TPTP Axioms File: LCL002-0.ax


%--------------------------------------------------------------------------
% File     : LCL002-0 : TPTP v7.5.0. 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 (   0 non-Horn;   8 unit;   0 RR)
%            Number of atoms      :    8 (   8 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    5 (   2 constant; 0-2 arity)
%            Number of variables  :   10 (   1 singleton)
%            Maximal term depth   :    5 (   2 average)
% 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) )).

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