%--------------------------------------------------------------------------
% File     : MGT077+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Domain   : Management
% Problem  : Both axes open intervals, overlapping => box Compatible
% Version  : Especial.
% English  : Width: gt 200 => (200,infinity) intersection lt 800 => 
%            (0,800) = (200,800) != null Compatible
%            Height: gt 100 => (100,infinity)  intersection  lt 500 => 
%            (0,500) = (100,500) != null Compatible
%            box_verdict(Compatible, Compatible) = Compatible
%            Both witnesses lie inside open intervals => requires density.

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : ODRL327-1.p [MC+26]

% Status   : Theorem
% Rating   : ? v9.3.1
% Syntax   : Number of formulae    :   45 (  22 unt;   0 def)
%            Number of atoms       :  109 (  33 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   81 (  17   ~;   9   |;  34   &)
%                                         (   8 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   0 prp; 1-4 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :   62 (  57   !;   5   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Requires MGT002+0.ax + MGT002+1.ax + MGT002+2.ax.
% Bugfixes : v9.3.1 - $distinct expanded to inequalities.
%--------------------------------------------------------------------------
include('Axioms/MGT002+0.ax').
include('Axioms/MGT002+1.ax').
include('Axioms/MGT002+2.ax').
%--------------------------------------------------------------------------
%----Named constants and ordering 
fof(val_v0,axiom,
    val(v0) ).

fof(val_v100,axiom,
    val(v100) ).

fof(val_v200,axiom,
    val(v200) ).

fof(val_v500,axiom,
    val(v500) ).

fof(val_v800,axiom,
    val(v800) ).

fof(ord_v0_v100,axiom,
    less(v0,v100) ).

fof(ord_v0_v200,axiom,
    less(v0,v200) ).

fof(ord_v0_v500,axiom,
    less(v0,v500) ).

fof(ord_v0_v800,axiom,
    less(v0,v800) ).

fof(ord_v100_v200,axiom,
    less(v100,v200) ).

fof(ord_v100_v500,axiom,
    less(v100,v500) ).

fof(ord_v100_v800,axiom,
    less(v100,v800) ).

fof(ord_v200_v500,axiom,
    less(v200,v500) ).

fof(ord_v200_v800,axiom,
    less(v200,v800) ).

fof(ord_v500_v800,axiom,
    less(v500,v800) ).

fof(distinct,axiom,
    ( v0 != v100
    & v0 != v200
    & v0 != v500
    & v0 != v800
    & v100 != v200
    & v100 != v500
    & v100 != v800
    & v200 != v500
    & v200 != v800
    & v500 != v800 ) ).

fof(odrl327,conjecture,
    ? [X,Y] :
      ( less(v200,X)
      & in_open(X,v0,v800)
      & less(v100,Y)
      & in_open(Y,v0,v500) ) ).

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