TPTP Problem File: LAT016-1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : LAT016-1 : TPTP v9.0.0. Bugfixed v2.2.1.
% Domain : Lattice Theory (Ortholattices)
% Problem : E1 fails for Ortholattices.
% Version : [McC98b] (equality) axioms.
% English : Show that Ortholattices do not necessarily satisfy equation E1.
% Refs : [McC98a] McCune (1998), Automatic Proofs and Counterexamples f
% : [McC98b] McCune (1998), Email to G. Sutcliffe
% Source : [McC98b]
% Names : OL-1 [McC98b]
% Status : Satisfiable
% Rating : 0.43 v9.0.0, 0.44 v8.2.0, 0.40 v8.1.0, 0.25 v7.5.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.40 v5.5.0, 0.60 v5.4.0, 0.50 v5.3.0, 0.67 v5.2.0, 0.33 v2.6.0, 0.67 v2.5.0, 1.00 v2.2.1
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 1 RR)
% Number of literals : 11 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn)
% SPC : CNF_SAT_RFO_PEQ_UEQ
% Comments : Ortholattice lemmas are included in McCunes original, but have
% been removed here.
% : The smallest model has 10 elements.
% Bugfixes : v2.2.1 - Bugfix in LAT003-0.ax.
%--------------------------------------------------------------------------
%----Include ortholattice axioms
include('Axioms/LAT003-0.ax').
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%----Denial of equation E1
cnf(prove_e1,negated_conjecture,
join(complement(join(meet(a,complement(b)),complement(a))),join(meet(a,complement(b)),join(meet(complement(a),meet(join(a,complement(b)),join(a,b))),meet(complement(a),complement(meet(join(a,complement(b)),join(a,b))))))) != n1 ).
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