TPTP Axioms File: LAT001-3.ax
%--------------------------------------------------------------------------
% File : LAT001-3 : TPTP v9.0.0. 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 ) ).
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