,44]),
[iquote('0:SpR:2.0,44.0')] ).
cnf(71,plain,
equal(least_upper_bound(c,d),d),
inference(rew,[status(thm),theory(equality)],[8,64]),
[iquote('0:Rew:8.0,64.0')] ).
cnf(435,plain,
equal(least_upper_bound(multiply(a,u),multiply(b,u)),multiply(b,u)),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(793,plain,
equal(least_upper_bound(multiply(u,c),multiply(u,d)),multiply(u,d)),
inference(spr,[status(thm),theory(equality)],[71,15]),
[iquote('0:SpR:71.0,15.0')] ).
cnf(1137,plain,
equal(least_upper_bound(multiply(a,u),least_upper_bound(multiply(b,u),v)),least_upper_bound(multiply(b,u),v)),
inference(spr,[status(thm),theory(equality)],[435,10]),
[iquote('0:SpR:435.0,10.0')] ).
cnf(23024,plain,
equal(least_upper_bound(multiply(a,c),multiply(b,d)),multiply(b,d)),
inference(spr,[status(thm),theory(equality)],[793,1137]),
[iquote('0:SpR:793.0,1137.0')] ).
cnf(23050,plain,
$false,
inference(mrr,[status(thm)],[23024,3]),
[iquote('0:MRR:23024.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.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 : Mon Jun 13 22:08:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.10/6.30
% 6.10/6.30 SPASS V 3.9
% 6.10/6.30 SPASS beiseite: Proof found.
% 6.10/6.30 % SZS status Theorem
% 6.10/6.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.10/6.30 SPASS derived 15160 clauses, backtracked 0 clauses, performed 0 splits and kept 2781 clauses.
% 6.10/6.30 SPASS allocated 85877 KBytes.
% 6.10/6.30 SPASS spent 0:00:05.82 on the problem.
% 6.10/6.30 0:00:00.03 for the input.
% 6.10/6.30 0:00:00.00 for the FLOTTER CNF translation.
% 6.10/6.30 0:00:00.10 for inferences.
% 6.10/6.30 0:00:00.00 for the backtracking.
% 6.10/6.30 0:00:05.65 for the reduction.
% 6.10/6.30
% 6.10/6.30
% 6.10/6.30 Here is a proof with depth 4, length 17 :
% 6.10/6.30 % SZS output start Refutation
% See solution above
% 6.10/6.30 Formulae used in the proof : p03d_1 p03d_2 prove_p03d symmetry_of_glb symmetry_of_lub associativity_of_lub lub_absorbtion monotony_lub1 monotony_lub2
% 6.10/6.30
%------------------------------------------------------------------------------