%--------------------------------------------------------------------------
% File     : LCL164-1 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Logic Calculi (Wajsberg Algebra)
% Problem  : The 4th Wajsberg algebra axiom, from the alternative axioms
% Version  : [Bon91] (equality) axioms.
% English  :

% Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras
%          : [AB90]  Anantharaman & Bonacina (1990), An Application of the
%          : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
% Source   : [Bon91]
% Names    : W axiom 4 [Bon91]

% Status   : Unsatisfiable
% Rating   : 0.05 v8.2.0, 0.04 v8.1.0, 0.10 v7.5.0, 0.08 v7.4.0, 0.17 v7.3.0, 0.11 v7.1.0, 0.06 v7.0.0, 0.11 v6.3.0, 0.18 v6.2.0, 0.21 v6.1.0, 0.12 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.00 v5.2.0, 0.07 v5.1.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 v2.0.0
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;   2 RR)
%            Number of literals    :   14 (  14 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (   1 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Include Alternative Wajsberg algebra axioms
include('Axioms/LCL002-0.ax').
%--------------------------------------------------------------------------
%----Include some Alternative Wajsberg algebra definitions
% include('Axioms/LCL002-1.ax').
%----Definition that and_star is AC and xor is C
cnf(xor_commutativity,axiom,
    xor(X,Y) = xor(Y,X) ).

cnf(and_star_associativity,axiom,
    and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ).

cnf(and_star_commutativity,axiom,
    and_star(X,Y) = and_star(Y,X) ).

%----Definition of false in terms of true
cnf(false_definition,axiom,
    not(truth) = falsehood ).

%----Include the definition of implies in terms of xor and and_star
cnf(implies_definition,axiom,
    implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ).

cnf(prove_wajsberg_axiom,negated_conjecture,
    implies(implies(not(x),not(y)),implies(y,x)) != truth ).

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