%--------------------------------------------------------------------------
% File     : HEN005-2 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Henkin Models
% Problem  : The relation less_equal is transitive
% Version  : [MOW76] axioms : Augmented.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [MOW76]
% Names    : H5 [MOW76]

% Status   : Unsatisfiable
% Rating   : 0.00 v6.0.0, 0.22 v5.5.0, 0.25 v5.4.0, 0.27 v5.3.0, 0.33 v5.2.0, 0.25 v5.1.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.00 v3.1.0, 0.22 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.3.0, 0.17 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.40 v2.0.0
% Syntax   : Number of clauses     :   16 (  10 unt;   0 nHn;   9 RR)
%            Number of literals    :   28 (   2 equ;  13 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-3 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   29 (   5 sgn)
% SPC      : CNF_UNS_RFO_SEQ_HRN

% Comments :
%--------------------------------------------------------------------------
%----Include Henkin model axioms
include('Axioms/HEN001-0.ax').
%--------------------------------------------------------------------------
%----McCharen uses these earlier results too. I don't
cnf(everything_divide_identity_is_zero,axiom,
    quotient(X,identity,zero) ).

cnf(zero_divide_anything_is_zero,axiom,
    quotient(zero,X,zero) ).

cnf(x_divide_x_is_zero,axiom,
    quotient(X,X,zero) ).

cnf(x_divde_zero_is_x,axiom,
    quotient(X,zero,X) ).

cnf(xLEy,hypothesis,
    less_equal(x,y) ).

cnf(yLEz,hypothesis,
    less_equal(y,z) ).

cnf(prove_transitivity_of_less_equal,negated_conjecture,
    ~ less_equal(x,z) ).

%--------------------------------------------------------------------------