%--------------------------------------------------------------------------
% File     : LCL002-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Logic Calculi (Wajsberg Algebras)
% Axioms   : Alternative Wajsberg algebra
% Version  : [AB90] (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    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    8 (   8 unt;   0 nHn;   0 RR)
%            Number of literals    :    8 (   8 equ;   0 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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   10 (   1 sgn)
% SPC      : 

% Comments : Requires LAT003-0.ax
%--------------------------------------------------------------------------
cnf(axiom_1,axiom,
    not(X) = xor(X,truth) ).

cnf(axiom_2,axiom,
    xor(X,falsehood) = X ).

cnf(axiom_3,axiom,
    xor(X,X) = falsehood ).

cnf(axiom_4,axiom,
    and_star(X,truth) = X ).

cnf(axiom_5,axiom,
    and_star(X,falsehood) = falsehood ).

cnf(axiom_6,axiom,
    and_star(xor(truth,X),X) = falsehood ).

cnf(axiom_7,axiom,
    xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ).

cnf(axiom_8,axiom,
    and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ).

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