%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP145-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:45:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 11 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(greatest_lower_bound(greatest_lower_bound(a,b),b),greatest_lower_bound(a,b)),
file('GRP145-1.p',unknown),
[] ).
cnf(5,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP145-1.p',unknown),
[] ).
cnf(6,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP145-1.p',unknown),
[] ).
cnf(11,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP145-1.p',unknown),
[] ).
cnf(12,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP145-1.p',unknown),
[] ).
cnf(17,plain,
~ equal(greatest_lower_bound(b,greatest_lower_bound(a,b)),greatest_lower_bound(a,b)),
inference(rew,[status(thm),theory(equality)],[5,1]),
[iquote('0:Rew:5.0,1.0')] ).
cnf(29,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(37,plain,
equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[5,11]),
[iquote('0:SpR:5.0,11.0')] ).
cnf(55,plain,
equal(greatest_lower_bound(greatest_lower_bound(u,v),v),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[37,29]),
[iquote('0:SpR:37.0,29.0')] ).
cnf(61,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(v,u)),greatest_lower_bound(v,u)),
inference(rew,[status(thm),theory(equality)],[5,55]),
[iquote('0:Rew:5.0,55.0')] ).
cnf(62,plain,
$false,
inference(unc,[status(thm)],[61,17]),
[iquote('0:UnC:61.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP145-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.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 14:31:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 42 clauses, backtracked 0 clauses, performed 0 splits and kept 22 clauses.
% 0.19/0.41 SPASS allocated 63132 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 2, length 11 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : prove_ax_glb3b symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion
% 0.19/0.41
%------------------------------------------------------------------------------