%--------------------------------------------------------------------------
% File     : LAT001-2 : TPTP v9.0.0. 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 unt;   0 nHn;   3 RR)
%            Number of literals    :    7 (   4 equ;   4 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : 

% Comments : Requires LAT001-0.ax
%--------------------------------------------------------------------------
%----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) ) ).

%--------------------------------------------------------------------------