%--------------------------------------------------------------------------
% File     : HEN002-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Henkin Models
% Axioms   : Henkin model axioms
% Version  : [MOW76] axioms.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    7 (   4 unt;   0 nHn;   3 RR)
%            Number of literals    :   11 (   3 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   13 (   3 sgn)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
%----A0: Definition of less_equal
cnf(quotient_less_equal1,axiom,
    ( ~ less_equal(X,Y)
    | divide(X,Y) = zero ) ).

cnf(quotient_less_equal2,axiom,
    ( divide(X,Y) != zero
    | less_equal(X,Y) ) ).

%----A1: x/y <= x
cnf(quotient_smaller_than_numerator,axiom,
    less_equal(divide(X,Y),X) ).

%----A2: (x/z) / (y/z) <= (x/y) / z
cnf(quotient_property,axiom,
    less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ).

%----A3: 0<=x
cnf(zero_is_smallest,axiom,
    less_equal(zero,X) ).

%----A4: x <= y and y <= x implies that x = y
cnf(less_equal_and_equal,axiom,
    ( ~ less_equal(X,Y)
    | ~ less_equal(Y,X)
    | X = Y ) ).

%----A5: x <= identity (Thus an implicative model with unit )
cnf(identity_is_largest,axiom,
    less_equal(X,identity) ).

%----Implicit in equality formulation: '/' is well defined
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