%--------------------------------------------------------------------------
% File     : LAT001-3 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Lattice Theory
% Axioms   : Lattice theory unique complement (equality) axioms
% Version  : [McC88] (equality) axioms.
% English  :

% Refs     : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic
%          : [McC88] McCune (1988), Challenge Equality Problems in Lattice
% Source   : [McC88]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    4 (   0 unt;   1 nHn;   4 RR)
%            Number of literals    :   11 (   2 equ;   6 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    9 (   0 sgn)
% SPC      : 

% Comments : Requires LAT001-0.ax LAT001-1.ax
%--------------------------------------------------------------------------
%----Definition of unique complement
cnf(unique_complement1,axiom,
    ( ~ unique_complement(X,Y)
    | complement(X,Y) ) ).

cnf(unique_complement2,axiom,
    ( ~ unique_complement(X,Y)
    | ~ complement(X,Z)
    | Z = Y ) ).

cnf(unique_complement3,axiom,
    ( unique_complement(X,Y)
    | ~ complement(X,Y)
    | complement(X,f(X,Y)) ) ).

cnf(unique_complement4,axiom,
    ( unique_complement(X,Y)
    | ~ complement(X,Y)
    | f(X,Y) != Y ) ).

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