%--------------------------------------------------------------------------
% File     : LCL002-1 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Logic Calculi (Wajsberg Algebras)
% Axioms   : Alternative Wajsberg algebra definitions
% 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     :    6 (   6 unt;   0 nHn;   1 RR)
%            Number of literals    :    6 (   6 equ;   0 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;   2 con; 0-2 aty)
%            Number of variables   :   11 (   0 sgn)
% SPC      : 

% Comments : Requires LCL001-0.ax LCL001-2.ax
%--------------------------------------------------------------------------
%----Definitions of and_star and xor, where and_star is AC and xor is C
cnf(xor_definition,axiom,
    xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ).

cnf(xor_commutativity,axiom,
    xor(X,Y) = xor(Y,X) ).

cnf(and_star_definition,axiom,
    and_star(X,Y) = not(or(not(X),not(Y))) ).

%---I guess the next two can be derived from the AC of and
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 truth
cnf(false_definition,axiom,
    not(truth) = falsehood ).

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