%--------------------------------------------------------------------------
% File     : MGT068+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Management
% Problem  : Full reasoning chain across 6 axiom files
% Version  : Especial.
% English  : ODRL Policy / Axis Decomposition
%            Six properties derived from ordering chain n0<n3<n5<n10<
%            n20: conflict propagation, density witness, open-interval
%            criterion, conflict completion, compatible completion, box 
%            verdict. No intermediate results given - prover derives 
%            everything from first principles.

% Refs     : [MC+26] Mustafa et al. (2026), Axis Decomposition for ODRL
% Source   : [MC+26]
% Names    : HARD001+1.p [MC+26]

% Status   : Theorem
% Rating   : 0.48 v9.3.0
% Syntax   : Number of formulae    :   60 (  26 unt;   0 def)
%            Number of atoms       :  145 (  27 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   94 (   9   ~;  11   |;  40   &)
%                                         (  13 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   18 (  17 usr;   0 prp; 1-8 aty)
%            Number of functors    :   18 (  18 usr;  17 con; 0-2 aty)
%            Number of variables   :  106 ( 102   !;   4   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Hard tier - requires all 5 axiom files simultaneously.
%          : Conjecture is 6-way conjunction; each part tests one paper
%            theorem.
%--------------------------------------------------------------------------
include('Axioms/MGT002+0.ax').
include('Axioms/MGT002+1.ax').
include('Axioms/MGT002+2.ax').
include('Axioms/MGT002+4.ax').
include('Axioms/MGT002+5.ax').
%--------------------------------------------------------------------------
%----Hypotheses: raw ordering facts + domain bounds only.
%----No axis_conflict, axis_subsumes, or completion facts are given.
%----Ordering chain: n0 < n3 < n5 < n10 < n20
fof(h_0_3,hypothesis,
    less(n0,n3) ).

fof(h_3_5,hypothesis,
    less(n3,n5) ).

fof(h_5_10,hypothesis,
    less(n5,n10) ).

fof(h_10_20,hypothesis,
    less(n10,n20) ).

%----Domain bounds: ninf is the infimum, nsup is the supremum.
%----Every domain value lies in [ninf, nsup].
fof(h_inf_lb,hypothesis,
    ! [X] : leq(ninf,X) ).

fof(h_sup_ub,hypothesis,
    ! [X] : leq(X,nsup) ).

%----Conjecture: six properties derived from the ordering chain above.
%----Part A: Conflict propagation through subsumption
%----Part B: Density witness inside open interval (n5, n10)
%----Part C: Open intervals (n5,nsup] and [ninf,n10) are not disjoint
%----Part D: Conflict completion exists for an unconstrained axis
%----Part E: Compatible completion exists for an unconstrained axis
%----Part F: Conflict dominates Unknown in box aggregation
fof(hard_chain,conjecture,
    ( axis_conflict(n0,n3,n10,n20)
    & ? [Z] :
        ( less(n5,Z)
        & less(Z,n10) )
    & ~ disjoint(n5,nsup,o,c,ninf,n10,c,o)
    & completion_conflict(n5,n10,ninf,nsup)
    & completion_compatible(n5,ninf,nsup)
    & box_verdict(conflict,unknown) = conflict ) ).

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