TSTP Solution File: GRP143-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP143-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:45:54 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 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),a),greatest_lower_bound(a,b)),
file('GRP143-1.p',unknown),
[] ).
cnf(5,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP143-1.p',unknown),
[] ).
cnf(6,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP143-1.p',unknown),
[] ).
cnf(11,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP143-1.p',unknown),
[] ).
cnf(12,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP143-1.p',unknown),
[] ).
cnf(17,plain,
~ equal(greatest_lower_bound(a,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(49,plain,
equal(greatest_lower_bound(greatest_lower_bound(u,v),u),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[11,29]),
[iquote('0:SpR:11.0,29.0')] ).
cnf(51,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(u,v)),greatest_lower_bound(u,v)),
inference(rew,[status(thm),theory(equality)],[5,49]),
[iquote('0:Rew:5.0,49.0')] ).
cnf(52,plain,
$false,
inference(unc,[status(thm)],[51,17]),
[iquote('0:UnC:51.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP143-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 04:46:38 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 33 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.12/0.40 SPASS allocated 63123 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 2, length 10 :
% 0.12/0.40 % SZS output start Refutation
% See solution above
% 0.12/0.40 Formulae used in the proof : prove_ax_glb2b symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion
% 0.12/0.40
%------------------------------------------------------------------------------