TPTP Axioms File: LCL001-0.ax


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% File     : LCL001-0 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Logic Calculi (Wajsberg Algebras)
% Axioms   : Wajsberg algebra
% Version  : [Bon91] (equality) axioms.
% English  :

% Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras
%          : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
%          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
% Source   : [MW92]
% Names    : MV Sentential Calculus [MW92]

% Status   : Satisfiable
% Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR)
%            Number of atoms      :    4 (   4 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    3 (   1 constant; 0-2 arity)
%            Number of variables  :    8 (   0 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      : 

% Comments :
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cnf(wajsberg_1,axiom,
    ( implies(truth,X) = X )).

cnf(wajsberg_2,axiom,
    ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )).

cnf(wajsberg_3,axiom,
    ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )).

cnf(wajsberg_4,axiom,
    ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )).

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