%------------------------------------------------------------------------------
% File     : LAT005-0 : TPTP v9.0.0. Released v2.2.0.
% Domain   : Lattice Theory (Weakly Associative Lattices)
% Axioms   : Weakly Associative Lattices theory (equality) axioms
% Version  : [McC98b] (equality) axioms.
% English  :

% Refs     : [McC98] McCune (1998), Email to G. Sutcliffe
%          : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source   : [McC98]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    6 (   6 unt;   0 nHn;   0 RR)
%            Number of literals    :    6 (   6 equ;   0 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 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   :   12 (   4 sgn)
% SPC      : 

% Comments :
%------------------------------------------------------------------------------
%----Axioms for a weakly associative lattice:
cnf(idempotence_of_meet,axiom,
    meet(X,X) = X ).

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

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

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

cnf(wal_1,axiom,
    meet(meet(join(X,Y),join(Z,Y)),Y) = Y ).

cnf(wal_2,axiom,
    join(join(meet(X,Y),meet(Z,Y)),Y) = Y ).

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