%--------------------------------------------------------------------------
% File     : LAT001-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Lattice Theory
% Axioms   : Lattice theory (equality) axioms
% Version  : [McC88] (equality) axioms.
% English  :

% Refs     : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic
%          : [McC88] McCune (1988), Challenge Equality Problems in Lattice
%          : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% Source   : [McC88]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    8 (   8 unt;   0 nHn;   0 RR)
%            Number of literals    :    8 (   8 equ;   0 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :   16 (   2 sgn)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
%----The following 8 clauses characterise lattices
cnf(idempotence_of_meet,axiom,
    meet(X,X) = X ).

cnf(idempotence_of_join,axiom,
    join(X,X) = X ).

cnf(absorption1,axiom,
    meet(X,join(X,Y)) = X ).

cnf(absorption2,axiom,
    join(X,meet(X,Y)) = X ).

cnf(commutativity_of_meet,axiom,
    meet(X,Y) = meet(Y,X) ).

cnf(commutativity_of_join,axiom,
    join(X,Y) = join(Y,X) ).

cnf(associativity_of_meet,axiom,
    meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ).

cnf(associativity_of_join,axiom,
    join(join(X,Y),Z) = join(X,join(Y,Z)) ).

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