%--------------------------------------------------------------------------
% File     : LAT052-1 : TPTP v8.2.0. Released v2.5.0.
% Domain   : Lattice Theory
% Problem  : Modular lattice is not modular ortholattice
% Version  : [McC88] (equality) axioms.
% English  :

% Refs     : [McC88] McCune (1988), Challenge Equality Problems in Lattice
%          : [RW01]  Rose & Wilkinson (2001), Application of Model Search
% Source   : [RW01]
% Names    : mace-g1.in [RW01]

% Status   : Satisfiable
% Rating   : 0.44 v8.2.0, 0.20 v8.1.0, 0.25 v7.5.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.40 v6.0.0, 0.20 v5.5.0, 0.40 v5.4.0, 0.50 v5.3.0, 0.67 v5.2.0, 0.33 v4.1.0, 0.67 v4.0.1, 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.6.0, 0.67 v2.5.0
% Syntax   : Number of clauses     :   13 (  13 unt;   0 nHn;   1 RR)
%            Number of literals    :   13 (  13 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   22 (   2 sgn)
% SPC      : CNF_SAT_RFO_PEQ_UEQ

% Comments : First part of the problem. The second part, mace-g2.in, requires
%            MACE specific input.
%--------------------------------------------------------------------------
%----Include lattice axioms
include('Axioms/LAT001-0.ax').
%--------------------------------------------------------------------------
%----Invertability (5)
cnf(invertability1,axiom,
    join(complement(X),X) = n1 ).

cnf(invertability2,axiom,
    meet(complement(X),X) = n0 ).

cnf(invertability3,axiom,
    complement(complement(X)) = X ).

%----Modular law (7)
cnf(modular_law,axiom,
    join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ).

%----Denial of compatibility (6)
cnf(prove_compatibility_law,negated_conjecture,
    complement(join(a,b)) != meet(complement(a),complement(b)) ).

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