%--------------------------------------------------------------------------
% File     : LAT001-1 : TPTP v9.0.0. 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 (   4 unt;   0 nHn;   0 RR)
%            Number of literals    :    6 (   6 equ;   1 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    7 (   2 sgn)
% 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)) ) ).

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