TPTP Problem File: MGT038+2.p
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% File : MGT038+2 : TPTP v8.2.0. Released v2.0.0.
% Domain : Management (Organisation Theory)
% Problem : FMs become extinct in stable environments
% Version : [PM93] axioms.
% English : First movers become extinct past a certain point in 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 : THEOREM 7 [PM93]
% : T7 [PB+94]
% Status : CounterSatisfiable
% Rating : 0.00 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0, 0.33 v7.0.0, 0.00 v6.4.0, 0.33 v6.2.0, 0.18 v6.1.0, 0.27 v6.0.0, 0.46 v5.5.0, 0.25 v5.4.0, 0.43 v5.2.0, 0.33 v5.0.0, 0.43 v4.1.0, 0.80 v4.0.1, 0.60 v4.0.0, 0.50 v3.7.0, 0.33 v3.5.0, 0.67 v3.4.0, 0.33 v3.1.0, 0.67 v2.6.0, 0.75 v2.5.0, 0.67 v2.4.0, 1.00 v2.1.0
% Syntax : Number of formulae : 16 ( 1 unt; 0 def)
% Number of atoms : 70 ( 4 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 54 ( 0 ~; 3 |; 32 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
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%----Subsitution axioms
%----Problem axioms
%----MP7. The number of the first movers is always a non-negative integer.
fof(mp7_first_movers_exist,axiom,
finite_set(first_movers) ).
%----MP. If a set with finitely many elements always contracts past a
%----certain point of time, then it becomes empty sooner or later.
fof(mp_contracting_time,axiom,
! [S,To] :
( ( finite_set(S)
& contracts_from(To,S) )
=> ? [T2] :
( greater(T2,To)
& cardinality_at_time(s,t2) = zero ) ) ).
%----MP on "contracts from"
fof(mp_contracts_from,axiom,
! [E,To] :
( ( environment(E)
& stable(E)
& in_environment(E,To)
& ! [T] :
( ( greater(cardinality_at_time(first_movers,T),zero)
& greater_or_equal(T,To) )
=> greater(zero,growth_rate(first_movers,T)) ) )
=> contracts_from(To,first_movers) ) ).
%----MP. If the number of both first movers abd efficient producers is
%----positive in an environment, then the population in this environment
%----contains a first mover and an efficient producer subpopulation.
fof(mp_contains_FM_and_EP,axiom,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(cardinality_at_time(first_movers,T),zero)
& greater(cardinality_at_time(efficient_producers,T),zero) )
=> subpopulations(first_movers,efficient_producers,E,T) ) ).
%----MP. Stable environments are long.
fof(mp_long_stable_environments,axiom,
! [E,T1,T2] :
( ( environment(E)
& stable(E)
& in_environment(E,T1)
& greater(T2,T1) )
=> in_environment(E,T2) ) ).
%----MP. First movers appear in stable environments.
fof(mp_stable_first_movers,axiom,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,appear(first_movers,E)) ) ).
%----MP. Efficient producers appear in stable environments.
fof(mp_stable_efficient_producers,axiom,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,appear(efficient_producers,E)) ) ).
%----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)) ) ) ) ).
%----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 ) ) ).
%----A3. First movers appear sooner in the environment, than efficient
%----producers.
fof(a3,hypothesis,
! [E] :
( environment(E)
=> greater(appear(efficient_producers,e),appear(first_movers,E)) ) ).
%----A5. The state of equilibrium is reached in stable environments.
fof(a5,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [T] :
( in_environment(E,T)
& greater_or_equal(T,equilibrium(E)) ) ) ).
%----T6. Once appeared in an environment, efficient producers do not
%----disappear.
fof(t6,hypothesis,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater_or_equal(T,appear(efficient_producers,E)) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ) ).
%----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: T7. First movers disappear past a certain time after their
%----appearence in stable environments.
fof(prove_t7,conjecture,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& greater(To,appear(first_movers,E))
& cardinality_at_time(first_movers,to) = zero ) ) ).
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