TPTP Problem File: MGT028+1.p

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% File     : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Domain   : Management (Organisation Theory)
% Problem  : FMs have a negative growth rate in stable environments
% Version  : [PB+94] axioms : Reduced & Augmented > Complete.
% English  : First movers have negative growth rate past a certain point
%            of time (also after the appearence of efficient producers)
%            in stable environments.

% 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   : Theorem
% Rating   : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v5.5.0, 0.08 v5.4.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    3 (   0 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :   10 (   7 avg)
%            Number of connectives :   20 (   0   ~;   0   |;  13   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   6 usr;   0 prp; 1-4 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   11 (   7   !;   4   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments :
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%----MP. If first movers have negative growth rate past time t1 in a
%----stable environment, then there is also a time, t2, which is after the
%----appearence of EP,  and FM has negative growth rate past t2.
fof(mp_first_movers_negative_growth,axiom,
    ! [E] :
      ( ( environment(E)
        & stable(E)
        & ? [T1] :
            ( in_environment(E,T1)
            & ! [T] :
                ( ( subpopulations(first_movers,efficient_producers,E,T)
                  & greater_or_equal(T,T1) )
               => greater(zero,growth_rate(first_movers,T)) ) ) )
     => ? [T2] :
          ( greater(T2,appear(efficient_producers,E))
          & ! [T] :
              ( ( subpopulations(first_movers,efficient_producers,E,T)
                & greater_or_equal(T,T2) )
             => greater(zero,growth_rate(first_movers,T)) ) ) ) ).

%----L11. Efficient producers have positive, while first movers have
%----negative growth rate past a certain point of time in stable
%----environments.
fof(l11,hypothesis,
    ! [E] :
      ( ( environment(E)
        & stable(E) )
     => ? [To] :
          ( in_environment(E,To)
          & ! [T] :
              ( ( subpopulations(first_movers,efficient_producers,E,T)
                & greater_or_equal(T,To) )
             => ( greater(growth_rate(efficient_producers,T),zero)
                & greater(zero,growth_rate(first_movers,T)) ) ) ) ) ).

%----GOAL:L10. First movers have negative growth rate past a certain point
%----of time (also after the appearence of efficient producers) in stable
%----environments.
fof(prove_l10,conjecture,
    ! [E] :
      ( ( environment(E)
        & stable(E) )
     => ? [To] :
          ( greater(To,appear(efficient_producers,E))
          & ! [T] :
              ( ( subpopulations(first_movers,efficient_producers,E,T)
                & greater_or_equal(T,To) )
             => greater(zero,growth_rate(first_movers,T)) ) ) ) ).

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