%--------------------------------------------------------------------------
% File     : MGT075+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Domain   : Management
% Problem  : width < 600 vs width >= 600: open/closed boundary
% Version  : Especial.
% English  : width lt 600   => (0, 600) width gteq 600 => [600, infinity)
%            (0, 600) intersection [600, infinity) = null
%            Conflict Criterion: u1=600 open, l2=600 closed => u1 =< l2.
%            Proof is order contradiction (X<600 & X>=600); density not
%            needed.

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : ODRL302-1.p [MC+26]

% Status   : Theorem
% Rating   : ? v9.3.1
% Syntax   : Number of formulae    :   32 (  11 unt;   0 def)
%            Number of atoms       :   83 (  24 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   60 (   9   ~;   9   |;  22   &)
%                                         (   8 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   0 prp; 1-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   58 (  55   !;   3   ?)
% 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 
%----v0 = domain lower bound (excluded); v600 = constraint value
%----in_open(X,v0,v600) encodes (0,600) = sem(lt 600) over D_k=(0,inf)
fof(val_v0,axiom,
    val(v0) ).

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

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

fof(distinct,axiom,
    v0 != v600 ).

fof(odrl302,conjecture,
    ~ ? [X] :
        ( in_open(X,v0,v600)
        & leq(v600,X) ) ).

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