TSTP Solution File: MGT025+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT025+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 : n024.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 22:26:57 EDT 2022
% Result : Theorem 0.18s 0.55s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 08:54:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 (* PROOF-FOUND *)
% 0.18/0.55 (* BEGIN-PROOF *)
% 0.18/0.55 % SZS output start Proof
% 0.18/0.55 1. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 2. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 3. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.18/0.55 4. (-. (in_environment T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### Extension/test/mp_time_point_occurctrp 2 3
% 0.18/0.55 5. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 6. (-. (subpopulation (first_movers) T_0 T_1)) (subpopulation (first_movers) T_0 T_1) ### Axiom
% 0.18/0.55 7. ((subpopulation (first_movers) T_0 T_1) /\ (subpopulation (efficient_producers) T_0 T_1)) (-. (subpopulation (first_movers) T_0 T_1)) ### And 6
% 0.18/0.55 8. (((environment T_0) /\ (in_environment T_0 T_1)) => ((subpopulation (first_movers) T_0 T_1) /\ (subpopulation (efficient_producers) T_0 T_1))) (-. (subpopulation (first_movers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 5 4 7
% 0.18/0.55 9. (All T, (((environment T_0) /\ (in_environment T_0 T)) => ((subpopulation (first_movers) T_0 T) /\ (subpopulation (efficient_producers) T_0 T)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulation (first_movers) T_0 T_1)) ### All 8
% 0.18/0.55 10. (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (-. (subpopulation (first_movers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 9
% 0.18/0.55 11. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 12. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.18/0.55 13. (-. (greater (cardinality_at_time (first_movers) T_1) (zero))) (greater (cardinality_at_time (first_movers) T_1) (zero)) ### Axiom
% 0.18/0.55 14. ((greater (cardinality_at_time (first_movers) T_1) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (-. (greater (cardinality_at_time (first_movers) T_1) (zero))) ### And 13
% 0.18/0.55 15. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => ((greater (cardinality_at_time (first_movers) T_1) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero)))) (-. (greater (cardinality_at_time (first_movers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 11 12 14
% 0.18/0.55 16. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater (cardinality_at_time (first_movers) T_1) (zero))) ### All 15
% 0.18/0.55 17. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (cardinality_at_time (first_movers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 16
% 0.18/0.55 18. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 19. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 20. (-. (subpopulation (efficient_producers) T_0 T_1)) (subpopulation (efficient_producers) T_0 T_1) ### Axiom
% 0.18/0.55 21. ((subpopulation (first_movers) T_0 T_1) /\ (subpopulation (efficient_producers) T_0 T_1)) (-. (subpopulation (efficient_producers) T_0 T_1)) ### And 20
% 0.18/0.55 22. (((environment T_0) /\ (in_environment T_0 T_1)) => ((subpopulation (first_movers) T_0 T_1) /\ (subpopulation (efficient_producers) T_0 T_1))) (-. (subpopulation (efficient_producers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 19 4 21
% 0.18/0.55 23. (All T, (((environment T_0) /\ (in_environment T_0 T)) => ((subpopulation (first_movers) T_0 T) /\ (subpopulation (efficient_producers) T_0 T)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulation (efficient_producers) T_0 T_1)) ### All 22
% 0.18/0.55 24. (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (-. (subpopulation (efficient_producers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 23
% 0.18/0.55 25. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 26. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.18/0.55 27. (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (greater (cardinality_at_time (efficient_producers) T_1) (zero)) ### Axiom
% 0.18/0.55 28. ((greater (cardinality_at_time (first_movers) T_1) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) ### And 27
% 0.18/0.55 29. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => ((greater (cardinality_at_time (first_movers) T_1) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero)))) (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 25 26 28
% 0.18/0.55 30. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) ### All 29
% 0.18/0.55 31. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 30
% 0.18/0.55 32. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.55 33. ((first_movers) != (first_movers)) ### NotEqual
% 0.18/0.55 34. (-. ((greater (cardinality_at_time (first_movers) T_1) (zero)) => (((first_movers) = (efficient_producers)) \/ ((first_movers) = (first_movers))))) ### ConjTree 33
% 0.18/0.55 35. ((number_of_organizations T_0 T_1) != (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) ((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) ### Axiom
% 0.18/0.55 36. (((environment T_0) /\ ((subpopulation (first_movers) T_0 T_1) /\ ((greater (cardinality_at_time (first_movers) T_1) (zero)) => (((first_movers) = (efficient_producers)) \/ ((first_movers) = (first_movers)))))) => ((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1)))) ((number_of_organizations T_0 T_1) != (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) ### DisjTree 32 10 34 35
% 0.18/0.55 37. (All T, (((environment T_0) /\ ((subpopulation (first_movers) T_0 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) => (((first_movers) = (efficient_producers)) \/ ((first_movers) = (first_movers)))))) => ((number_of_organizations T_0 T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) ((number_of_organizations T_0 T_1) != (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) ### All 36
% 0.18/0.56 38. (All X, (All T, (((environment T_0) /\ ((subpopulation X T_0 T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations T_0 T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T)))))) ((number_of_organizations T_0 T_1) != (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) ### All 37
% 0.18/0.56 39. (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) ((number_of_organizations T_0 T_1) != (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) ### All 38
% 0.18/0.56 40. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.18/0.56 41. (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (cardinality_at_time (first_movers) T_1)) ### Axiom
% 0.18/0.56 42. ((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) ### And 41
% 0.18/0.56 43. (-. (increases (cardinality_at_time (first_movers) T_1))) (increases (cardinality_at_time (first_movers) T_1)) ### Axiom
% 0.18/0.56 44. ((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) ### And 43
% 0.18/0.56 45. (-. (increases (cardinality_at_time (efficient_producers) T_1))) (increases (cardinality_at_time (efficient_producers) T_1)) ### Axiom
% 0.18/0.56 46. ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### And 45
% 0.18/0.56 47. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 40 42 44 46
% 0.18/0.56 48. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### All 47
% 0.18/0.56 49. (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (greater (growth_rate (efficient_producers) T_1) (zero)) ### Axiom
% 0.18/0.56 50. ((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) ### Imply 48 49
% 0.18/0.56 51. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### ConjTree 50
% 0.18/0.56 52. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 18 4 24 31 51
% 0.18/0.56 53. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 52
% 0.18/0.56 54. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 53
% 0.18/0.56 55. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 54
% 0.18/0.56 56. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### All 55
% 0.18/0.56 57. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 56
% 0.18/0.56 58. (-. (greater (growth_rate (first_movers) T_1) (zero))) (greater (growth_rate (first_movers) T_1) (zero)) ### Axiom
% 0.18/0.56 59. ((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 57 58
% 0.18/0.56 60. ((growth_rate (first_movers) T_1) != (zero)) ((growth_rate (first_movers) T_1) = (zero)) ### Axiom
% 0.18/0.56 61. ((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) ### Imply 59 60
% 0.18/0.56 62. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) ### ConjTree 61
% 0.18/0.56 63. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (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)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 1 4 10 17 62
% 0.18/0.56 64. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) ### All 63
% 0.18/0.56 65. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (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)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 64
% 0.18/0.56 66. (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) ### All 65
% 0.18/0.56 67. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.56 68. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.18/0.56 69. (-. (decreases (cardinality_at_time (first_movers) T_1))) (decreases (cardinality_at_time (first_movers) T_1)) ### Axiom
% 0.18/0.56 70. ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### And 69
% 0.18/0.56 71. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 68 42 44 70
% 0.18/0.57 72. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### All 71
% 0.18/0.57 73. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### All 72
% 0.18/0.57 74. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### All 73
% 0.18/0.57 75. (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (zero) (growth_rate (first_movers) T_1)) ### Axiom
% 0.18/0.57 76. ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 74 75
% 0.18/0.57 77. (-. (greater (growth_rate (first_movers) T_1) (zero))) (greater (growth_rate (first_movers) T_1) (zero)) ### Axiom
% 0.18/0.57 78. ((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) ### Imply 76 77
% 0.18/0.57 79. ((growth_rate (first_movers) T_1) != (zero)) ((growth_rate (first_movers) T_1) = (zero)) ### Axiom
% 0.18/0.57 80. ((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) ((growth_rate (first_movers) T_1) != (zero)) ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) ### Imply 78 79
% 0.18/0.57 81. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) ### ConjTree 80
% 0.18/0.57 82. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (zero) (growth_rate (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 67 4 10 17 81
% 0.18/0.57 83. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) ### All 82
% 0.18/0.57 84. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (zero) (growth_rate (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 83
% 0.18/0.57 85. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (first_movers) T_1) != (zero)) ### All 84
% 0.18/0.57 86. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### NotAnd 66 85
% 0.18/0.57 87. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.57 88. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.57 89. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.18/0.57 90. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.57 91. (decreases (cardinality_at_time (efficient_producers) T_1)) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) ### Axiom
% 0.18/0.57 92. (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.18/0.57 93. ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (decreases (cardinality_at_time (efficient_producers) T_1)) ### Imply 91 92
% 0.18/0.57 94. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (decreases (cardinality_at_time (efficient_producers) T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### ConjTree 93
% 0.18/0.57 95. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (decreases (cardinality_at_time (efficient_producers) T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 90 4 24 31 94
% 0.18/0.57 96. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (decreases (cardinality_at_time (efficient_producers) T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### All 95
% 0.18/0.57 97. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (decreases (cardinality_at_time (efficient_producers) T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 96
% 0.18/0.57 98. ((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ### And 97
% 0.18/0.57 99. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 89 42 98 46
% 0.18/0.57 100. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### All 99
% 0.18/0.57 101. (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (greater (growth_rate (efficient_producers) T_1) (zero)) ### Axiom
% 0.18/0.57 102. ((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) ### Imply 100 101
% 0.18/0.57 103. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### ConjTree 102
% 0.18/0.57 104. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 88 4 24 31 103
% 0.18/0.58 105. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 104
% 0.18/0.58 106. (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 105
% 0.18/0.58 107. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 106
% 0.18/0.58 108. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### All 107
% 0.18/0.58 109. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ### All 108
% 0.18/0.58 110. ((growth_rate (first_movers) T_1) != (zero)) ((growth_rate (first_movers) T_1) = (zero)) ### Axiom
% 0.18/0.58 111. ((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 109 110
% 0.18/0.58 112. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) ### ConjTree 111
% 0.18/0.58 113. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 87 4 10 17 112
% 0.18/0.58 114. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) ### All 113
% 0.18/0.58 115. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 114
% 0.18/0.58 116. (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ((growth_rate (first_movers) T_1) != (zero)) ### All 115
% 0.18/0.58 117. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.58 118. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.58 119. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.18/0.58 120. (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (decreases (cardinality_at_time (efficient_producers) T_1)) ### Axiom
% 0.18/0.58 121. ((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) ### And 120
% 0.18/0.58 122. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 119 42 121 70
% 0.18/0.58 123. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### All 122
% 0.18/0.58 124. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### All 123
% 0.18/0.58 125. (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.18/0.58 126. ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) ### Imply 124 125
% 0.18/0.58 127. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### ConjTree 126
% 0.18/0.58 128. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 118 4 24 31 127
% 0.18/0.58 129. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### All 128
% 0.18/0.58 130. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 129
% 0.18/0.58 131. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### All 130
% 0.18/0.58 132. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### All 131
% 0.18/0.58 133. (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (zero) (growth_rate (first_movers) T_1)) ### Axiom
% 0.18/0.58 134. ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (constant (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 132 133
% 0.18/0.58 135. ((growth_rate (first_movers) T_1) != (zero)) ((growth_rate (first_movers) T_1) = (zero)) ### Axiom
% 0.18/0.58 136. ((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) ### Imply 134 135
% 0.18/0.58 137. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) ### ConjTree 136
% 0.18/0.58 138. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 117 4 10 17 137
% 0.18/0.58 139. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) ### All 138
% 0.18/0.58 140. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) ((growth_rate (first_movers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 139
% 0.18/0.58 141. (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) ### All 140
% 0.18/0.59 142. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ((growth_rate (first_movers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### NotAnd 116 141
% 0.18/0.59 143. (-. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (first_movers) T_1) != (zero)) (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ### NotAnd 86 142
% 0.18/0.59 144. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.59 145. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.59 146. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.18/0.59 147. (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (cardinality_at_time (efficient_producers) T_1)) ### Axiom
% 0.18/0.59 148. ((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) ### And 147
% 0.18/0.59 149. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 146 148 44 46
% 0.18/0.59 150. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### All 149
% 0.18/0.59 151. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### All 150
% 0.18/0.59 152. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### All 151
% 0.18/0.59 153. (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (greater (growth_rate (efficient_producers) T_1) (zero)) ### Axiom
% 0.18/0.59 154. ((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 152 153
% 0.18/0.59 155. ((growth_rate (efficient_producers) T_1) != (zero)) ((growth_rate (efficient_producers) T_1) = (zero)) ### Axiom
% 0.18/0.59 156. ((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) ### Imply 154 155
% 0.18/0.59 157. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) ### ConjTree 156
% 0.18/0.59 158. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 145 4 24 31 157
% 0.18/0.59 159. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (increases (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 158
% 0.18/0.59 160. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 159
% 0.18/0.59 161. (-. (greater (growth_rate (first_movers) T_1) (zero))) (greater (growth_rate (first_movers) T_1) (zero)) ### Axiom
% 0.18/0.59 162. ((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ### Imply 160 161
% 0.18/0.59 163. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### ConjTree 162
% 0.18/0.59 164. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 144 4 10 17 163
% 0.18/0.60 165. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### All 164
% 0.18/0.60 166. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 165
% 0.18/0.60 167. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) ### All 166
% 0.18/0.60 168. (-. (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### All 167
% 0.18/0.60 169. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.60 170. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.18/0.60 171. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.18/0.60 172. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 171 148 44 70
% 0.18/0.60 173. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### All 172
% 0.18/0.60 174. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### All 173
% 0.18/0.60 175. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### All 174
% 0.18/0.60 176. ((growth_rate (efficient_producers) T_1) != (zero)) ((growth_rate (efficient_producers) T_1) = (zero)) ### Axiom
% 0.18/0.60 177. ((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 175 176
% 0.18/0.60 178. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) ### ConjTree 177
% 0.18/0.60 179. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 170 4 24 31 178
% 0.18/0.60 180. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 179
% 0.18/0.60 181. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (increases (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 180
% 0.18/0.60 182. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (increases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 181
% 0.18/0.60 183. (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (zero) (growth_rate (first_movers) T_1)) ### Axiom
% 0.18/0.60 184. ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (increases (cardinality_at_time (first_movers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### Imply 182 183
% 0.18/0.60 185. (-. (greater (growth_rate (first_movers) T_1) (zero))) (greater (growth_rate (first_movers) T_1) (zero)) ### Axiom
% 0.18/0.60 186. ((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) ### Imply 184 185
% 0.43/0.60 187. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### ConjTree 186
% 0.43/0.60 188. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) ((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)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 169 4 10 17 187
% 0.43/0.60 189. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### All 188
% 0.43/0.60 190. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) ((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)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 189
% 0.43/0.61 191. (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### All 190
% 0.43/0.61 192. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (growth_rate (first_movers) T_1) (zero))) ### NotAnd 168 191
% 0.43/0.61 193. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.43/0.61 194. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.43/0.61 195. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 194 148 121 46
% 0.43/0.61 196. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### All 195
% 0.43/0.61 197. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### All 196
% 0.43/0.61 198. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) ### All 197
% 0.43/0.61 199. (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.43/0.61 200. ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (increases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 198 199
% 0.43/0.61 201. (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (greater (growth_rate (efficient_producers) T_1) (zero)) ### Axiom
% 0.43/0.61 202. ((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) ### Imply 200 201
% 0.43/0.61 203. ((growth_rate (efficient_producers) T_1) != (zero)) ((growth_rate (efficient_producers) T_1) = (zero)) ### Axiom
% 0.43/0.61 204. ((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) ((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) ### Imply 202 203
% 0.43/0.61 205. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) ### ConjTree 204
% 0.43/0.61 206. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 193 4 24 31 205
% 0.43/0.61 207. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 206
% 0.43/0.61 208. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 207
% 0.43/0.61 209. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (growth_rate (efficient_producers) T_1) (zero))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 208
% 0.43/0.61 210. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.43/0.61 211. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.43/0.61 212. (constant (number_of_organizations T_0 T_1)) (-. (constant (number_of_organizations T_0 T_1))) ### Axiom
% 0.43/0.61 213. ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) (cardinality_at_time (efficient_producers) T_1))) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant (cardinality_at_time (efficient_producers) T_1))) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases (cardinality_at_time (efficient_producers) T_1))) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases (cardinality_at_time (efficient_producers) T_1)))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### DisjTree 39 212 148 121 70
% 0.43/0.61 214. (All C, ((((number_of_organizations T_0 T_1) = (sum (cardinality_at_time (first_movers) T_1) C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant (cardinality_at_time (first_movers) T_1)) /\ (constant C)) \/ (((increases (cardinality_at_time (first_movers) T_1)) /\ (decreases C)) \/ ((decreases (cardinality_at_time (first_movers) T_1)) /\ (increases C)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (first_movers) T_1))) ### All 213
% 0.43/0.61 215. (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (first_movers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) ### All 214
% 0.43/0.61 216. (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (zero) (growth_rate (first_movers) T_1)) ### Axiom
% 0.43/0.61 217. ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (environment T_0) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) ### Imply 215 216
% 0.43/0.61 218. (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1))))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (environment T_0) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### ConjTree 217
% 0.43/0.61 219. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (first_movers) T_0 T_1) /\ (greater (cardinality_at_time (first_movers) T_1) (zero))))) => (((constant (cardinality_at_time (first_movers) T_1)) => ((growth_rate (first_movers) T_1) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T_1)) => (greater (growth_rate (first_movers) T_1) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T_1)) => (greater (zero) (growth_rate (first_movers) T_1)))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 211 4 10 17 218
% 0.43/0.61 220. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (first_movers) T_0 T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### All 219
% 0.43/0.61 221. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (first_movers) E T) /\ (greater (cardinality_at_time (first_movers) T) (zero))))) => (((constant (cardinality_at_time (first_movers) T)) => ((growth_rate (first_movers) T) = (zero))) /\ (((increases (cardinality_at_time (first_movers) T)) => (greater (growth_rate (first_movers) T) (zero))) /\ ((decreases (cardinality_at_time (first_movers) T)) => (greater (zero) (growth_rate (first_movers) T)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 220
% 0.43/0.61 222. (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All B, (All C, ((((number_of_organizations T_0 T_1) = (sum B C)) /\ (constant (number_of_organizations T_0 T_1))) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C))))))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) ### All 221
% 0.43/0.61 223. (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (-. (decreases (cardinality_at_time (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### All 222
% 0.43/0.61 224. (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.43/0.61 225. ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (constant (cardinality_at_time (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### Imply 223 224
% 0.43/0.61 226. ((growth_rate (efficient_producers) T_1) != (zero)) ((growth_rate (efficient_producers) T_1) = (zero)) ### Axiom
% 0.43/0.61 227. ((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))) ### Imply 225 226
% 0.43/0.61 228. (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) ### ConjTree 227
% 0.45/0.62 229. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((subpopulation (efficient_producers) T_0 T_1) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T_1)) => ((growth_rate (efficient_producers) T_1) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T_1)) => (greater (growth_rate (efficient_producers) T_1) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T_1)) => (greater (zero) (growth_rate (efficient_producers) T_1)))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 210 4 24 31 228
% 0.45/0.62 230. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((subpopulation (efficient_producers) T_0 T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 229
% 0.45/0.62 231. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation (efficient_producers) E T) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (((constant (cardinality_at_time (efficient_producers) T)) => ((growth_rate (efficient_producers) T) = (zero))) /\ (((increases (cardinality_at_time (efficient_producers) T)) => (greater (growth_rate (efficient_producers) T) (zero))) /\ ((decreases (cardinality_at_time (efficient_producers) T)) => (greater (zero) (growth_rate (efficient_producers) T)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 230
% 0.45/0.62 232. (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) ### All 231
% 0.45/0.62 233. (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ((growth_rate (efficient_producers) T_1) != (zero)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) ### NotAnd 209 232
% 0.45/0.62 234. (-. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1)))) (constant (number_of_organizations T_0 T_1)) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ((growth_rate (efficient_producers) T_1) != (zero)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (-. ((greater (growth_rate (efficient_producers) T_1) (zero)) /\ (greater (zero) (growth_rate (first_movers) T_1)))) ### NotAnd 192 233
% 0.45/0.62 235. (-. (((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)))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (constant (number_of_organizations T_0 T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (-. ((greater (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1)))) ### NotAnd 143 234
% 0.45/0.62 236. (-. (((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))))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### ConjTree 235
% 0.45/0.62 237. (-. (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)))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) ### NotAllEx 236
% 0.45/0.62 238. (-. (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)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero)))))) (All E, (All X, (All T, (((environment E) /\ ((subpopulation X E T) /\ ((greater (cardinality_at_time X T) (zero)) => ((X = (efficient_producers)) \/ (X = (first_movers)))))) => ((number_of_organizations E T) = (sum (cardinality_at_time (first_movers) T) (cardinality_at_time (efficient_producers) T))))))) (All X, (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((subpopulation X E T) /\ (greater (cardinality_at_time X T) (zero))))) => (((constant (cardinality_at_time X T)) => ((growth_rate X T) = (zero))) /\ (((increases (cardinality_at_time X T)) => (greater (growth_rate X T) (zero))) /\ ((decreases (cardinality_at_time X T)) => (greater (zero) (growth_rate X T))))))))) (All A, (All B, (All C, (((A = (sum B C)) /\ (constant A)) => (((constant B) /\ (constant C)) \/ (((increases B) /\ (decreases C)) \/ ((decreases B) /\ (increases C)))))))) ### NotAllEx 237
% 0.45/0.62 % SZS output end Proof
% 0.45/0.62 (* END-PROOF *)
%------------------------------------------------------------------------------