%--------------------------------------------------------------------------
% File     : MGT001+0 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Management (Organisation Theory)
% Axioms   : Inequalities.
% Version  : [Han98] axioms.
% English  :

% Refs     : [Kam00] Kamps (2000), Email to G. Sutcliffe
%            [CH00]  Carroll & Hannan (2000), The Demography of Corporation
%            [Han98] Hannan (1998), Rethinking Age Dependence in Organizati
% Source   : [Kam00]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    6 (   0 unt;   0 def)
%            Number of atoms       :   16 (   3 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   11 (   1   ~;   4   |;   2   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   13 (  13   !;   0   ?)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
%----Definition of smaller_or_equal (i.t.o. smaller and equal).
fof(definition_smaller_or_equal,axiom,
    ! [X,Y] :
      ( smaller_or_equal(X,Y)
    <=> ( smaller(X,Y)
        | X = Y ) ) ).

%%----Definition of smaller_or_equal (i.t.o. greater).
%input_formula(definition_smaller_or_equal, axiom, (
%    ! [X,Y] :
%      ( smaller_or_equal(X,Y)
%    <=> ( ~ greater(X,Y) ) ) )).

%----Definition of greater_or_equal (i.t.o. greater and equal).
fof(definition_greater_or_equal,axiom,
    ! [X,Y] :
      ( greater_or_equal(X,Y)
    <=> ( greater(X,Y)
        | X = Y ) ) ).

%%----Definition of greater_or_equal (i.t.o. greater and equal).
%input_formula(definition_greater_or_equal, axiom, (
%    ! [X,Y] :
%      ( greater_or_equal(X,Y)
%    <=> ( ~ greater(Y,X) ) ) )).

%----Definition of smaller (i.t.o. greater).
fof(definition_smaller,axiom,
    ! [X,Y] :
      ( smaller(X,Y)
    <=> greater(Y,X) ) ).

%----Our notion of greater is strict (irreflexive and antisymmetric).
fof(meaning_postulate_greater_strict,axiom,
    ! [X,Y] :
      ~ ( greater(X,Y)
        & greater(Y,X) ) ).

%%----Derivable from above.
%input_formula(meaning_postulate_greater_strict2, axiom, (
%    ! [X] :
%      ( ~ greater(X,X) ) )).

%----Our notion of greater is transitive.
fof(meaning_postulate_greater_transitive,axiom,
    ! [X,Y,Z] :
      ( ( greater(X,Y)
        & greater(Y,Z) )
     => greater(X,Z) ) ).

%----Hazards of mortality are comparable.
%input_formula(background_ass_a1, axiom, (
%  ! [X,T0,T] :
%    ( organization(X)
%   => ( ( greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0))
%        | equal(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) )
%       => smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ) )).

%----Trichotomy statement for everything.
%input_formula(meaning_postulate_greater_comparable, axiom, (
%    ! [X,Y] :
%      ( greater(Y,X)
%      | equal(X,Y)
%      | greater(X,Y) ) )).
fof(meaning_postulate_greater_comparable,axiom,
    ! [X,Y] :
      ( smaller(X,Y)
      | X = Y
      | greater(X,Y) ) ).

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