TSTP Solution File: MGT027+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:26:57 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 11:50:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 (* PROOF-FOUND *)
% 0.19/0.45 (* BEGIN-PROOF *)
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 1. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 2. (stable T_0) (-. (stable T_0)) ### Axiom
% 0.19/0.45 3. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 4. (stable T_0) (-. (stable T_0)) ### Axiom
% 0.19/0.45 5. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 6. (stable T_0) (-. (stable T_0)) ### Axiom
% 0.19/0.45 7. (-. (in_environment T_0 (appear (efficient_producers) T_0))) (in_environment T_0 (appear (efficient_producers) T_0)) ### Axiom
% 0.19/0.45 8. (((environment T_0) /\ (stable T_0)) => (in_environment T_0 (appear (efficient_producers) T_0))) (-. (in_environment T_0 (appear (efficient_producers) T_0))) (stable T_0) (environment T_0) ### DisjTree 5 6 7
% 0.19/0.45 9. (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (environment T_0) (stable T_0) (-. (in_environment T_0 (appear (efficient_producers) T_0))) ### All 8
% 0.19/0.45 10. (greater T_1 (appear (efficient_producers) T_0)) (-. (greater T_1 (appear (efficient_producers) T_0))) ### Axiom
% 0.19/0.45 11. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 12. (stable T_0) (-. (stable T_0)) ### Axiom
% 0.19/0.45 13. (in_environment T_0 T_1) (-. (in_environment T_0 T_1)) ### Axiom
% 0.19/0.45 14. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 15. (stable T_0) (-. (stable T_0)) ### Axiom
% 0.19/0.45 16. (in_environment T_0 T_1) (-. (in_environment T_0 T_1)) ### Axiom
% 0.19/0.45 17. (greater T_2 T_1) (-. (greater T_2 T_1)) ### Axiom
% 0.19/0.45 18. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 19. (in_environment T_0 T_2) (-. (in_environment T_0 T_2)) ### Axiom
% 0.19/0.45 20. (greater (cardinality_at_time (first_movers) T_2) (zero)) (-. (greater (cardinality_at_time (first_movers) T_2) (zero))) ### Axiom
% 0.19/0.45 21. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.45 22. (in_environment T_0 T_2) (-. (in_environment T_0 T_2)) ### Axiom
% 0.19/0.45 23. (greater T_2 T_1) (-. (greater T_2 T_1)) ### Axiom
% 0.19/0.45 24. (greater T_1 (appear (efficient_producers) T_0)) (-. (greater T_1 (appear (efficient_producers) T_0))) ### Axiom
% 0.19/0.45 25. (-. (greater T_2 (appear (efficient_producers) T_0))) (greater T_2 (appear (efficient_producers) T_0)) ### Axiom
% 0.19/0.45 26. (((greater T_2 T_1) /\ (greater T_1 (appear (efficient_producers) T_0))) => (greater T_2 (appear (efficient_producers) T_0))) (-. (greater T_2 (appear (efficient_producers) T_0))) (greater T_1 (appear (efficient_producers) T_0)) (greater T_2 T_1) ### DisjTree 23 24 25
% 0.19/0.45 27. (All Z, (((greater T_2 T_1) /\ (greater T_1 Z)) => (greater T_2 Z))) (greater T_2 T_1) (greater T_1 (appear (efficient_producers) T_0)) (-. (greater T_2 (appear (efficient_producers) T_0))) ### All 26
% 0.19/0.45 28. (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (-. (greater T_2 (appear (efficient_producers) T_0))) (greater T_1 (appear (efficient_producers) T_0)) (greater T_2 T_1) ### All 27
% 0.19/0.45 29. (-. (greater_or_equal T_2 (appear (efficient_producers) T_0))) (greater T_2 T_1) (greater T_1 (appear (efficient_producers) T_0)) (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) ### Extension/test/not_mp_greater_or_equal 28
% 0.19/0.45 30. (-. (greater (cardinality_at_time (efficient_producers) T_2) (zero))) (greater (cardinality_at_time (efficient_producers) T_2) (zero)) ### Axiom
% 0.19/0.45 31. (((environment T_0) /\ ((in_environment T_0 T_2) /\ (greater_or_equal T_2 (appear (efficient_producers) T_0)))) => (greater (cardinality_at_time (efficient_producers) T_2) (zero))) (-. (greater (cardinality_at_time (efficient_producers) T_2) (zero))) (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (greater T_1 (appear (efficient_producers) T_0)) (greater T_2 T_1) (in_environment T_0 T_2) (environment T_0) ### DisjTree 21 22 29 30
% 0.19/0.45 32. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ (greater_or_equal T (appear (efficient_producers) T_0)))) => (greater (cardinality_at_time (efficient_producers) T) (zero)))) (environment T_0) (in_environment T_0 T_2) (greater T_2 T_1) (greater T_1 (appear (efficient_producers) T_0)) (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (-. (greater (cardinality_at_time (efficient_producers) T_2) (zero))) ### All 31
% 0.19/0.45 33. (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) T_2) (zero))) (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (greater T_1 (appear (efficient_producers) T_0)) (greater T_2 T_1) (in_environment T_0 T_2) (environment T_0) ### All 32
% 0.19/0.45 34. (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (subpopulations (first_movers) (efficient_producers) T_0 T_2) ### Axiom
% 0.19/0.45 35. (((environment T_0) /\ ((in_environment T_0 T_2) /\ ((greater (cardinality_at_time (first_movers) T_2) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T_2) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (greater T_2 T_1) (greater T_1 (appear (efficient_producers) T_0)) (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (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 (first_movers) T_2) (zero)) (in_environment T_0 T_2) (environment T_0) ### DisjTree 18 19 20 33 34
% 0.19/0.45 36. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (in_environment T_0 T_2) (greater (cardinality_at_time (first_movers) T_2) (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 Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (greater T_1 (appear (efficient_producers) T_0)) (greater T_2 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) ### All 35
% 0.19/0.45 37. (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)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (greater T_2 T_1) (greater T_1 (appear (efficient_producers) T_0)) (All Y, (All Z, (((greater T_2 Y) /\ (greater Y Z)) => (greater T_2 Z)))) (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 (first_movers) T_2) (zero)) (in_environment T_0 T_2) (environment T_0) ### All 36
% 0.19/0.45 38. (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (environment T_0) (in_environment T_0 T_2) (greater (cardinality_at_time (first_movers) T_2) (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))))) (greater T_1 (appear (efficient_producers) T_0)) (greater T_2 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (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 37
% 0.19/0.45 39. (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T_1) /\ (greater T_2 T_1)))) => (in_environment T_0 T_2)) (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)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (greater T_1 (appear (efficient_producers) T_0)) (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 (first_movers) T_2) (zero)) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (greater T_2 T_1) (in_environment T_0 T_1) (stable T_0) (environment T_0) ### DisjTree 14 15 16 17 38
% 0.19/0.46 40. (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T_1) /\ (greater T2 T_1)))) => (in_environment T_0 T2))) (environment T_0) (stable T_0) (in_environment T_0 T_1) (greater T_2 T_1) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (greater (cardinality_at_time (first_movers) T_2) (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))))) (greater T_1 (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_2)) (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 39
% 0.19/0.46 41. (greater T_2 T_1) (-. (greater T_2 T_1)) ### Axiom
% 0.19/0.46 42. (-. (greater_or_equal T_2 T_1)) (greater T_2 T_1) ### Extension/test/not_mp_greater_or_equal 41
% 0.19/0.46 43. (-. (greater (zero) (growth_rate (first_movers) T_2))) (greater (zero) (growth_rate (first_movers) T_2)) ### Axiom
% 0.19/0.46 44. (((subpopulations (first_movers) (efficient_producers) T_0 T_2) /\ (greater_or_equal T_2 T_1)) => (greater (zero) (growth_rate (first_movers) T_2))) (-. (greater (zero) (growth_rate (first_movers) T_2))) (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)))) (greater T_1 (appear (efficient_producers) T_0)) (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 (first_movers) T_2) (zero)) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (greater T_2 T_1) (in_environment T_0 T_1) (stable T_0) (environment T_0) (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T_1) /\ (greater T2 T_1)))) => (in_environment T_0 T2))) ### DisjTree 40 42 43
% 0.19/0.46 45. (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T_1) /\ (greater T2 T_1)))) => (in_environment T_0 T2))) (environment T_0) (stable T_0) (in_environment T_0 T_1) (greater T_2 T_1) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (greater (cardinality_at_time (first_movers) T_2) (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))))) (greater T_1 (appear (efficient_producers) T_0)) (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)))) (-. (greater (zero) (growth_rate (first_movers) T_2))) ### All 44
% 0.19/0.46 46. (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (-. (greater (zero) (growth_rate (first_movers) T_2))) (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)))) (greater T_1 (appear (efficient_producers) T_0)) (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 (first_movers) T_2) (zero)) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (greater T_2 T_1) (in_environment T_0 T_1) (stable T_0) (environment T_0) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) ### All 45
% 0.19/0.46 47. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.46 48. (in_environment T_0 T_1) (-. (in_environment T_0 T_1)) ### Axiom
% 0.19/0.46 49. ((first_movers) != (first_movers)) ### NotEqual
% 0.19/0.46 50. (T_2 = T_1) (T_2 != T_1) ### Axiom
% 0.19/0.46 51. ((cardinality_at_time (first_movers) T_2) != (cardinality_at_time (first_movers) T_1)) (T_2 = T_1) ### NotEqual 49 50
% 0.19/0.46 52. ((zero) != (zero)) ### NotEqual
% 0.19/0.46 53. (-. (greater (cardinality_at_time (first_movers) T_1) (zero))) (greater (cardinality_at_time (first_movers) T_2) (zero)) (T_2 = T_1) ### P-NotP 51 52
% 0.19/0.46 54. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.46 55. (in_environment T_0 T_1) (-. (in_environment T_0 T_1)) ### Axiom
% 0.19/0.46 56. (greater T_1 (appear (efficient_producers) T_0)) (-. (greater T_1 (appear (efficient_producers) T_0))) ### Axiom
% 0.19/0.46 57. (-. (greater_or_equal T_1 (appear (efficient_producers) T_0))) (greater T_1 (appear (efficient_producers) T_0)) ### Extension/test/not_mp_greater_or_equal 56
% 0.19/0.46 58. (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (greater (cardinality_at_time (efficient_producers) T_1) (zero)) ### Axiom
% 0.19/0.46 59. (((environment T_0) /\ ((in_environment T_0 T_1) /\ (greater_or_equal T_1 (appear (efficient_producers) T_0)))) => (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 T_1) (environment T_0) ### DisjTree 54 55 57 58
% 0.19/0.46 60. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ (greater_or_equal T (appear (efficient_producers) T_0)))) => (greater (cardinality_at_time (efficient_producers) T) (zero)))) (environment T_0) (in_environment T_0 T_1) (greater T_1 (appear (efficient_producers) T_0)) (-. (greater (cardinality_at_time (efficient_producers) T_1) (zero))) ### All 59
% 0.19/0.46 61. (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) T_1) (zero))) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 T_1) (environment T_0) ### All 60
% 0.19/0.46 62. (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) ### Axiom
% 0.19/0.46 63. (((environment T_0) /\ ((in_environment T_0 T_1) /\ ((greater (cardinality_at_time (first_movers) T_1) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T_1) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater T_1 (appear (efficient_producers) T_0)) (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))))) (T_2 = T_1) (greater (cardinality_at_time (first_movers) T_2) (zero)) (in_environment T_0 T_1) (environment T_0) ### DisjTree 47 48 53 61 62
% 0.19/0.46 64. (All T, (((environment T_0) /\ ((in_environment T_0 T) /\ ((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater (cardinality_at_time (efficient_producers) T) (zero))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (in_environment T_0 T_1) (greater (cardinality_at_time (first_movers) T_2) (zero)) (T_2 = 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))))) (greater T_1 (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### All 63
% 0.19/0.47 65. (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)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater T_1 (appear (efficient_producers) T_0)) (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))))) (T_2 = T_1) (greater (cardinality_at_time (first_movers) T_2) (zero)) (in_environment T_0 T_1) (environment T_0) ### All 64
% 0.19/0.47 66. (T_1 != T_1) ### Refl(=)
% 0.19/0.47 67. (-. (greater_or_equal T_1 T_1)) ### Extension/test/not_mp_greater_or_equal 66
% 0.19/0.47 68. (T_2 = T_1) (T_1 != T_2) ### Sym(=)
% 0.19/0.47 69. ((growth_rate (first_movers) T_1) != (growth_rate (first_movers) T_2)) (T_2 = T_1) ### NotEqual 49 68
% 0.19/0.47 70. (-. (greater (zero) (growth_rate (first_movers) T_2))) (greater (zero) (growth_rate (first_movers) T_1)) (T_2 = T_1) ### P-NotP 52 69
% 0.19/0.47 71. (((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (greater_or_equal T_1 T_1)) => (greater (zero) (growth_rate (first_movers) T_1))) (-. (greater (zero) (growth_rate (first_movers) T_2))) (environment T_0) (in_environment T_0 T_1) (greater (cardinality_at_time (first_movers) T_2) (zero)) (T_2 = 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))))) (greater T_1 (appear (efficient_producers) T_0)) (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)))) ### DisjTree 65 67 70
% 0.19/0.47 72. (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) 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)))) (greater T_1 (appear (efficient_producers) T_0)) (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))))) (T_2 = T_1) (greater (cardinality_at_time (first_movers) T_2) (zero)) (in_environment T_0 T_1) (environment T_0) (-. (greater (zero) (growth_rate (first_movers) T_2))) ### All 71
% 0.19/0.47 73. (greater_or_equal T_2 T_1) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (environment T_0) (stable T_0) (in_environment T_0 T_1) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (greater (cardinality_at_time (first_movers) T_2) (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))))) (greater T_1 (appear (efficient_producers) T_0)) (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)))) (-. (greater (zero) (growth_rate (first_movers) T_2))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) ### Extension/test/mp_greater_or_equal 46 72
% 0.19/0.47 74. (-. (((greater (cardinality_at_time (first_movers) T_2) (zero)) /\ (greater_or_equal T_2 T_1)) => (greater (zero) (growth_rate (first_movers) T_2)))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (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)))) (greater T_1 (appear (efficient_producers) T_0)) (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 X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (in_environment T_0 T_1) (stable T_0) (environment T_0) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) ### ConjTree 73
% 0.19/0.47 75. (-. (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T))))) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (environment T_0) (stable T_0) (in_environment T_0 T_1) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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 T_1 (appear (efficient_producers) T_0)) (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 T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) ### NotAllEx 74
% 0.19/0.47 76. (greater T_1 (appear (efficient_producers) T_0)) (-. (greater T_1 (appear (efficient_producers) T_0))) ### Axiom
% 0.19/0.47 77. (contracts_from T_1 (first_movers)) (-. (contracts_from T_1 (first_movers))) ### Axiom
% 0.19/0.47 78. (-. ((greater T_1 (appear (efficient_producers) T_0)) /\ (contracts_from T_1 (first_movers)))) (contracts_from T_1 (first_movers)) (greater T_1 (appear (efficient_producers) T_0)) ### NotAnd 76 77
% 0.19/0.47 79. (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (greater T_1 (appear (efficient_producers) T_0)) (contracts_from T_1 (first_movers)) ### NotExists 78
% 0.19/0.47 80. (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T_1) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from T_1 (first_movers))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (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)))) (greater T_1 (appear (efficient_producers) T_0)) (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 X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (in_environment T_0 T_1) (stable T_0) (environment T_0) ### DisjTree 11 12 13 75 79
% 0.19/0.47 81. (All To, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers)))) (environment T_0) (stable T_0) (in_environment T_0 T_1) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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 T_1 (appear (efficient_producers) T_0)) (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 T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) ### All 80
% 0.19/0.47 82. (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 (appear (efficient_producers) T_0)) /\ (greater T_1 (appear (efficient_producers) T_0))))) => (in_environment T_0 T_1)) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (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 T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (All To, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers)))) (greater T_1 (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (stable T_0) (environment T_0) ### DisjTree 3 4 9 10 81
% 0.19/0.47 83. (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 (appear (efficient_producers) T_0)) /\ (greater T2 (appear (efficient_producers) T_0))))) => (in_environment T_0 T2))) (environment T_0) (stable T_0) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (greater T_1 (appear (efficient_producers) T_0)) (All To, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers)))) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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, (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 T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) ### All 82
% 0.19/0.47 84. (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (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 T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (All To, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers)))) (greater T_1 (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (stable T_0) (environment T_0) ### All 83
% 0.19/0.47 85. (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (environment T_0) (stable T_0) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (greater T_1 (appear (efficient_producers) T_0)) (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T)))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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, (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 T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) ### All 84
% 0.19/0.47 86. ((greater T_1 (appear (efficient_producers) T_0)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T T_1)) => (greater (zero) (growth_rate (first_movers) T))))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (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 T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (stable T_0) (environment T_0) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) ### And 85
% 0.19/0.47 87. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T)))))) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (environment T_0) (stable T_0) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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, (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 T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) ### Exists 86
% 0.19/0.47 88. (((environment T_0) /\ (stable T_0)) => (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (All T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (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 T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (stable T_0) (environment T_0) ### DisjTree 1 2 87
% 0.19/0.47 89. (All E, (((environment E) /\ (stable E)) => (Ex To, ((greater To (appear (efficient_producers) E)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T)))))))) (environment T_0) (stable T_0) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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, (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 T1, (All T2, (((environment T_0) /\ ((stable T_0) /\ ((in_environment T_0 T1) /\ (greater T2 T1)))) => (in_environment T_0 T2)))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) ### All 88
% 0.19/0.47 90. (All E, (All T1, (All T2, (((environment E) /\ ((stable E) /\ ((in_environment E T1) /\ (greater T2 T1)))) => (in_environment E T2))))) (-. (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers))))) (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 T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (stable T_0) (environment T_0) (All E, (((environment E) /\ (stable E)) => (Ex To, ((greater To (appear (efficient_producers) E)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T)))))))) ### All 89
% 0.19/0.47 91. (-. (((environment T_0) /\ (stable T_0)) => (Ex To, ((greater To (appear (efficient_producers) T_0)) /\ (contracts_from To (first_movers)))))) (All E, (((environment E) /\ (stable E)) => (Ex To, ((greater To (appear (efficient_producers) E)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T)))))))) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (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, (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 T1, (All T2, (((environment E) /\ ((stable E) /\ ((in_environment E T1) /\ (greater T2 T1)))) => (in_environment E T2))))) ### ConjTree 90
% 0.19/0.47 92. (-. (All E, (((environment E) /\ (stable E)) => (Ex To, ((greater To (appear (efficient_producers) E)) /\ (contracts_from To (first_movers))))))) (All E, (All T1, (All T2, (((environment E) /\ ((stable E) /\ ((in_environment E T1) /\ (greater T2 T1)))) => (in_environment E T2))))) (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 T (appear (efficient_producers) E)))) => (greater (cardinality_at_time (efficient_producers) T) (zero))))) (All X, (All Y, (All Z, (((greater X Y) /\ (greater Y Z)) => (greater X Z))))) (All E, (((environment E) /\ (stable E)) => (in_environment E (appear (efficient_producers) E)))) (All E, (All To, (((environment E) /\ ((stable E) /\ ((in_environment E To) /\ (All T, (((greater (cardinality_at_time (first_movers) T) (zero)) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T))))))) => (contracts_from To (first_movers))))) (All E, (((environment E) /\ (stable E)) => (Ex To, ((greater To (appear (efficient_producers) E)) /\ (All T, (((subpopulations (first_movers) (efficient_producers) E T) /\ (greater_or_equal T To)) => (greater (zero) (growth_rate (first_movers) T)))))))) ### NotAllEx 91
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 (* END-PROOF *)
%------------------------------------------------------------------------------