%--------------------------------------------------------------------------
% File     : MGT086+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Domain   : Management
% Problem  : and-B vs xone-A: ~A_x & A_y branch matches => Compatible
% Version  : Especial.
% English  : PolicyA: xone(width lteq 600, height lteq 400)
%            PolicyB: and(width gteq 800, height lteq 200)
%            Branch (~A_x & A_y): X>=800>600 => X not_in (0,600], 
%            Y in (0,200]subseteq(0,400] => A_y
%            Witness: X=v800, Y=v200. verdictXone=Compatible

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : ODRL462-1.p [MC+26]

% Status   : Theorem
% Rating   : ? v9.3.1
% Syntax   : Number of formulae    :   44 (  22 unt;   0 def)
%            Number of atoms       :  108 (  33 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   83 (  19   ~;  10   |;  34   &)
%                                         (   8 <=>;  12  =>;   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   :   59 (  55   !;   4   ?)
% SPC      : FOF_THM_RFO_SEQ

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

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

fof(val_v400,axiom,
    val(v400) ).

fof(val_v600,axiom,
    val(v600) ).

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

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

fof(ord_v0_v400,axiom,
    less(v0,v400) ).

fof(ord_v0_v600,axiom,
    less(v0,v600) ).

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

fof(ord_v200_v400,axiom,
    less(v200,v400) ).

fof(ord_v200_v600,axiom,
    less(v200,v600) ).

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

fof(ord_v400_v600,axiom,
    less(v400,v600) ).

fof(ord_v400_v800,axiom,
    less(v400,v800) ).

fof(ord_v600_v800,axiom,
    less(v600,v800) ).

fof(distinct,axiom,
    ( v0 != v200
    & v0 != v400
    & v0 != v600
    & v0 != v800
    & v200 != v400
    & v200 != v600
    & v200 != v800
    & v400 != v600
    & v400 != v800
    & v600 != v800 ) ).

fof(odrl462,conjecture,
    ? [X,Y] :
      ( leq(v800,X)
      & in_lopen(Y,v0,v200)
      & ( ( in_lopen(X,v0,v600)
          & ~ in_lopen(Y,v0,v400) )
        | ( ~ in_lopen(X,v0,v600)
          & in_lopen(Y,v0,v400) ) ) ) ).

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