## TPTP Problem File: MGT032+2.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% Domain   : Management (Organisation Theory)
% Problem  : Selection favours EPs above FMs
% Version  : [PM93] axioms.
% English  : In stable environments, selection favors efficient producers
%            above first movers past a certain point in time.

% 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
%          : [Kam95] Kamps (1995), Email to G. Sutcliffe
% Source   : [PM93]
% Names    : THEOREM 1 [PM93]
%          : T1 [PB+94]

% Status   : Theorem
% Rating   : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    3 (   0 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :   13 (   0   ~;   0   |;   8   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   7 usr;   0 prp; 1-4 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   10 (   8   !;   2   ?)
% SPC      : FOF_THM_RFO_NEQ

%--------------------------------------------------------------------------
%----MP1. Selection favors subpopulations with higher growth rates.
fof(mp1_high_growth_rates,axiom,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(growth_rate(S2,T),growth_rate(S1,T)) )
=> selection_favors(S2,S1,T) ) ).

%----L1. The growth rate of efficient producers exceeds the growth rate of
%----first movers past a certain time in stable environments.
fof(l1,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),growth_rate(first_movers,T)) ) ) ) ).

%----GOAL: T1. Selection favors efficient producers above first movers
%----past a certain time in stable environments.
fof(prove_t1,conjecture,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> selection_favors(efficient_producers,first_movers,T) ) ) ) ).

%--------------------------------------------------------------------------
```