TPTP Axioms File: LCL001-1.ax


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% File     : LCL001-1 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Logic Calculi (Wajsberg Algebras)
% Axioms   : Wajsberg algebra lattice structure definitions
% Version  : [Bon91] (equality) axioms.
% English  :

% Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras
%          : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
% Source   : [Bon91]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    4 (   0 non-Horn;   2 unit;   2 RR)
%            Number of atoms      :    6 (   4 equality)
%            Maximal clause size  :    2 (   2 average)
%            Number of predicates :    2 (   0 propositional; 2-2 arity)
%            Number of functors   :    5 (   1 constant; 0-2 arity)
%            Number of variables  :    8 (   0 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      : 

% Comments : Requires LCL001-0.ax
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%----Definitions of big_V and big_hat
cnf(big_V_definition,axiom,
    ( big_V(X,Y) = implies(implies(X,Y),Y) )).

cnf(big_hat_definition,axiom,
    ( big_hat(X,Y) = not(big_V(not(X),not(Y))) )).

%----Definition of partial order
cnf(partial_order_definition1,axiom,
    ( ~ ordered(X,Y)
    | implies(X,Y) = truth )).

cnf(partial_order_definition2,axiom,
    ( implies(X,Y) != truth
    | ordered(X,Y) )).

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