%--------------------------------------------------------------------------
% File     : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Domain   : Management
% Problem  : 3D eq conflict via distinctness (7 constants)
% Version  : Especial.
% English  : Width: eq 600 intersection eq 601 = {600}intersection{601} = 
%            null Conflict (distinct)
%            Height: gt 300 intersection lt 500 = (300,500) Compatible
%            Depth: gteq 16 intersection lteq 32 = [16,32] Compatible
%            Conflict proved by X distinctness - no density needed.

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : ODRL411-1.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_v16,axiom,
    val(v16) ).

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

fof(val_v300,axiom,
    val(v300) ).

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

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

fof(val_v601,axiom,
    val(v601) ).

fof(ord_v0_v16,axiom,
    less(v0,v16) ).

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

fof(ord_v0_v300,axiom,
    less(v0,v300) ).

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

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

fof(ord_v0_v601,axiom,
    less(v0,v601) ).

fof(ord_v16_v32,axiom,
    less(v16,v32) ).

fof(ord_v16_v300,axiom,
    less(v16,v300) ).

fof(ord_v16_v500,axiom,
    less(v16,v500) ).

fof(ord_v16_v600,axiom,
    less(v16,v600) ).

fof(ord_v16_v601,axiom,
    less(v16,v601) ).

fof(ord_v32_v300,axiom,
    less(v32,v300) ).

fof(ord_v32_v500,axiom,
    less(v32,v500) ).

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

fof(ord_v32_v601,axiom,
    less(v32,v601) ).

fof(ord_v300_v500,axiom,
    less(v300,v500) ).

fof(ord_v300_v600,axiom,
    less(v300,v600) ).

fof(ord_v300_v601,axiom,
    less(v300,v601) ).

fof(ord_v500_v600,axiom,
    less(v500,v600) ).

fof(ord_v500_v601,axiom,
    less(v500,v601) ).

fof(ord_v600_v601,axiom,
    less(v600,v601) ).

fof(distinct,axiom,
    ( v0 != v16
    & v0 != v32
    & v0 != v300
    & v0 != v500
    & v0 != v600
    & v0 != v601
    & v16 != v32
    & v16 != v300
    & v16 != v500
    & v16 != v600
    & v16 != v601
    & v32 != v300
    & v32 != v500
    & v32 != v600
    & v32 != v601
    & v300 != v500
    & v300 != v600
    & v300 != v601
    & v500 != v600
    & v500 != v601
    & v600 != v601 ) ).

fof(odrl411,conjecture,
    ~ ? [X,Y,Z] :
        ( in_closed(X,v600,v600)
        & in_closed(X,v601,v601)
        & less(v300,Y)
        & in_open(Y,v0,v500)
        & leq(v16,Z)
        & in_lopen(Z,v0,v32) ) ).

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