TPTP Problem File: MGT029+1.p
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% File : MGT029+1 : TPTP v8.2.0. Released v2.0.0.
% Domain : Management (Organisation Theory)
% Problem : EPs have positive and FMs have negative growth rates
% Version : [PB+94] axioms : Reduced & Augmented > Complete.
% English : Efficient producers have positive, while first movers have
% negative growth rate past a certain point of time 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 : 0.25 v8.2.0, 0.19 v8.1.0, 0.28 v7.5.0, 0.31 v7.4.0, 0.17 v7.3.0, 0.21 v7.2.0, 0.17 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.13 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.41 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.33 v4.1.0, 0.35 v4.0.1, 0.39 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.32 v3.4.0, 0.42 v3.3.0, 0.50 v3.2.0, 0.45 v3.1.0, 0.44 v2.7.0, 0.50 v2.6.0, 0.57 v2.5.0, 0.62 v2.4.0, 0.75 v2.3.0, 0.67 v2.2.1, 0.00 v2.1.0
% Syntax : Number of formulae : 7 ( 0 unt; 0 def)
% Number of atoms : 37 ( 4 equ)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 30 ( 0 ~; 5 |; 16 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 15 !; 3 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
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%----Subsitution axioms
%----Problem axioms
%----MP. inequality
fof(mp_greater_transitivity,axiom,
! [X,Y,Z] :
( ( greater(X,Y)
& greater(Y,Z) )
=> greater(X,Z) ) ).
%----MP. times in environment
fof(mp_times_in_environment,axiom,
! [E,T1,T2] :
( ( in_environment(E,T1)
& in_environment(E,T2) )
=> ( greater(T2,T1)
| T2 = T1
| greater(T1,T2) ) ) ).
%----MP. on "greater or equal to"
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( greater(X,Y)
| X = Y ) ) ).
%----L6. If a subpopulation has positive growth rate, then the
%----other subpopulation must have negative growth rate in equilibrium.
fof(l6,hypothesis,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,equilibrium(E)) )
=> ( ( growth_rate(first_movers,T) = zero
& growth_rate(efficient_producers,T) = zero )
| ( greater(growth_rate(first_movers,T),zero)
& greater(zero,growth_rate(efficient_producers,T)) )
| ( greater(growth_rate(efficient_producers,T),zero)
& greater(zero,growth_rate(first_movers,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)) ) ) ) ).
%----A4. The state of equilibrium is reached in stable environments.
fof(a4,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [T] :
( in_environment(E,T)
& greater_or_equal(T,equilibrium(E)) ) ) ).
%----GOAL: L11. Efficient producers have positive, while first movers have
%----negative growth rate past a certain point of time in stable
%----environments.
fof(prove_l11,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),zero)
& greater(zero,growth_rate(first_movers,T)) ) ) ) ) ).
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