%--------------------------------------------------------------------------
% File     : LCL001-2 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Logic Calculi (Wajsberg Algebras)
% Axioms   : Wajsberg algebra AND and OR 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;   0 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    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :   14 (   0 sgn)
% SPC      : 

% Comments : Requires LCL001-0.ax
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%----Definitions of or and and, which are AC
cnf(or_definition,axiom,
    or(X,Y) = implies(not(X),Y) ).

cnf(or_associativity,axiom,
    or(or(X,Y),Z) = or(X,or(Y,Z)) ).

cnf(or_commutativity,axiom,
    or(X,Y) = or(Y,X) ).

cnf(and_definition,axiom,
    and(X,Y) = not(or(not(X),not(Y))) ).

cnf(and_associativity,axiom,
    and(and(X,Y),Z) = and(X,and(Y,Z)) ).

cnf(and_commutativity,axiom,
    and(X,Y) = and(Y,X) ).

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