%--------------------------------------------------------------------------
% File     : LAT010-1 : TPTP v9.0.0. Released v2.2.0.
% Domain   : Lattice Theory
% Problem  : McKenzie's basis for the variety generated by N5.
% Version  : [MP96] (equality) axioms : Especial.
% English  : McKenzie's basis for the variety generated by N5.

% Refs     : [McC98] McCune (1998), Email to G. Sutcliffe
%          : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source   : [McC98]
% Names    : LT-6 [MP96]

% Status   : Unsatisfiable
% Rating   : 0.18 v9.0.0, 0.14 v8.2.0, 0.25 v8.1.0, 0.30 v7.5.0, 0.21 v7.4.0, 0.26 v7.3.0, 0.16 v7.1.0, 0.06 v7.0.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.25 v6.0.0, 0.43 v5.5.0, 0.42 v5.4.0, 0.27 v5.3.0, 0.17 v5.2.0, 0.21 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.07 v3.2.0, 0.00 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1
% Syntax   : Number of clauses     :   12 (  12 unt;   0 nHn;   1 RR)
%            Number of literals    :   12 (  12 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   27 (   2 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Include lattice axioms
include('Axioms/LAT001-0.ax').
%--------------------------------------------------------------------------
%----Hypotheses:
cnf(n5_1,hypothesis,
    meet(X,join(Y,meet(Z,join(X,U)))) = join(meet(X,join(Y,meet(X,Z))),meet(X,join(meet(X,Y),meet(Z,U)))) ).

cnf(n5_2,hypothesis,
    join(X,meet(Y,join(Z,meet(X,U)))) = meet(join(X,meet(Y,join(X,Z))),join(X,meet(join(X,Y),join(Z,U)))) ).

cnf(nr_3,hypothesis,
    meet(join(X,meet(Y,Z)),join(Z,meet(X,Y))) = join(meet(Z,join(X,meet(Y,Z))),meet(X,join(Y,Z))) ).

%----Denial of the conclusion:
cnf(prove_this,negated_conjecture,
    meet(a,meet(join(b,c),join(b,d))) != meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))) ).

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