%--------------------------------------------------------------------------
% File     : MGT073+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Management
% Problem  : Compatible verdict implies joint witness exists
% Version  : Especial.
% English  : If axis_compatible holds for two closed intervals then some 
%            value belongs to both. Establishes Compatible is never a 
%            false positive (prop:no-false-verdict, Compatible direction).

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : NFV002+1.p [MC+26]

% Status   : Theorem
% Rating   : 0.04 v9.3.0
% Syntax   : Number of formulae    :   40 (  10 unt;   0 def)
%            Number of atoms       :  109 (  24 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   76 (   7   ~;  10   |;  30   &)
%                                         (  17 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   0 prp; 1-9 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  103 ( 100   !;   3   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Hard tier - prop:no-false-verdict Compatible direction.
%          : axis_compatible given as hypothesis; prover finds witness.
%--------------------------------------------------------------------------
include('Axioms/MGT002+0.ax').
include('Axioms/MGT002+2.ax').
include('Axioms/MGT002+6.ax').
%--------------------------------------------------------------------------
%----Domain constants: n0 < n5 < n10
fof(order_0_5,hypothesis,
    less(n0,n5) ).

fof(order_5_10,hypothesis,
    less(n5,n10) ).

%----The two intervals [n0,n10] and [n5,n10] overlap (n5 is in both).
%----axis_compatible is defined in AXIS000 Section B as the existence of a
%----shared witness; we assert it here directly as a ground hypothesis to
%----exercise the no-false-verdict claim independently of the criterion
%----proof.
fof(compatible_hyp,hypothesis,
    axis_compatible(n0,n10,n5,n10) ).

%----Conjecture: some value lies in both intervals.
%----Compatible => every axis was examined and admits overlap.
fof(no_false_compatible,conjecture,
    ? [X] :
      ( in_closed(X,n0,n10)
      & in_closed(X,n5,n10) ) ).

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