%--------------------------------------------------------------------------
% File     : LAT043-1 : TPTP v9.0.0. Released v2.5.0.
% Domain   : Lattice Theory
% Problem  : Lattice compatability from Boolean algebra
% 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    : eqp-a2.in [RW01]

% Status   : Unsatisfiable
% Rating   : 0.05 v8.2.0, 0.08 v8.1.0, 0.10 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.05 v7.1.0, 0.00 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.18 v6.2.0, 0.21 v6.1.0, 0.19 v6.0.0, 0.33 v5.5.0, 0.37 v5.4.0, 0.20 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.18 v4.0.1, 0.14 v4.0.0, 0.08 v3.7.0, 0.11 v3.4.0, 0.00 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    :    3 (   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_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Include lattice axioms
include('Axioms/LAT001-0.ax').
%--------------------------------------------------------------------------
%----Distributivity (4)
cnf(distributivity,axiom,
    meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).

%----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 ).

%----Preceding gives us Boolean Algebra
%----Denial of compatability
cnf(prove_compatability_law,negated_conjecture,
    complement(join(c,d)) != meet(complement(c),complement(d)) ).

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