%--------------------------------------------------------------------------
% File     : MGT022+2 : TPTP v9.0.0. Released v2.0.0.
% Domain   : Management (Organisation Theory)
% Problem  : Decreasing resource availability affects FMS more than EPs
% Version  : [PM93] axioms.
% English  : Decreasing resource availability affects the disbanding rate
%            of first movers more than the disbanding rate of efficient
%            producers.

% 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 4 [PM93]
%          : L4 [PB+94]

% Status   : Theorem
% Rating   : 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    :    4 (   1 unt;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :   14 (   2   ~;   0   |;   5   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   6 usr;   0 prp; 1-4 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :    7 (   7   !;   0   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments :
%--------------------------------------------------------------------------
%----MP. If something is constant, then it does not decreases.
fof(mp_constant_not_decrease,axiom,
    ! [X] :
      ( constant(X)
     => ~ decreases(X) ) ).

%----A6. Less resilient subpopulations are more affected by decreasing
%----resource availability.
fof(a6,hypothesis,
    ! [E,S1,S2,T] :
      ( ( environment(E)
        & subpopulations(S1,S2,E,T)
        & greater(resilience(S2),resilience(S1)) )
     => ( ( decreases(resources(E,T))
         => increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
        & ( constant(resources(E,T))
         => constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ) ).

%----A2. Efficient producers are more resilient than first movers.
fof(a2,hypothesis,
    greater(resilience(efficient_producers),resilience(first_movers)) ).

%----GOAL: L4. A decreasing resource availability affects the disbanding
%----rate of first movers more than the disbanding rate of efficient
%----producers.
fof(prove_l4,conjecture,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => ( ( decreases(resources(E,T))
         => increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
        & ( constant(resources(E,T))
         => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ) ).

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