%--------------------------------------------------------------------------
% File     : MGT069+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Domain   : Management
% Problem  : Hypothesis set of HARD001 is self-consistent (SAT companion)
% Version  : Especial.
% English  : The ordering chain n0<n3<n5<n10<n20 with universal domain 
%            bounds is satisfiable - the hypotheses of HARD001 do not 
%            self-contradict. 

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

% Status   : Satisfiable
% Rating   : ? v9.3.1
% Syntax   : Number of formulae    :   59 (  26 unt;   0 def)
%            Number of atoms       :  156 (  47 equ)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives :  126 (  29   ~;  11   |;  53   &)
%                                         (  13 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   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   :  102 ( 100   !;   2   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments : SAT companion for HARD001+1.p. No conjecture - a model finder
%          : (Mace4, Paradox, Vampire-FMB) should return a finite model
%          : establishing satisfiability of the hypothesis set.
%          : MGT002+1.ax (density) intentionally excluded: density forces
%          : infinite models on any non-trivial ordering chain, defeating
%          : finite model finders. HARD001+1.p (THM) keeps density.
% Bugfixes : v9.3.1 - $distinct expanded to inequalities.
%--------------------------------------------------------------------------
include('Axioms/MGT002+0.ax').
include('Axioms/MGT002+2.ax').
include('Axioms/MGT002+4.ax').
include('Axioms/MGT002+5.ax').
%--------------------------------------------------------------------------
fof(h_0_3,axiom,
    less(n0,n3) ).

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

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

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

fof(h_inf_lb,axiom,
    ! [X] : leq(ninf,X) ).

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

fof(distinct,axiom,
    ( ninf != n0
    & ninf != n3
    & ninf != n5
    & ninf != n10
    & ninf != n20
    & ninf != nsup
    & n0 != n3
    & n0 != n5
    & n0 != n10
    & n0 != n20
    & n0 != nsup
    & n3 != n5
    & n3 != n10
    & n3 != n20
    & n3 != nsup
    & n5 != n10
    & n5 != n20
    & n5 != nsup
    & n10 != n20
    & n10 != nsup
    & n20 != nsup ) ).

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