TPTP Axioms File: LAT001-4.ax


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% File     : LAT001-4 : TPTP v7.5.0. Released v3.1.0.
% Domain   : Lattice Theory
% Axioms   : Lattice theory unique complementation (equality) axioms
% Version  : [McC05] (equality) axioms.
% English  :

% Refs     : [McC05] McCune (2005), Email to Geoff Sutcliffe
% Source   : [McC05]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    3 (   0 non-Horn;   2 unit;   1 RR)
%            Number of atoms       :    5 (   5 equality)
%            Maximal clause size   :    3 (   2 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    5 (   2 constant; 0-2 arity)
%            Number of variables   :    4 (   0 singleton)
%            Maximal term depth    :    3 (   2 average)
% SPC      : 

% Comments : Requires LAT001-0.ax
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%----Unique complementation
cnf(complement_join,axiom,
    ( join(X,complement(X)) = one )).

cnf(complement_meet,axiom,
    ( meet(X,complement(X)) = zero )).

cnf(meet_join_complement,axiom,
    ( meet(X,Y) != zero
    | join(X,Y) != one
    | complement(X) = Y )).

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