TPTP Axioms File: LAT004-0.ax


%--------------------------------------------------------------------------
% File     : LAT004-0 : TPTP v7.5.0. Released v2.2.0.
% Domain   : Lattice Theory (Quasilattices)
% Axioms   : Quasilattice 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    :    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  :   18 (   0 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
%----Quasilattice theory:
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(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)) )).

cnf(quasi_lattice1,axiom,
    ( join(meet(X,join(Y,Z)),meet(X,Y)) = meet(X,join(Y,Z)) )).

cnf(quasi_lattice2,axiom,
    ( meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) )).

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