TSTP Solution File: MGT039+2 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT039+2 : 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 : n017.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 22:27:02 EDT 2022
% Result : Theorem 8.17s 8.36s
% Output : Proof 8.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT039+2 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 11:31:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.17/8.36 % SZS status Theorem
% 8.17/8.36 (* PROOF-FOUND *)
% 8.17/8.36 (* BEGIN-PROOF *)
% 8.17/8.36 % SZS output start Proof
% 8.17/8.36 1. (observational_period T_0) (-. (observational_period T_0)) ### Axiom
% 8.17/8.36 2. (propagation_strategy (first_movers)) (-. (propagation_strategy (first_movers))) ### Axiom
% 8.17/8.36 3. (propagation_strategy (efficient_producers)) (-. (propagation_strategy (efficient_producers))) ### Axiom
% 8.17/8.36 4. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.36 5. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.36 6. (observational_period T_0) (-. (observational_period T_0)) ### Axiom
% 8.17/8.36 7. (slow_change T_0) (-. (slow_change T_0)) ### Axiom
% 8.17/8.36 8. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.36 9. (in_environment T_0 T_1) (-. (in_environment T_0 T_1)) ### Axiom
% 8.17/8.36 10. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.36 11. (in_environment T_1 T_2) (-. (in_environment T_1 T_2)) ### Axiom
% 8.17/8.36 12. (-. (greater (end_time T_1) T_2)) (greater (end_time T_1) T_2) ### Axiom
% 8.17/8.36 13. ((end_time T_1) != T_2) ((end_time T_1) = T_2) ### Axiom
% 8.17/8.36 14. ((greater (end_time T_1) T_2) \/ ((end_time T_1) = T_2)) ((end_time T_1) != T_2) (-. (greater (end_time T_1) T_2)) ### Or 12 13
% 8.17/8.36 15. (greater_or_equal (end_time T_1) T_2) (-. (greater (end_time T_1) T_2)) ((end_time T_1) != T_2) ### Definition-Pseudo(greater_or_equal) 14
% 8.17/8.36 16. (((environment T_1) /\ (in_environment T_1 T_2)) => (greater_or_equal (end_time T_1) T_2)) ((end_time T_1) != T_2) (-. (greater (end_time T_1) T_2)) (in_environment T_1 T_2) (environment T_1) ### DisjTree 10 11 15
% 8.17/8.36 17. (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (environment T_1) (in_environment T_1 T_2) (-. (greater (end_time T_1) T_2)) ((end_time T_1) != T_2) ### All 16
% 8.17/8.36 18. ((critical_point T_1) != (critical_point T_1)) ### Refl(=)
% 8.17/8.36 19. (-. (greater (end_time T_1) (critical_point T_1))) (greater T_2 (critical_point T_1)) (in_environment T_1 T_2) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) ### Trans 17 18
% 8.17/8.36 20. ((in_environment T_1 T_2) /\ (greater T_2 (critical_point T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (environment T_1) (-. (greater (end_time T_1) (critical_point T_1))) ### And 19
% 8.17/8.36 21. (Ex T, ((in_environment T_1 T) /\ (greater T (critical_point T_1)))) (-. (greater (end_time T_1) (critical_point T_1))) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) ### Exists 20
% 8.17/8.36 22. (((environment T_1) /\ (in_environment T_0 T_1)) => (Ex T, ((in_environment T_1 T) /\ (greater T (critical_point T_1))))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (-. (greater (end_time T_1) (critical_point T_1))) (in_environment T_0 T_1) (environment T_1) ### DisjTree 8 9 21
% 8.17/8.36 23. (All E, (((environment E) /\ (in_environment T_0 E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))) (environment T_1) (in_environment T_0 T_1) (-. (greater (end_time T_1) (critical_point T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) ### All 22
% 8.17/8.36 24. (((observational_period T_0) /\ (slow_change T_0)) => (All E, (((environment E) /\ (in_environment T_0 E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E))))))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (-. (greater (end_time T_1) (critical_point T_1))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) ### DisjTree 6 7 23
% 8.17/8.36 25. (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (environment T_1) (in_environment T_0 T_1) (-. (greater (end_time T_1) (critical_point T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) ### All 24
% 8.17/8.36 26. ((start_time T_1) != (start_time T_1)) ### Refl(=)
% 8.17/8.36 27. (-. (greater (end_time T_1) (start_time T_1))) (greater (critical_point T_1) (start_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### Trans 25 26
% 8.17/8.36 28. ((start_time T_1) != (start_time T_1)) ### Refl(=)
% 8.17/8.36 29. (-. (greater (end_time T_1) (start_time T_1))) ((critical_point T_1) = (start_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### TransEq 25 25 28
% 8.17/8.36 30. ((greater (critical_point T_1) (start_time T_1)) \/ ((critical_point T_1) = (start_time T_1))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (environment T_1) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (-. (greater (end_time T_1) (start_time T_1))) ### Or 27 29
% 8.17/8.36 31. (greater_or_equal (critical_point T_1) (start_time T_1)) (-. (greater (end_time T_1) (start_time T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### Definition-Pseudo(greater_or_equal) 30
% 8.17/8.36 32. ((environment T_1) => (greater_or_equal (critical_point T_1) (start_time T_1))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (-. (greater (end_time T_1) (start_time T_1))) (environment T_1) ### Imply 5 31
% 8.17/8.36 33. (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (-. (greater (end_time T_1) (start_time T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### All 32
% 8.17/8.36 34. (-. ((greater (end_time T_1) (start_time T_1)) \/ ((end_time T_1) = (start_time T_1)))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) ### NotOr 33
% 8.17/8.36 35. (-. (greater_or_equal (end_time T_1) (start_time T_1))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### Definition-Pseudo(greater_or_equal) 34
% 8.17/8.38 36. ((end_time T_1) != (end_time T_1)) ### Refl(=)
% 8.17/8.38 37. (-. ((greater (end_time T_1) (end_time T_1)) \/ ((end_time T_1) = (end_time T_1)))) ### NotOr 36
% 8.17/8.38 38. (-. (greater_or_equal (end_time T_1) (end_time T_1))) ### Definition-Pseudo(greater_or_equal) 37
% 8.17/8.38 39. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.38 40. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.38 41. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.38 42. (in_environment T_1 (end_time T_1)) (-. (in_environment T_1 (end_time T_1))) ### Axiom
% 8.17/8.38 43. (-. (subpopulation (efficient_producers) T_1 (end_time T_1))) (subpopulation (efficient_producers) T_1 (end_time T_1)) ### Axiom
% 8.17/8.38 44. ((subpopulation (first_movers) T_1 (end_time T_1)) /\ (subpopulation (efficient_producers) T_1 (end_time T_1))) (-. (subpopulation (efficient_producers) T_1 (end_time T_1))) ### And 43
% 8.17/8.38 45. (((environment T_1) /\ (in_environment T_1 (end_time T_1))) => ((subpopulation (first_movers) T_1 (end_time T_1)) /\ (subpopulation (efficient_producers) T_1 (end_time T_1)))) (-. (subpopulation (efficient_producers) T_1 (end_time T_1))) (in_environment T_1 (end_time T_1)) (environment T_1) ### DisjTree 41 42 44
% 8.17/8.38 46. (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (environment T_1) (in_environment T_1 (end_time T_1)) (-. (subpopulation (efficient_producers) T_1 (end_time T_1))) ### All 45
% 8.17/8.38 47. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.38 48. (in_environment T_1 (end_time T_1)) (-. (in_environment T_1 (end_time T_1))) ### Axiom
% 8.17/8.38 49. (-. (subpopulation (first_movers) T_1 (end_time T_1))) (subpopulation (first_movers) T_1 (end_time T_1)) ### Axiom
% 8.17/8.38 50. ((subpopulation (first_movers) T_1 (end_time T_1)) /\ (subpopulation (efficient_producers) T_1 (end_time T_1))) (-. (subpopulation (first_movers) T_1 (end_time T_1))) ### And 49
% 8.17/8.38 51. (((environment T_1) /\ (in_environment T_1 (end_time T_1))) => ((subpopulation (first_movers) T_1 (end_time T_1)) /\ (subpopulation (efficient_producers) T_1 (end_time T_1)))) (-. (subpopulation (first_movers) T_1 (end_time T_1))) (in_environment T_1 (end_time T_1)) (environment T_1) ### DisjTree 47 48 50
% 8.17/8.38 52. (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (environment T_1) (in_environment T_1 (end_time T_1)) (-. (subpopulation (first_movers) T_1 (end_time T_1))) ### All 51
% 8.17/8.38 53. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.38 54. (in_environment T_1 (end_time T_1)) (-. (in_environment T_1 (end_time T_1))) ### Axiom
% 8.17/8.38 55. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.17/8.38 56. ((appear (efficient_producers) T_1) != (appear (efficient_producers) T_1)) ### Refl(=)
% 8.17/8.38 57. (-. (greater (end_time T_1) (appear (efficient_producers) T_1))) (greater (critical_point T_1) (appear (efficient_producers) T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### Trans 25 56
% 8.17/8.38 58. ((appear (efficient_producers) T_1) != (appear (efficient_producers) T_1)) ### Refl(=)
% 8.17/8.38 59. (-. (greater (end_time T_1) (appear (efficient_producers) T_1))) ((critical_point T_1) = (appear (efficient_producers) T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### TransEq 25 25 58
% 8.17/8.38 60. ((greater (critical_point T_1) (appear (efficient_producers) T_1)) \/ ((critical_point T_1) = (appear (efficient_producers) T_1))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (environment T_1) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (-. (greater (end_time T_1) (appear (efficient_producers) T_1))) ### Or 57 59
% 8.17/8.38 61. (greater_or_equal (critical_point T_1) (appear (efficient_producers) T_1)) (-. (greater (end_time T_1) (appear (efficient_producers) T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### Definition-Pseudo(greater_or_equal) 60
% 8.17/8.38 62. ((environment T_1) => (greater_or_equal (critical_point T_1) (appear (efficient_producers) T_1))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (-. (greater (end_time T_1) (appear (efficient_producers) T_1))) (environment T_1) ### Imply 55 61
% 8.17/8.38 63. (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (environment T_1) (-. (greater (end_time T_1) (appear (efficient_producers) T_1))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### All 62
% 8.17/8.38 64. (-. ((greater (end_time T_1) (appear (efficient_producers) T_1)) \/ ((end_time T_1) = (appear (efficient_producers) T_1)))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) ### NotOr 63
% 8.17/8.38 65. (-. (greater_or_equal (end_time T_1) (appear (efficient_producers) T_1))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) ### Definition-Pseudo(greater_or_equal) 64
% 8.17/8.38 66. (-. (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero))) (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero)) ### Axiom
% 8.17/8.38 67. (((environment T_1) /\ ((in_environment T_1 (end_time T_1)) /\ (greater_or_equal (end_time T_1) (appear (efficient_producers) T_1)))) => (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero))) (-. (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (in_environment T_1 (end_time T_1)) (environment T_1) ### DisjTree 53 54 65 66
% 8.26/8.48 68. (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ (greater_or_equal T (appear (efficient_producers) T_1)))) => (greater (cardinality_at_time (efficient_producers) T) (zero)))) (environment T_1) (in_environment T_1 (end_time T_1)) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (-. (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero))) ### All 67
% 8.26/8.48 69. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (-. (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (in_environment T_1 (end_time T_1)) (environment T_1) ### All 68
% 8.26/8.48 70. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.26/8.48 71. (in_environment T_1 (end_time T_1)) (-. (in_environment T_1 (end_time T_1))) ### Axiom
% 8.26/8.48 72. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.26/8.48 73. (in_environment T_1 (end_time T_1)) (-. (in_environment T_1 (end_time T_1))) ### Axiom
% 8.26/8.48 74. (-. (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero))) (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero)) ### Axiom
% 8.26/8.48 75. ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) ((cardinality_at_time (first_movers) (end_time T_1)) = (zero)) ### Axiom
% 8.26/8.48 76. ((greater (cardinality_at_time (first_movers) (end_time T_1)) (zero)) \/ ((cardinality_at_time (first_movers) (end_time T_1)) = (zero))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) (-. (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero))) ### Or 74 75
% 8.26/8.48 77. (greater_or_equal (cardinality_at_time (first_movers) (end_time T_1)) (zero)) (-. (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) ### Definition-Pseudo(greater_or_equal) 76
% 8.26/8.48 78. (((environment T_1) /\ (in_environment T_1 (end_time T_1))) => (greater_or_equal (cardinality_at_time (first_movers) (end_time T_1)) (zero))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) (-. (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero))) (in_environment T_1 (end_time T_1)) (environment T_1) ### DisjTree 72 73 77
% 8.26/8.48 79. (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero)))) (environment T_1) (in_environment T_1 (end_time T_1)) (-. (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) ### All 78
% 8.26/8.48 80. (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) (-. (greater (cardinality_at_time (first_movers) (end_time T_1)) (zero))) (in_environment T_1 (end_time T_1)) (environment T_1) ### All 79
% 8.26/8.48 81. (-. (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1))) (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1)) ### Axiom
% 8.26/8.48 82. (((environment T_1) /\ ((in_environment T_1 (end_time T_1)) /\ ((greater (cardinality_at_time (first_movers) (end_time T_1)) (zero)) /\ (greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1))) (-. (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (in_environment T_1 (end_time T_1)) (environment T_1) ### DisjTree 70 71 80 69 81
% 8.26/8.48 83. (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (environment T_1) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) ((cardinality_at_time (first_movers) (end_time T_1)) != (zero)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (-. (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1))) ### All 82
% 8.26/8.48 84. (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (selection_favors (efficient_producers) (first_movers) (end_time T_1)) ### Axiom
% 8.26/8.48 85. (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 (end_time T_1)) /\ ((subpopulation (first_movers) T_1 (end_time T_1)) /\ ((greater (cardinality_at_time (efficient_producers) (end_time T_1)) (zero)) /\ ((cardinality_at_time (first_movers) (end_time T_1)) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (-. (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (environment T_1) ### DisjTree 40 46 52 69 83 84
% 8.26/8.50 86. (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) ### All 85
% 8.26/8.50 87. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.26/8.50 88. ((critical_point T_1) != (critical_point T_1)) ### Refl(=)
% 8.26/8.50 89. (observational_period T_0) (-. (observational_period T_0)) ### Axiom
% 8.26/8.50 90. (slow_change T_0) (-. (slow_change T_0)) ### Axiom
% 8.26/8.50 91. (environment T_1) (-. (environment T_1)) ### Axiom
% 8.26/8.50 92. (in_environment T_0 T_1) (-. (in_environment T_0 T_1)) ### Axiom
% 8.26/8.50 93. (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1))) ### Axiom
% 8.26/8.50 94. (((subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1)) /\ (greater (end_time T_1) (critical_point T_1))) => (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (in_environment T_1 T_2) (greater T_2 (critical_point T_1)) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (environment T_1) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) ### DisjTree 86 19 93
% 8.26/8.50 95. (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (greater T_2 (critical_point T_1)) (in_environment T_1 T_2) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) ### All 94
% 8.26/8.50 96. ((in_environment T_1 T_2) /\ (greater T_2 (critical_point T_1))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (environment T_1) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) ### And 95
% 8.26/8.50 97. (Ex T, ((in_environment T_1 T) /\ (greater T (critical_point T_1)))) (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (environment T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) ### Exists 96
% 8.26/8.50 98. (((environment T_1) /\ (in_environment T_0 T_1)) => (Ex T, ((in_environment T_1 T) /\ (greater T (critical_point T_1))))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (in_environment T_0 T_1) (environment T_1) ### DisjTree 91 92 97
% 8.26/8.50 99. (All E, (((environment E) /\ (in_environment T_0 E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))) (environment T_1) (in_environment T_0 T_1) (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) ### All 98
% 8.26/8.50 100. (((observational_period T_0) /\ (slow_change T_0)) => (All E, (((environment E) /\ (in_environment T_0 E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E))))))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) ### DisjTree 89 90 99
% 8.26/8.50 101. (observational_period T_0) (slow_change T_0) (environment T_1) (in_environment T_0 T_1) (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) ### All 100
% 8.26/8.50 102. ((-. (greater (growth_rate (efficient_producers) (critical_point T_1)) (growth_rate (first_movers) (critical_point T_1)))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (in_environment T_0 T_1) (environment T_1) (slow_change T_0) (observational_period T_0) ### And 101
% 8.26/8.50 103. (((environment T_1) /\ ((critical_point T_1) = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) (critical_point T_1)) (growth_rate (first_movers) (critical_point T_1)))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T (critical_point T_1))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (environment T_1) ### DisjTree 87 88 102
% 8.26/8.50 104. (All Tc, (((environment T_1) /\ (Tc = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (environment T_1) (-. (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) ### All 103
% 8.26/8.52 105. (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (selection_favors (efficient_producers) (first_movers) (end_time T_1)) ### Axiom
% 8.26/8.52 106. (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 (end_time T_1)) /\ (greater (growth_rate (efficient_producers) (end_time T_1)) (growth_rate (first_movers) (end_time T_1))))) => (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All Tc, (((environment T_1) /\ (Tc = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (in_environment T_1 (end_time T_1)) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (environment T_1) ### DisjTree 39 86 104 105
% 8.26/8.52 107. (All T, (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) => (selection_favors (efficient_producers) (first_movers) T))) (environment T_1) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (in_environment T_1 (end_time T_1)) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All Tc, (((environment T_1) /\ (Tc = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) ### All 106
% 8.26/8.52 108. (((environment T_1) /\ ((greater_or_equal (end_time T_1) (start_time T_1)) /\ (greater_or_equal (end_time T_1) (end_time T_1)))) => (in_environment T_1 (end_time T_1))) (All Tc, (((environment T_1) /\ (Tc = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) => (selection_favors (efficient_producers) (first_movers) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) ### DisjTree 4 35 38 107
% 8.26/8.52 109. (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All T, (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All T, (((environment T_1) /\ ((in_environment T_1 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_1 T))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All Tc, (((environment T_1) /\ (Tc = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) ### All 108
% 8.26/8.52 110. (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All Tc, (((environment T_1) /\ (Tc = (critical_point T_1))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) => (selection_favors (efficient_producers) (first_movers) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) ### All 109
% 8.26/8.52 111. (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All T, (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => ((subpopulation (first_movers) T_1 T) /\ (subpopulation (efficient_producers) T_1 T)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) ### All 110
% 8.26/8.52 112. (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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All T, (((environment T_1) /\ ((subpopulations (first_movers) (efficient_producers) T_1 T) /\ (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) => (selection_favors (efficient_producers) (first_movers) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) ### All 111
% 8.26/8.53 113. (All S2, (All T, (((environment T_1) /\ ((subpopulations (first_movers) S2 T_1 T) /\ (greater (growth_rate S2 T) (growth_rate (first_movers) T)))) => (selection_favors S2 (first_movers) T)))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) ### All 112
% 8.26/8.53 114. (All S1, (All S2, (All T, (((environment T_1) /\ ((subpopulations S1 S2 T_1 T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation (first_movers) T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time (first_movers) T) = (zero)))))) => (selection_favors (efficient_producers) (first_movers) T))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) ### All 113
% 8.26/8.53 115. (All S2, (All T, (((environment T_1) /\ ((subpopulation (efficient_producers) T_1 T) /\ ((subpopulation S2 T_1 T) /\ ((greater (cardinality_at_time (efficient_producers) T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors (efficient_producers) S2 T)))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All S1, (All S2, (All T, (((environment T_1) /\ ((subpopulations S1 S2 T_1 T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T))))) ### All 114
% 8.26/8.53 116. (All S1, (All S2, (All T, (((environment T_1) /\ ((subpopulation S1 T_1 T) /\ ((subpopulation S2 T_1 T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 T))))) (All S1, (All S2, (All T, (((environment T_1) /\ ((subpopulations S1 S2 T_1 T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) ### All 115
% 8.26/8.53 117. (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All S1, (All S2, (All T, (((environment T_1) /\ ((subpopulation S1 T_1 T) /\ ((subpopulation S2 T_1 T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 T))))) ### All 116
% 8.26/8.53 118. (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All T, (((environment T_1) /\ ((greater_or_equal T (start_time T_1)) /\ (greater_or_equal (end_time T_1) T))) => (in_environment T_1 T))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) ### All 117
% 8.26/8.53 119. (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (environment T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All T, (((environment T_1) /\ (in_environment T_1 T)) => (greater_or_equal (end_time T_1) T))) (in_environment T_0 T_1) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 T)))))) ### All 118
% 8.26/8.53 120. (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (-. (selection_favors (efficient_producers) (first_movers) (end_time T_1))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (in_environment T_0 T_1) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (environment T_1) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) ### All 119
% 8.26/8.53 121. (-. (((environment T_1) /\ (in_environment T_0 T_1)) => (selection_favors (efficient_producers) (first_movers) (end_time T_1)))) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (slow_change T_0) (observational_period T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 T)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) ### ConjTree 120
% 8.26/8.53 122. (-. (All E, (((environment E) /\ (in_environment T_0 E)) => (selection_favors (efficient_producers) (first_movers) (end_time E))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (observational_period T_0) (slow_change T_0) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) ### NotAllEx 121
% 8.26/8.53 123. (-. (selection_favors (efficient_producers) (first_movers) T_0)) (selection_favors (efficient_producers) (first_movers) T_0) ### Axiom
% 8.26/8.53 124. (((observational_period T_0) /\ ((propagation_strategy (first_movers)) /\ ((propagation_strategy (efficient_producers)) /\ (All E, (((environment E) /\ (in_environment T_0 E)) => (selection_favors (efficient_producers) (first_movers) (end_time E))))))) => (selection_favors (efficient_producers) (first_movers) T_0)) (-. (selection_favors (efficient_producers) (first_movers) T_0)) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (slow_change T_0) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 T)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) (propagation_strategy (efficient_producers)) (propagation_strategy (first_movers)) (observational_period T_0) ### DisjTree 1 2 3 122 123
% 8.26/8.53 125. (All P, (((observational_period P) /\ ((propagation_strategy (first_movers)) /\ ((propagation_strategy (efficient_producers)) /\ (All E, (((environment E) /\ (in_environment P E)) => (selection_favors (efficient_producers) (first_movers) (end_time E))))))) => (selection_favors (efficient_producers) (first_movers) P))) (observational_period T_0) (propagation_strategy (first_movers)) (propagation_strategy (efficient_producers)) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (slow_change T_0) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) (-. (selection_favors (efficient_producers) (first_movers) T_0)) ### All 124
% 8.26/8.53 126. (-. (((observational_period T_0) /\ (slow_change T_0)) => (selection_favors (efficient_producers) (first_movers) T_0))) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => ((subpopulation (first_movers) E T) /\ (subpopulation (efficient_producers) E T))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 T)))))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) (propagation_strategy (efficient_producers)) (propagation_strategy (first_movers)) (All P, (((observational_period P) /\ ((propagation_strategy (first_movers)) /\ ((propagation_strategy (efficient_producers)) /\ (All E, (((environment E) /\ (in_environment P E)) => (selection_favors (efficient_producers) (first_movers) (end_time E))))))) => (selection_favors (efficient_producers) (first_movers) P))) ### ConjTree 125
% 8.26/8.53 127. (-. (All P, (((observational_period P) /\ (slow_change P)) => (selection_favors (efficient_producers) (first_movers) P)))) (All P, (((observational_period P) /\ ((propagation_strategy (first_movers)) /\ ((propagation_strategy (efficient_producers)) /\ (All E, (((environment E) /\ (in_environment P E)) => (selection_favors (efficient_producers) (first_movers) (end_time E))))))) => (selection_favors (efficient_producers) (first_movers) P))) (propagation_strategy (first_movers)) (propagation_strategy (efficient_producers)) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (end_time E) T)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulation S1 E T) /\ ((subpopulation S2 E T) /\ ((greater (cardinality_at_time S1 T) (zero)) /\ ((cardinality_at_time S2 T) = (zero)))))) => (selection_favors S1 S2 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) /\ ((in_environment E T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) E T)))) (All E, (All T, (((environment E) /\ (in_environment E T)) => (greater_or_equal (cardinality_at_time (first_movers) T) (zero))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ ((in_environment E T) /\ (greater_or_equal T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All P, (((observational_period P) /\ (slow_change P)) => (All E, (((environment E) /\ (in_environment P E)) => (Ex T, ((in_environment E T) /\ (greater T (critical_point E)))))))) (All E, ((environment E) => (greater_or_equal (critical_point E) (start_time E)))) (All E, (All Tc, (((environment E) /\ (Tc = (critical_point E))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((subpopulations S1 S2 E T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T)))))) (All E, (All T, (((environment E) /\ ((greater_or_equal T (start_time E)) /\ (greater_or_equal (end_time E) T))) => (in_environment E T)))) ### NotAllEx 126
% 8.26/8.53 % SZS output end Proof
% 8.26/8.53 (* END-PROOF *)
%------------------------------------------------------------------------------