TSTP Solution File: MGT034+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT034+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 : n021.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 22:26:59 EDT 2022
% Result : Theorem 0.38s 0.56s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n021.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 10:19:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.38/0.56 % SZS status Theorem
% 0.38/0.56 (* PROOF-FOUND *)
% 0.38/0.56 (* BEGIN-PROOF *)
% 0.38/0.56 % SZS output start Proof
% 0.38/0.56 1. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 2. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 3. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 4. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 5. ((appear (efficient_producers) T_0) != (appear (efficient_producers) T_0)) ### Refl(=)
% 0.38/0.56 6. (-. (greater_or_equal (appear (efficient_producers) T_0) (appear (efficient_producers) T_0))) ### Extension/test/not_mp_greater_or_equal 5
% 0.38/0.56 7. (in_environment T_0 (critical_point T_0)) (-. (in_environment T_0 (critical_point T_0))) ### Axiom
% 0.38/0.56 8. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 9. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 10. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 11. (in_environment T_0 (critical_point T_0)) (-. (in_environment T_0 (critical_point T_0))) ### Axiom
% 0.38/0.56 12. (-. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) ### Axiom
% 0.38/0.56 13. (((environment T_0) /\ (in_environment T_0 (critical_point T_0))) => (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) (in_environment T_0 (critical_point T_0)) (environment T_0) ### DisjTree 10 11 12
% 0.38/0.56 14. (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) (in_environment T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) ### All 13
% 0.38/0.56 15. (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) (greater (critical_point T_0) (appear (efficient_producers) T_0)) ### Axiom
% 0.38/0.56 16. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 17. ((critical_point T_0) != (critical_point T_0)) ### Refl(=)
% 0.38/0.56 18. (-. (greater_or_equal (critical_point T_0) (critical_point T_0))) ### Extension/test/not_mp_greater_or_equal 17
% 0.38/0.56 19. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.38/0.56 20. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) ### Axiom
% 0.38/0.56 21. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) ### Axiom
% 0.38/0.56 22. ((critical_point T_0) = (appear (efficient_producers) T_0)) ((appear (efficient_producers) T_0) != (critical_point T_0)) ### Sym(=)
% 0.38/0.56 23. (-. (greater_or_equal (appear (efficient_producers) T_0) (critical_point T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) ### Extension/test/not_mp_greater_or_equal 22
% 0.38/0.56 24. ((critical_point T_0) = (appear (efficient_producers) T_0)) ((critical_point T_0) != (appear (efficient_producers) T_0)) ### Axiom
% 0.38/0.56 25. (-. (greater_or_equal (critical_point T_0) (appear (efficient_producers) T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) ### Extension/test/not_mp_greater_or_equal 24
% 0.38/0.56 26. (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) ### Axiom
% 0.38/0.56 27. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal (appear (efficient_producers) T_0) (critical_point T_0)) /\ (greater_or_equal (critical_point T_0) (appear (efficient_producers) T_0)))))) => (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) (environment T_0) ### DisjTree 19 20 21 23 25 26
% 0.38/0.56 28. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal (critical_point T_0) T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) ((critical_point T_0) = (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) ### All 27
% 0.38/0.56 29. (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) (environment T_0) ### All 28
% 0.38/0.56 30. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal (critical_point T_0) (critical_point T_0)) /\ (greater_or_equal (critical_point T_0) (critical_point T_0)))))) => (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### DisjTree 16 14 14 18 18 29
% 0.38/0.56 31. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal (critical_point T_0) T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) ### All 30
% 0.38/0.56 32. ((critical_point T_0) = (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### All 31
% 0.39/0.57 33. (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) ### All 32
% 0.39/0.57 34. (greater_or_equal (critical_point T_0) (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) ### Extension/test/mp_greater_or_equal 15 33
% 0.39/0.57 35. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) => (greater_or_equal (critical_point T_0) (appear (efficient_producers) T_0))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### DisjTree 9 14 34
% 0.39/0.57 36. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) ### All 35
% 0.39/0.57 37. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### All 36
% 0.39/0.57 38. (-. (in_environment T_0 (appear (efficient_producers) T_0))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (environment T_0) (in_environment T_0 (critical_point T_0)) ### Extension/test/mp_critical_time_pointsctrp 6 7 8 37
% 0.39/0.57 39. (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) ### Axiom
% 0.39/0.57 40. (((environment T_0) /\ (in_environment T_0 (appear (efficient_producers) T_0))) => (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### DisjTree 4 38 39
% 0.39/0.57 41. (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) ### All 40
% 0.39/0.57 42. (greater T_1 (appear (efficient_producers) T_0)) (-. (greater T_1 (appear (efficient_producers) T_0))) ### Axiom
% 0.39/0.57 43. (-. (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 42
% 0.39/0.57 44. (greater (critical_point T_0) T_1) (-. (greater (critical_point T_0) T_1)) ### Axiom
% 0.39/0.57 45. (-. (greater_or_equal (critical_point T_0) T_1)) (greater (critical_point T_0) T_1) ### Extension/test/not_mp_greater_or_equal 44
% 0.39/0.57 46. (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) ### Axiom
% 0.39/0.57 47. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater_or_equal (critical_point T_0) T_1))))) => (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) ### DisjTree 3 41 14 43 45 46
% 0.39/0.57 48. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater_or_equal (critical_point T_0) T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### All 47
% 0.39/0.57 49. (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) ### All 48
% 0.39/0.57 50. (environment T_0) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### All 49
% 0.39/0.57 51. (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) ### All 50
% 0.39/0.57 52. (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (efficient_producers) (first_movers) T_0 T_1) ### Axiom
% 0.39/0.57 53. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### DisjTree 2 51 52
% 0.39/0.57 54. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (subpopulations (efficient_producers) (first_movers) T_0 T))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) ### All 53
% 0.39/0.57 55. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### All 54
% 0.39/0.58 56. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.58 57. (in_environment T_0 (critical_point T_0)) (-. (in_environment T_0 (critical_point T_0))) ### Axiom
% 0.39/0.58 58. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.58 59. (greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0)))) (-. (greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))))) ### Axiom
% 0.39/0.58 60. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.58 61. ((critical_point T_0) != (critical_point T_0)) ### Refl(=)
% 0.39/0.58 62. (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0))) (-. (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0)))) ### Axiom
% 0.39/0.58 63. ((-. (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0)))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater T (critical_point T_0))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))) (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0))) ### And 62
% 0.39/0.58 64. (((environment T_0) /\ ((critical_point T_0) = (critical_point T_0))) => ((-. (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0)))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater T (critical_point T_0))) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))))) (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0))) (environment T_0) ### DisjTree 60 61 63
% 0.39/0.58 65. (All Tc, (((environment T_0) /\ (Tc = (critical_point T_0))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (environment T_0) (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0))) ### All 64
% 0.39/0.58 66. ((greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0)))) <=> (greater (growth_rate (efficient_producers) (critical_point T_0)) (growth_rate (first_movers) (critical_point T_0)))) (environment T_0) (All Tc, (((environment T_0) /\ (Tc = (critical_point T_0))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0)))) ### Equiv 59 65
% 0.39/0.58 67. (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0)))) (All Tc, (((environment T_0) /\ (Tc = (critical_point T_0))) => ((-. (greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc))) /\ (All T, (((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (greater T Tc)) => (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) (environment T_0) ### All 66
% 0.39/0.58 68. (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_0) (greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0)))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) ### All 67
% 0.39/0.58 69. (-. (greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero))) (greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero)) ### Axiom
% 0.39/0.58 70. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ (-. (greater (zero) (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))))))) => (greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero))) (-. (greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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)))))))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### DisjTree 58 14 68 69
% 0.39/0.58 71. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (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, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (-. (greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero))) ### All 70
% 0.39/0.58 72. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (-. (greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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)))))))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### All 71
% 0.39/0.58 73. (greater (critical_point T_0) T_1) (-. (greater (critical_point T_0) T_1)) ### Axiom
% 0.39/0.58 74. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.58 75. (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1))) ### Axiom
% 0.39/0.58 76. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### DisjTree 74 51 75
% 0.39/0.58 77. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) ### All 76
% 0.39/0.58 78. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### All 77
% 0.39/0.58 79. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.58 80. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) (-. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1)))) ### Axiom
% 0.39/0.58 81. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (-. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))))) (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### DisjTree 79 51 80
% 0.39/0.58 82. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T)))))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) ### All 81
% 0.39/0.59 83. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### All 82
% 0.39/0.59 84. (-. (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) ### Axiom
% 0.39/0.59 85. (((decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))))) => (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) (-. (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) ### DisjTree 78 83 84
% 0.39/0.59 86. (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) ### All 85
% 0.39/0.59 87. (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero)) ### Axiom
% 0.39/0.59 88. (((environment T_0) /\ ((in_environment T_0 (critical_point T_0)) /\ ((greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater (critical_point T_0) T_1))))) => ((decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) => (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero)))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (in_environment T_0 (critical_point T_0)) (environment T_0) ### DisjTree 56 57 72 43 73 86 87
% 0.39/0.59 89. (All To, (((environment T_0) /\ ((in_environment T_0 To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater To T_1))))) => ((decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) => (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))))) (environment T_0) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) ### All 88
% 0.39/0.59 90. (All T, (All To, (((environment T_0) /\ ((in_environment T_0 To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (in_environment T_0 (critical_point T_0)) (environment T_0) ### All 89
% 0.39/0.59 91. (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (environment T_0) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) ### All 90
% 0.39/0.59 92. (-. (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.39/0.59 93. ((greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero)) <=> (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (in_environment T_0 (critical_point T_0)) (environment T_0) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) ### Equiv 91 92
% 0.39/0.59 94. (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (environment T_0) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) ### All 93
% 0.39/0.59 95. (-. (selection_favors (first_movers) (efficient_producers) T_1)) (selection_favors (first_movers) (efficient_producers) T_1) ### Axiom
% 0.39/0.59 96. (((environment T_0) /\ ((subpopulations (efficient_producers) (first_movers) T_0 T_1) /\ (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) => (selection_favors (first_movers) (efficient_producers) T_1)) (-. (selection_favors (first_movers) (efficient_producers) T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) 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, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (environment T_0) ### DisjTree 1 55 94 95
% 0.39/0.59 97. (All T, (((environment T_0) /\ ((subpopulations (efficient_producers) (first_movers) T_0 T) /\ (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) => (selection_favors (first_movers) (efficient_producers) T))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) ### All 96
% 0.39/0.59 98. (All S2, (All T, (((environment T_0) /\ ((subpopulations (efficient_producers) S2 T_0 T) /\ (greater (growth_rate S2 T) (growth_rate (efficient_producers) T)))) => (selection_favors S2 (efficient_producers) T)))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) 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, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (environment T_0) ### All 97
% 0.39/0.59 99. (All S1, (All S2, (All T, (((environment T_0) /\ ((subpopulations S1 S2 T_0 T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T))))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater T_1 (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) ### All 98
% 0.39/0.59 100. (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)))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) 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, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (greater (critical_point T_0) T_1) (greater T_1 (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (environment T_0) ### All 99
% 0.39/0.59 101. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 102. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 103. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 104. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 105. (in_environment T_0 (critical_point T_0)) (-. (in_environment T_0 (critical_point T_0))) ### Axiom
% 0.39/0.59 106. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 107. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 108. (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) (greater (critical_point T_0) (appear (efficient_producers) T_0)) ### Axiom
% 0.39/0.59 109. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.59 110. (T_1 != T_1) ### Refl(=)
% 0.39/0.59 111. ((critical_point T_0) = (appear (efficient_producers) T_0)) ((appear (efficient_producers) T_0) != (critical_point T_0)) ### Sym(=)
% 0.39/0.59 112. (T_1 != (critical_point T_0)) (T_1 = (appear (efficient_producers) T_0)) ((critical_point T_0) = (appear (efficient_producers) T_0)) ### Trans 110 111
% 0.39/0.59 113. (-. (greater_or_equal T_1 (critical_point T_0))) ((critical_point T_0) = (appear (efficient_producers) T_0)) (T_1 = (appear (efficient_producers) T_0)) ### Extension/test/not_mp_greater_or_equal 112
% 0.39/0.59 114. (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) ### Axiom
% 0.39/0.59 115. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T_1 (critical_point T_0)) /\ (greater_or_equal (critical_point T_0) T_1))))) => (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) ((critical_point T_0) = (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### DisjTree 109 14 14 113 45 114
% 0.39/0.59 116. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal (critical_point T_0) T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) ((critical_point T_0) = (appear (efficient_producers) T_0)) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### All 115
% 0.39/0.59 117. (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (critical_point T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) ((critical_point T_0) = (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### All 116
% 0.39/0.59 118. (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) ((critical_point T_0) = (appear (efficient_producers) T_0)) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### All 117
% 0.39/0.59 119. (greater_or_equal (critical_point T_0) (appear (efficient_producers) T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) ### Extension/test/mp_greater_or_equal 108 118
% 0.39/0.59 120. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0))) => (greater_or_equal (critical_point T_0) (appear (efficient_producers) T_0))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (environment T_0) ### DisjTree 107 14 119
% 0.39/0.60 121. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (environment T_0) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (-. (greater (critical_point T_0) (appear (efficient_producers) T_0))) ### All 120
% 0.39/0.60 122. (-. (in_environment T_0 (appear (efficient_producers) T_0))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (environment T_0) (in_environment T_0 (critical_point T_0)) ### Extension/test/mp_critical_time_pointsctrp 6 105 106 121
% 0.39/0.60 123. (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) ### Axiom
% 0.39/0.60 124. (((environment T_0) /\ (in_environment T_0 (appear (efficient_producers) T_0))) => (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (environment T_0) ### DisjTree 104 122 123
% 0.39/0.60 125. (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (-. (subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0))) ### All 124
% 0.39/0.60 126. (T_1 = (appear (efficient_producers) T_0)) (T_1 != (appear (efficient_producers) T_0)) ### Axiom
% 0.39/0.60 127. (-. (greater_or_equal T_1 (appear (efficient_producers) T_0))) (T_1 = (appear (efficient_producers) T_0)) ### Extension/test/not_mp_greater_or_equal 126
% 0.39/0.60 128. (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) ### Axiom
% 0.39/0.60 129. (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater_or_equal (critical_point T_0) T_1))))) => (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) ### DisjTree 103 125 14 127 45 128
% 0.39/0.60 130. (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (critical_point T_0)) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater_or_equal (critical_point T_0) T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))) (environment T_0) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) ### All 129
% 0.39/0.60 131. (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 (appear (efficient_producers) T_0)) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T)))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) ### All 130
% 0.39/0.60 132. (environment T_0) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All T1, (All T2, (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T1) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) T_0 T))))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) ### All 131
% 0.39/0.60 133. (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (environment T_0) ### All 132
% 0.39/0.60 134. (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (efficient_producers) (first_movers) T_0 T_1) ### Axiom
% 0.39/0.60 135. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### DisjTree 102 133 134
% 0.39/0.60 136. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (subpopulations (efficient_producers) (first_movers) T_0 T))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) ### All 135
% 0.39/0.60 137. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### All 136
% 0.39/0.60 138. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.60 139. (in_environment T_0 (critical_point T_0)) (-. (in_environment T_0 (critical_point T_0))) ### Axiom
% 0.39/0.60 140. (greater (critical_point T_0) T_1) (-. (greater (critical_point T_0) T_1)) ### Axiom
% 0.39/0.60 141. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.60 142. (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1))) ### Axiom
% 0.39/0.60 143. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### DisjTree 141 133 142
% 0.39/0.60 144. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) ### All 143
% 0.39/0.60 145. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (-. (decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### All 144
% 0.39/0.60 146. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.39/0.60 147. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) (-. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1)))) ### Axiom
% 0.39/0.60 148. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (-. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))))) (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### DisjTree 146 133 147
% 0.39/0.60 149. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T)))))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) ### All 148
% 0.39/0.60 150. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) ### All 149
% 0.39/0.60 151. (-. (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) ### Axiom
% 0.39/0.60 152. (((decreases (difference (founding_rate (first_movers) T_1) (founding_rate (efficient_producers) T_1))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T_1) (disbanding_rate (efficient_producers) T_1))))) => (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) (-. (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (environment T_0) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) ### DisjTree 145 150 151
% 0.39/0.60 153. (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) ### All 152
% 0.39/0.60 154. (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero)) ### Axiom
% 0.39/0.60 155. (((environment T_0) /\ ((in_environment T_0 (critical_point T_0)) /\ ((greater_or_equal (difference (growth_rate (first_movers) (critical_point T_0)) (growth_rate (efficient_producers) (critical_point T_0))) (zero)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater (critical_point T_0) T_1))))) => ((decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) => (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero)))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)))) (in_environment T_0 (critical_point T_0)) (environment T_0) ### DisjTree 138 139 71 127 140 153 154
% 0.39/0.60 156. (All To, (((environment T_0) /\ ((in_environment T_0 To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater To T_1))))) => ((decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) => (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))))) (environment T_0) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) ### All 155
% 0.39/0.61 157. (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (environment T_0) (All To, (((environment T_0) /\ ((in_environment T_0 To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater To T_1))))) => ((decreases (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) => (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))))) ### All 156
% 0.39/0.61 158. (All T, (All To, (((environment T_0) /\ ((in_environment T_0 To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)))))) (environment T_0) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) ### All 157
% 0.39/0.61 159. (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (-. (greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (environment T_0) ### All 158
% 0.39/0.61 160. (-. (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.39/0.61 161. ((greater (difference (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)) (zero)) <=> (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) (-. (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) (environment T_0) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) ### Equiv 159 160
% 0.39/0.61 162. (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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 E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (environment T_0) (-. (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1))) ### All 161
% 0.39/0.61 163. (-. (selection_favors (first_movers) (efficient_producers) T_1)) (selection_favors (first_movers) (efficient_producers) T_1) ### Axiom
% 0.39/0.61 164. (((environment T_0) /\ ((subpopulations (efficient_producers) (first_movers) T_0 T_1) /\ (greater (growth_rate (first_movers) T_1) (growth_rate (efficient_producers) T_1)))) => (selection_favors (first_movers) (efficient_producers) T_1)) (-. (selection_favors (first_movers) (efficient_producers) 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (environment T_0) ### DisjTree 101 137 162 163
% 0.39/0.61 165. (All T, (((environment T_0) /\ ((subpopulations (efficient_producers) (first_movers) T_0 T) /\ (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) => (selection_favors (first_movers) (efficient_producers) T))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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)))))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) ### All 164
% 0.39/0.61 166. (All S2, (All T, (((environment T_0) /\ ((subpopulations (efficient_producers) S2 T_0 T) /\ (greater (growth_rate S2 T) (growth_rate (efficient_producers) T)))) => (selection_favors S2 (efficient_producers) T)))) (-. (selection_favors (first_movers) (efficient_producers) 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (environment T_0) ### All 165
% 0.39/0.61 167. (All S1, (All S2, (All T, (((environment T_0) /\ ((subpopulations S1 S2 T_0 T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T))))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (greater_or_equal T (appear (efficient_producers) T_0)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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)))))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) ### All 166
% 0.39/0.61 168. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (-. (selection_favors (first_movers) (efficient_producers) 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 T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (in_environment T_0 (critical_point T_0)) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (greater (critical_point T_0) T_1) (T_1 = (appear (efficient_producers) T_0)) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (environment T_0) (All S1, (All S2, (All T, (((environment T_0) /\ ((subpopulations S1 S2 T_0 T) /\ (greater (growth_rate S2 T) (growth_rate S1 T)))) => (selection_favors S2 S1 T))))) ### All 167
% 0.39/0.61 169. (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)))))) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (T_1 = (appear (efficient_producers) T_0)) (greater (critical_point T_0) T_1) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (in_environment T_0 (critical_point T_0)) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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)))))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) ### All 168
% 0.39/0.61 170. (greater_or_equal T_1 (appear (efficient_producers) T_0)) (environment T_0) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (in_environment T_0 (critical_point T_0)) (greater (critical_point T_0) T_1) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (-. (selection_favors (first_movers) (efficient_producers) T_1)) (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)))))) ### Extension/test/mp_greater_or_equal 100 169
% 0.39/0.62 171. (-. (((environment T_0) /\ ((in_environment T_0 (critical_point T_0)) /\ ((greater_or_equal T_1 (appear (efficient_producers) T_0)) /\ (greater (critical_point T_0) T_1)))) => (selection_favors (first_movers) (efficient_producers) T_1))) (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) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) 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, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) ### ConjTree 170
% 0.39/0.62 172. (-. (All T, (((environment T_0) /\ ((in_environment T_0 (critical_point T_0)) /\ ((greater_or_equal T (appear (efficient_producers) T_0)) /\ (greater (critical_point T_0) T)))) => (selection_favors (first_movers) (efficient_producers) T)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All T, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (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, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) 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)))))) ### NotAllEx 171
% 0.39/0.62 173. (-. (All E, (All T, (((environment E) /\ ((in_environment E (critical_point E)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater (critical_point E) T)))) => (selection_favors (first_movers) (efficient_producers) 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) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T)))))) (All T, (((decreases (difference (founding_rate (first_movers) T) (founding_rate (efficient_producers) T))) /\ (-. (decreases (difference (disbanding_rate (first_movers) T) (disbanding_rate (efficient_producers) T))))) => (decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) 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, ((greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) <=> (greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T)))) (All E, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (-. (greater (zero) (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))))) => (greater_or_equal (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))) (All E, (All T, (All To, (((environment E) /\ ((in_environment E To) /\ ((greater_or_equal (difference (growth_rate (first_movers) To) (growth_rate (efficient_producers) To)) (zero)) /\ ((greater_or_equal T (appear (efficient_producers) E)) /\ (greater To T))))) => ((decreases (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T))) => (greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero))))))) (All T, ((greater (difference (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)) (zero)) <=> (greater (growth_rate (first_movers) T) (growth_rate (efficient_producers) T)))) (All E, (All T1, (All T2, (All T, (((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T1) /\ ((subpopulations (first_movers) (efficient_producers) E T2) /\ ((greater_or_equal T T1) /\ (greater_or_equal T2 T))))) => (subpopulations (first_movers) (efficient_producers) E T)))))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (greater_or_equal T (appear (efficient_producers) E))))) (All E, (((environment E) /\ (in_environment E (critical_point E))) => (subpopulations (first_movers) (efficient_producers) E (critical_point E)))) (All E, (((environment E) /\ (in_environment E (appear (efficient_producers) E))) => (subpopulations (first_movers) (efficient_producers) E (appear (efficient_producers) E)))) (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (subpopulations (efficient_producers) (first_movers) E T)))) ### NotAllEx 172
% 0.39/0.62 % SZS output end Proof
% 0.39/0.62 (* END-PROOF *)
%------------------------------------------------------------------------------