%--------------------------------------------------------------------------
% File     : MGT078+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Domain   : Management
% Problem  : Width conflict × height+depth compatible => box Conflict
% Version  : Especial.
% English  : Width:  lteq 600  => (0,600] intersection gteq 1200 => 
%            [1200,infinity) = null Conflict
%            Height: lteq 800 => (0,800] intersection gteq 200  => 
%            [200,infinity) != null Compatible
%            Depth: lteq 32 => (0,32] intersection gteq 8 => 
%            [8,infinity) != null Compatible
%            box_verdict(Conflict, box_verdict(Compatible, Compatible)) =
%            Conflict

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : ODRL341-1.p [MC+26]

% Status   : Theorem
% Rating   : ? v9.3.1
% Syntax   : Number of formulae    :   57 (  35 unt;   0 def)
%            Number of atoms       :  132 (  44 equ)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives :  104 (  29   ~;   9   |;  46   &)
%                                         (   8 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   0 prp; 1-4 aty)
%            Number of functors    :   11 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :   60 (  55   !;   5   ?)
% 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_v8,axiom,
    val(v8) ).

fof(val_v32,axiom,
    val(v32) ).

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

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

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

fof(val_v1200,axiom,
    val(v1200) ).

fof(ord_v0_v8,axiom,
    less(v0,v8) ).

fof(ord_v0_v32,axiom,
    less(v0,v32) ).

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

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

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

fof(ord_v0_v1200,axiom,
    less(v0,v1200) ).

fof(ord_v8_v32,axiom,
    less(v8,v32) ).

fof(ord_v8_v200,axiom,
    less(v8,v200) ).

fof(ord_v8_v600,axiom,
    less(v8,v600) ).

fof(ord_v8_v800,axiom,
    less(v8,v800) ).

fof(ord_v8_v1200,axiom,
    less(v8,v1200) ).

fof(ord_v32_v200,axiom,
    less(v32,v200) ).

fof(ord_v32_v600,axiom,
    less(v32,v600) ).

fof(ord_v32_v800,axiom,
    less(v32,v800) ).

fof(ord_v32_v1200,axiom,
    less(v32,v1200) ).

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

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

fof(ord_v200_v1200,axiom,
    less(v200,v1200) ).

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

fof(ord_v600_v1200,axiom,
    less(v600,v1200) ).

fof(ord_v800_v1200,axiom,
    less(v800,v1200) ).

fof(distinct,axiom,
    ( v0 != v8
    & v0 != v32
    & v0 != v200
    & v0 != v600
    & v0 != v800
    & v0 != v1200
    & v8 != v32
    & v8 != v200
    & v8 != v600
    & v8 != v800
    & v8 != v1200
    & v32 != v200
    & v32 != v600
    & v32 != v800
    & v32 != v1200
    & v200 != v600
    & v200 != v800
    & v200 != v1200
    & v600 != v800
    & v600 != v1200
    & v800 != v1200 ) ).

fof(odrl341,conjecture,
    ~ ? [X,Y,Z] :
        ( in_lopen(X,v0,v600)
        & leq(v1200,X)
        & in_lopen(Y,v0,v800)
        & leq(v200,Y)
        & in_lopen(Z,v0,v32)
        & leq(v8,Z) ) ).

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