TPTP Axioms File: LAT001-1.ax


%--------------------------------------------------------------------------
% File     : LAT001-1 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Lattice Theory
% Axioms   : Lattice theory modularity (equality) axioms
% Version  : [McC88] (equality) axioms.
% English  :

% Refs     : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic
%          : [McC88] McCune (1988), Challenge Equality Problems in Lattice
%          : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% Source   : [McC88]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    5 (   0 non-Horn;   4 unit;   0 RR)
%            Number of atoms      :    6 (   6 equality)
%            Maximal clause size  :    2 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    4 (   2 constant; 0-2 arity)
%            Number of variables  :    7 (   2 singleton)
%            Maximal term depth   :    3 (   2 average)
% SPC      : 

% Comments : Requires LAT001-0.ax
%          : These axioms, with 4 extra redundant axioms about 0 & 1, are
%            used in [Wos88] p.217.
%--------------------------------------------------------------------------
%----Include 1 and 0 in the lattice
cnf(x_meet_0,axiom,
    ( meet(X,n0) = n0 )).

cnf(x_join_0,axiom,
    ( join(X,n0) = X )).

cnf(x_meet_1,axiom,
    ( meet(X,n1) = X )).

cnf(x_join_1,axiom,
    ( join(X,n1) = n1 )).

%----Require the lattice to be modular
cnf(modular,axiom,
    ( meet(X,Z) != X
    | meet(Z,join(X,Y)) = join(X,meet(Y,Z)) )).

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