%--------------------------------------------------------------------------
% File     : LCL001-1 : TPTP v9.0.0. 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 (   2 unt;   0 nHn;   2 RR)
%            Number of literals    :    6 (   4 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn)
% 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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