## TPTP Axioms File: LAT001-0.ax

```%--------------------------------------------------------------------------
% File     : LAT001-0 : TPTP v7.5.0. 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 (   0 non-Horn;   8 unit;   0 RR)
%            Number of atoms      :    8 (   8 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    2 (   0 constant; 2-2 arity)
%            Number of variables  :   16 (   2 singleton)
%            Maximal term depth   :    3 (   2 average)
% 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)) )).

%--------------------------------------------------------------------------
```