TPTP Problem File: MGT019+2.p

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% File     : MGT019+2 : TPTP v8.1.0. Released v2.0.0.
% Domain   : Management (Organisation Theory)
% Problem  : Growth rate of EPs exceeds that of FMs in stable environments
% Version  : [PM93] axioms.
% English  : The growth rate of efficent producers exceeds the growth rate
%            of first movers past a certain time in stable environments.

% Refs     : [PM93]  Peli & Masuch (1993), The Logic of Propogation Strateg
%          : [PM94]  Peli & Masuch (1994), The Logic of Propogation Strateg
%          : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing
% Source   : [PM93]
% Names    : LEMMA 1 [PM93]
%          : L1 [PB+94]

% Status   : CounterSatisfiable
% Rating   : 0.00 v7.5.0, 0.20 v7.4.0, 0.00 v6.1.0, 0.09 v6.0.0, 0.00 v4.1.0, 0.20 v4.0.1, 0.00 v3.5.0, 0.33 v3.4.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    5 (   0 unt;   0 def)
%            Number of atoms       :   21 (   1 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   17 (   1   ~;   1   |;   8   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   0 prp; 1-4 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   11 (   9   !;   2   ?)
% SPC      : FOF_CSA_RFO_SEQ

% Comments : There is no MGT019+1 as Kamps did not send it to me.
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%----Subsitution axioms
%----Problem axioms
%----L2. The disbanding rate of first movers exceeds the disbanding
%----rate of efficient producers.
fof(l2,axiom,
    ~ ! [E,T] :
        ( ( environment(E)
          & subpopulations(first_movers,efficient_producers,E,T) )
       => greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ) ).

%----If EP have lower disbanding rate and not lower founding rate than
%----FM, then EP have higher growth rate.
fof(mp_EP_lower_disbanding_rate,axiom,
    ! [T] :
      ( ( greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))
        & greater_or_equal(founding_rate(efficient_producers,T),founding_rate(first_movers,T)) )
     => greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ).

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

%----A8.  The founding rate of first movers does not exceed the founding
%----rate of efficient producers past a certain point in a stable
%----environment.
fof(a8,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_or_equal(founding_rate(efficient_producers,T),founding_rate(first_movers,T)) ) ) ) ).

%----GOAL: L1. The growth rate of efficient producers exceeds the growth
%----rate of first movers past a certain time in stable environments.
fof(prove_l1,conjecture,
    ! [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),growth_rate(first_movers,T)) ) ) ) ).

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