TPTP Axioms File: LAT005-0.ax


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% File     : LAT005-0 : TPTP v7.5.0. 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 (   0 non-Horn;   6 unit;   0 RR)
%            Number of atoms      :    6 (   6 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  :   12 (   4 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      : 

% Comments :
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%----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 )).

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