TPTP Axioms File: LAT003-0.ax


%--------------------------------------------------------------------------
% File     : LAT003-0 : TPTP v7.5.0. Bugfixed v2.2.1.
% Domain   : Lattice Theory (Ortholattices)
% Axioms   : Ortholattice theory (equality) axioms
% Version  : [McC98b] (equality) axioms.
% English  :

% Refs     : [McC98a] McCune (1998), Automatic Proofs and Counterexamples f
%          : [McC98b] McCune (1998), Email to G. Sutcliffe
% Source   : [McC98b]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :   10 (   0 non-Horn;  10 unit;   0 RR)
%            Number of atoms      :   10 (  10 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    5 (   2 constant; 0-2 arity)
%            Number of variables  :   19 (   2 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      : 

% Comments :
% Bugfixes : v2.2.1 - Added clauses top and bottom.
%--------------------------------------------------------------------------
%----Axioms for an Ortholattice:
cnf(top,axiom,
    ( join(complement(X),X) = n1 )).

cnf(bottom,axiom,
    ( meet(complement(X),X) = n0 )).

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)) )).

cnf(complement_involution,axiom,
    ( complement(complement(X)) = X )).

cnf(join_complement,axiom,
    ( join(X,join(Y,complement(Y))) = join(Y,complement(Y)) )).

cnf(meet_complement,axiom,
    ( meet(X,Y) = complement(join(complement(X),complement(Y))) )).

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