TSTP Solution File: LAT045-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 : Sun Jul 17 06:48:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 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(3,axiom,
equal(join(complement(u),u),n1),
file('LAT045-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(join(u,v),join(u,w)),join(u,meet(v,join(u,w)))),
file('LAT045-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(join(a,meet(complement(a),join(a,b))),join(a,b)),
file('LAT045-1.p',unknown),
[] ).
cnf(10,axiom,
equal(meet(u,join(u,v)),u),
file('LAT045-1.p',unknown),
[] ).
cnf(12,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT045-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,v),join(v,u)),
file('LAT045-1.p',unknown),
[] ).
cnf(16,plain,
equal(join(u,complement(u)),n1),
inference(rew,[status(thm),theory(equality)],[13,3]),
[iquote('0:Rew:13.0,3.0')] ).
cnf(36,plain,
equal(meet(u,n1),u),
inference(spr,[status(thm),theory(equality)],[16,10]),
[iquote('0:SpR:16.0,10.0')] ).
cnf(73,plain,
equal(meet(n1,u),u),
inference(spr,[status(thm),theory(equality)],[12,36]),
[iquote('0:SpR:12.0,36.0')] ).
cnf(1025,plain,
equal(join(u,meet(complement(u),join(u,v))),meet(n1,join(u,v))),
inference(spr,[status(thm),theory(equality)],[16,6]),
[iquote('0:SpR:16.0,6.0')] ).
cnf(1064,plain,
equal(join(u,meet(complement(u),join(u,v))),join(u,v)),
inference(rew,[status(thm),theory(equality)],[73,1025]),
[iquote('0:Rew:73.0,1025.0')] ).
cnf(1065,plain,
$false,
inference(unc,[status(thm)],[1064,7]),
[iquote('0:UnC:1064.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 21:09:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 790 clauses, backtracked 0 clauses, performed 0 splits and kept 156 clauses.
% 0.20/0.49 SPASS allocated 63917 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.06 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 2, length 12 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : invertability1 modular_law prove_orthomodular_law absorption1 commutativity_of_meet commutativity_of_join
% 0.20/0.49
%------------------------------------------------------------------------------