TPTP Axioms File: LAT001-2.ax


%--------------------------------------------------------------------------
% File     : LAT001-2 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Lattice Theory
% Axioms   : Lattice theory complement (equality) axioms
% Version  : [McC88] (equality) axioms.
% English  :

% Refs     : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic
%          : [McC88] McCune (1988), Challenge Equality Problems in Lattice
% Source   : [McC88]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    3 (   0 non-Horn;   0 unit;   3 RR)
%            Number of atoms      :    7 (   4 equality)
%            Maximal clause size  :    3 (   2 average)
%            Number of predicates :    2 (   0 propositional; 2-2 arity)
%            Number of functors   :    4 (   2 constant; 0-2 arity)
%            Number of variables  :    6 (   0 singleton)
%            Maximal term depth   :    2 (   1 average)
% SPC      : 

% Comments : Requires LAT001-0.ax
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%----Definition of complement
cnf(complement_meet,axiom,
    ( ~ complement(X,Y)
    | meet(X,Y) = n0 )).

cnf(complement_join,axiom,
    ( ~ complement(X,Y)
    | join(X,Y) = n1 )).

cnf(meet_join_complement,axiom,
    ( meet(X,Y) != n0
    | join(X,Y) != n1
    | complement(X,Y) )).

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