%--------------------------------------------------------------------------
% File     : HEN007-2 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Henkin Models
% Problem  : X <= Y => Z/Y <= Z/X
% Version  : [MOW76] axioms : Augmented.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [MOW76]
% Names    : H7 [MOW76]

% Status   : Unsatisfiable
% Rating   : 0.08 v9.0.0, 0.06 v8.2.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.20 v2.0.0
% Syntax   : Number of clauses     :   19 (  11 unt;   0 nHn;  12 RR)
%            Number of literals    :   36 (   2 equ;  18 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    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   37 (   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(transitivity_of_less_equal,axiom,
    ( ~ less_equal(X,Y)
    | ~ less_equal(Y,Z)
    | less_equal(X,Z) ) ).

cnf(xQyLEz_implies_xQzLEy,axiom,
    ( ~ quotient(X,Y,W1)
    | ~ less_equal(W1,Z)
    | ~ quotient(X,Z,W2)
    | less_equal(W2,Y) ) ).

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

cnf(zQy,hypothesis,
    quotient(z,y,zQy) ).

cnf(zQx,hypothesis,
    quotient(z,x,zQx) ).

cnf(prove_zQyLEzQx,negated_conjecture,
    ~ less_equal(zQy,zQx) ).

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