## TPTP Axioms File: LCL001-2.ax

```%--------------------------------------------------------------------------
% File     : LCL001-2 : TPTP v7.5.0. 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 (   0 non-Horn;   6 unit;   0 RR)
%            Number of atoms      :    6 (   6 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    4 (   0 constant; 1-2 arity)
%            Number of variables  :   14 (   0 singleton)
%            Maximal term depth   :    4 (   3 average)
% SPC      :

%--------------------------------------------------------------------------
%----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) )).

%--------------------------------------------------------------------------
```