TSTP Solution File: MGT024+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:26:56 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 08:08:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 (* PROOF-FOUND *)
% 0.20/0.41 (* BEGIN-PROOF *)
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 1. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 2. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.41 3. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 4. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 5. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.41 6. (-. (in_environment T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### Extension/test/mp_time_point_occurctrp 4 5
% 0.20/0.41 7. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 8. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 9. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.41 10. (-. (greater (number_of_organizations T_0 T_1) (zero))) (greater (number_of_organizations T_0 T_1) (zero)) ### Axiom
% 0.20/0.41 11. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (greater (number_of_organizations T_0 T_1) (zero))) (-. (greater (number_of_organizations T_0 T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 8 9 10
% 0.20/0.41 12. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater (number_of_organizations T_0 T) (zero)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater (number_of_organizations T_0 T_1) (zero))) ### All 11
% 0.20/0.41 13. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (-. (greater (number_of_organizations T_0 T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 12
% 0.20/0.41 14. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 15. (greater_or_equal T_1 (equilibrium T_0)) (-. (greater_or_equal T_1 (equilibrium T_0))) ### Axiom
% 0.20/0.41 16. (greater (equilibrium T_0) T_1) (greater_or_equal T_1 (equilibrium T_0)) (environment T_0) ### Extension/test/mp_equilibriumctrp 14 15
% 0.20/0.41 17. (-. (-. (greater (equilibrium T_0) T_1))) (environment T_0) (greater_or_equal T_1 (equilibrium T_0)) ### NotNot 16
% 0.20/0.41 18. (-. (constant (resources T_0 T_1))) (constant (resources T_0 T_1)) ### Axiom
% 0.20/0.41 19. ((-. (greater (equilibrium T_0) T_1)) => (constant (resources T_0 T_1))) (-. (constant (resources T_0 T_1))) (greater_or_equal T_1 (equilibrium T_0)) (environment T_0) ### Imply 17 18
% 0.20/0.41 20. (((greater (equilibrium T_0) T_1) => (decreases (resources T_0 T_1))) /\ ((-. (greater (equilibrium T_0) T_1)) => (constant (resources T_0 T_1)))) (environment T_0) (greater_or_equal T_1 (equilibrium T_0)) (-. (constant (resources T_0 T_1))) ### And 19
% 0.20/0.41 21. (((environment T_0) /\ ((in_environment T_0 T_1) /\ (greater (number_of_organizations T_0 T_1) (zero)))) => (((greater (equilibrium T_0) T_1) => (decreases (resources T_0 T_1))) /\ ((-. (greater (equilibrium T_0) T_1)) => (constant (resources T_0 T_1))))) (-. (constant (resources T_0 T_1))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 7 6 13 20
% 0.20/0.41 22. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ (greater (number_of_organizations T_0 T) (zero)))) => (((greater (equilibrium T_0) T) => (decreases (resources T_0 T))) /\ ((-. (greater (equilibrium T_0) T)) => (constant (resources T_0 T)))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (-. (constant (resources T_0 T_1))) ### All 21
% 0.20/0.41 23. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (-. (constant (resources T_0 T_1))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 22
% 0.20/0.41 24. (-. (constant (number_of_organizations T_0 T_1))) (constant (number_of_organizations T_0 T_1)) ### Axiom
% 0.20/0.41 25. ((constant (resources T_0 T_1)) => (constant (number_of_organizations T_0 T_1))) (-. (constant (number_of_organizations T_0 T_1))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ### Imply 23 24
% 0.20/0.41 26. (((decreases (resources T_0 T_1)) => (-. (decreases (number_of_organizations T_0 T_1)))) /\ ((constant (resources T_0 T_1)) => (constant (number_of_organizations T_0 T_1)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (-. (constant (number_of_organizations T_0 T_1))) ### And 25
% 0.20/0.41 27. (((environment T_0) /\ (in_environment T_0 T_1)) => (((decreases (resources T_0 T_1)) => (-. (decreases (number_of_organizations T_0 T_1)))) /\ ((constant (resources T_0 T_1)) => (constant (number_of_organizations T_0 T_1))))) (-. (constant (number_of_organizations T_0 T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 3 6 26
% 0.20/0.41 28. (All T, (((environment T_0) /\ (in_environment T_0 T)) => (((decreases (resources T_0 T)) => (-. (decreases (number_of_organizations T_0 T)))) /\ ((constant (resources T_0 T)) => (constant (number_of_organizations T_0 T)))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (-. (constant (number_of_organizations T_0 T_1))) ### All 27
% 0.20/0.41 29. (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (-. (constant (number_of_organizations T_0 T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 28
% 0.20/0.41 30. ((growth_rate (first_movers) T_1) != (zero)) ((growth_rate (first_movers) T_1) = (zero)) ### Axiom
% 0.20/0.41 31. (((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) ((growth_rate (first_movers) T_1) != (zero)) ### And 30
% 0.20/0.41 32. (-. (greater (growth_rate (first_movers) T_1) (zero))) (greater (growth_rate (first_movers) T_1) (zero)) ### Axiom
% 0.20/0.41 33. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### And 32
% 0.20/0.41 34. (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (greater (growth_rate (efficient_producers) T_1) (zero)) ### Axiom
% 0.20/0.41 35. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### And 34
% 0.20/0.41 36. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 1 2 29 31 33 35
% 0.20/0.41 37. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 36
% 0.20/0.41 38. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 37
% 0.20/0.41 39. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 40. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.41 41. (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (zero) (growth_rate (first_movers) T_1)) ### Axiom
% 0.20/0.41 42. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### And 41
% 0.20/0.41 43. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 39 40 29 31 33 42
% 0.20/0.41 44. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### All 43
% 0.20/0.41 45. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 44
% 0.20/0.41 46. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ### NotAnd 38 45
% 0.20/0.41 47. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.41 48. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.41 49. (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.20/0.41 50. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### And 49
% 0.20/0.41 51. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 47 48 29 31 50 35
% 0.20/0.41 52. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 51
% 0.20/0.41 53. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 52
% 0.20/0.42 54. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.42 55. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.42 56. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 54 55 29 31 50 42
% 0.20/0.42 57. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### All 56
% 0.20/0.42 58. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 57
% 0.20/0.42 59. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ### NotAnd 53 58
% 0.20/0.42 60. (-. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ((growth_rate (first_movers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ### NotAnd 46 59
% 0.20/0.42 61. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.42 62. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.42 63. ((growth_rate (efficient_producers) T_1) != (zero)) ((growth_rate (efficient_producers) T_1) = (zero)) ### Axiom
% 0.20/0.42 64. (((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) ### And 63
% 0.20/0.42 65. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 61 62 29 64 33 35
% 0.20/0.42 66. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 65
% 0.20/0.42 67. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 66
% 0.20/0.42 68. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.42 69. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.42 70. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 68 69 29 64 33 42
% 0.20/0.42 71. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### All 70
% 0.20/0.42 72. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 71
% 0.20/0.43 73. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ### NotAnd 67 72
% 0.20/0.43 74. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.43 75. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.43 76. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 74 75 29 64 50 35
% 0.20/0.43 77. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 76
% 0.20/0.43 78. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 77
% 0.20/0.43 79. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.20/0.43 80. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.20/0.43 81. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (constant (number_of_organizations T_0 T_1)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 79 80 29 64 50 42
% 0.20/0.43 82. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (constant (number_of_organizations T_0 T)))) => ((((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))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### All 81
% 0.20/0.43 83. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 82
% 0.20/0.43 84. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ### NotAnd 78 83
% 0.20/0.43 85. (-. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ### NotAnd 73 84
% 0.20/0.43 86. (-. (((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero)))) (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (greater_or_equal T_1 (equilibrium T_0)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (-. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1)))) ### NotAnd 60 85
% 0.20/0.43 87. (-. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (greater_or_equal T_1 (equilibrium T_0)))) => ((((growth_rate (first_movers) T_1) = (zero)) /\ ((growth_rate (efficient_producers) T_1) = (zero))) \/ (((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) \/ ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) ### ConjTree 86
% 0.20/0.43 88. (-. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T (equilibrium T_0)))) => ((((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)))))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) ### NotAllEx 87
% 0.20/0.43 89. (-. (All E, (All 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))))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (constant (number_of_organizations E T)))) => ((((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)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater (number_of_organizations E T) (zero)))) => (((greater (equilibrium E) T) => (decreases (resources E T))) /\ ((-. (greater (equilibrium E) T)) => (constant (resources E T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater (number_of_organizations E T) (zero))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (((decreases (resources E T)) => (-. (decreases (number_of_organizations E T)))) /\ ((constant (resources E T)) => (constant (number_of_organizations E T))))))) ### NotAllEx 88
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 (* END-PROOF *)
%------------------------------------------------------------------------------