## TPTP Axioms File: LAT001-3.ax

```%--------------------------------------------------------------------------
% File     : LAT001-3 : TPTP v7.5.0. 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 (   1 non-Horn;   0 unit;   4 RR)
%            Number of atoms      :   11 (   2 equality)
%            Maximal clause size  :    3 (   3 average)
%            Number of predicates :    3 (   0 propositional; 2-2 arity)
%            Number of functors   :    1 (   0 constant; 2-2 arity)
%            Number of variables  :    9 (   0 singleton)
%            Maximal term depth   :    2 (   1 average)
% 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 )).

%--------------------------------------------------------------------------
```