%--------------------------------------------------------------------------
% File     : MGT031+1 : TPTP v9.0.0. Released v2.0.0.
% Domain   : Management (Organisation Theory)
% Problem  : First movers appear first in an environment
% Version  : [PB+94] axioms : Reduced & Augmented > Complete.
% English  :

% Refs     : [PM93]  Peli & Masuch (1993), The Logic of Propogation Strateg
%          : [PM94]  Peli & Masuch (1994), The Logic of Propogation Strateg
%          : [Kam95] Kamps (1995), Email to G. Sutcliffe
% Source   : [Kam95]
% Names    :

% Status   : CounterSatisfiable
% Rating   : 0.00 v7.5.0, 0.20 v7.4.0, 0.00 v6.1.0, 0.09 v6.0.0, 0.08 v5.5.0, 0.00 v4.1.0, 0.20 v4.0.1, 0.00 v3.5.0, 0.33 v3.4.0, 0.00 v3.1.0, 0.17 v2.7.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :   10 (   0 unt;   0 def)
%            Number of atoms       :   32 (   4 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   24 (   2   ~;   2   |;  10   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   0 prp; 1-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   19 (  18   !;   1   ?)
% SPC      : FOF_CSA_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Subsitution axioms
%----Problem axioms
%----MP. The number of organizations is positive in the environment when
%----they appear in this environment.
fof(mp_positive_number_when_appear,axiom,
    ! [E] :
      ( environment(E)
     => greater(number_of_organizations(e,appear(an_organisation,E)),zero) ) ).

%----MP. If the number of organizations is positive in the environment,
%----then there is a non-empty subpopulation in the environment.
fof(mp_number_mean_non_empty,axiom,
    ! [E,T] :
      ( ( environment(E)
        & greater(number_of_organizations(E,T),zero) )
     => ? [S] :
          ( subpopulation(S,E,T)
          & greater(cardinality_at_time(S,T),zero) ) ) ).

%----MP. There are no EP in the environment before their appearence.
fof(mp_no_EP_before_appearance,axiom,
    ! [E,T] :
      ( ( environment(E)
        & in_environment(E,T)
        & greater(appear(efficient_producers,E),T) )
     => ~ greater(cardinality_at_time(efficient_producers,T),zero) ) ).

%----MP. There are no FM in the environment before their appearence.
fof(mp_no_FM_before_appearance,axiom,
    ! [E,T] :
      ( ( environment(E)
        & in_environment(E,T)
        & greater(appear(first_movers,E),T) )
     => ~ greater(cardinality_at_time(first_movers,T),zero) ) ).

%----MP. The appearence of FM cannot precede the appearence of the first
%----organization in the environment.
fof(mp_FM_not_precede_first,axiom,
    ! [E] :
      ( environment(E)
     => greater_or_equal(appear(first_movers,E),appear(an_organisation,E)) ) ).

%----MP. inequality
fof(mp_greater_transitivity,axiom,
    ! [X,Y,Z] :
      ( ( greater(X,Y)
        & greater(Y,Z) )
     => greater(X,Z) ) ).

%----MP. on "greater or equal to"
fof(mp_greater_or_equal,axiom,
    ! [X,Y] :
      ( greater_or_equal(X,Y)
    <=> ( greater(X,Y)
        | X = Y ) ) ).

%----A9. The population contains only first movers and efficient
%----producers.
fof(a9,hypothesis,
    ! [E,X,T] :
      ( ( environment(E)
        & subpopulation(X,E,T)
        & greater(cardinality_at_time(X,T),zero) )
     => ( X = efficient_producers
        | X = first_movers ) ) ).

%----A13. First movers appear sooner in the environment, than efficient
%----producers.
fof(a13,hypothesis,
    ! [E] :
      ( environment(E)
     => greater(appear(efficient_producers,e),appear(first_movers,E)) ) ).

%----GOAL:L13. First movers are the first organizations that appear in the
%----environment.
fof(prove_l13,conjecture,
    ! [E] :
      ( ( environment(E)
        & in_environment(E,appear(an_organisation,E)) )
     => appear(an_organisation,E) = appear(first_movers,E) ) ).

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