%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT034+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:24:20 AM UTC 2026 % Result : Theorem 0.95s 1.21s % Output : Proof 0.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT034+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.07/0.33 % Computer : n018.cluster.edu % 0.07/0.33 % Model : x86_64 x86_64 % 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.33 % Memory : 8046.5625MB % 0.07/0.33 % OS : Linux 6.8.0-71-generic % 0.07/0.33 % CPULimit : 300 % 0.07/0.33 % WCLimit : 300 % 0.07/0.33 % DateTime : Mon Sep 7 12:33:22 UTC 2026 % 0.07/0.34 % CPUTime : % 0.95/1.21 (* PROOF-FOUND *) % 0.95/1.21 % SZS status Theorem % 0.95/1.21 (* BEGIN-PROOF *) % 0.95/1.21 % SZS output start Proof % 0.95/1.21 Theorem prove_t3 : (forall E : zenon_U, (forall T : zenon_U, (((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)))). % 0.95/1.21 Proof. % 0.95/1.21 assert (zenon_L1_ : forall (zenon_TE_w : zenon_U), (~(greater_or_equal (appear (efficient_producers) zenon_TE_w) (appear (efficient_producers) zenon_TE_w))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H15. % 0.95/1.21 generalize (mp_greater_or_equal (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H17. % 0.95/1.21 generalize (zenon_H17 (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H18. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H15; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_H19 ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.95/1.21 apply zenon_H1c. apply refl_equal. % 0.95/1.21 exact (zenon_H15 zenon_H1a). % 0.95/1.21 (* end of lemma zenon_L1_ *) % 0.95/1.21 assert (zenon_L2_ : forall (zenon_TE_w : zenon_U), (environment zenon_TE_w) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (~(subpopulations (first_movers) (efficient_producers) zenon_TE_w (critical_point zenon_TE_w))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H1e zenon_H1f zenon_H20. % 0.95/1.21 generalize (mp_critical_point_means_FM_and_EP zenon_TE_w). zenon_intro zenon_H21. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 exact (zenon_H24 zenon_H1f). % 0.95/1.21 exact (zenon_H20 zenon_H22). % 0.95/1.21 (* end of lemma zenon_L2_ *) % 0.95/1.21 assert (zenon_L3_ : forall (zenon_TE_w : zenon_U), (~(greater_or_equal (critical_point zenon_TE_w) (critical_point zenon_TE_w))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H26. % 0.95/1.21 generalize (mp_greater_or_equal (critical_point zenon_TE_w)). zenon_intro zenon_H27. % 0.95/1.21 generalize (zenon_H27 (critical_point zenon_TE_w)). zenon_intro zenon_H28. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H26; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.95/1.21 apply zenon_H2c. apply refl_equal. % 0.95/1.21 exact (zenon_H26 zenon_H2a). % 0.95/1.21 (* end of lemma zenon_L3_ *) % 0.95/1.21 assert (zenon_L4_ : forall (zenon_TE_w : zenon_U), (forall T : zenon_U, (((environment zenon_TE_w)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_w T))->(greater_or_equal T (appear (efficient_producers) zenon_TE_w)))) -> (environment zenon_TE_w) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (~((greater (critical_point zenon_TE_w) (appear (efficient_producers) zenon_TE_w))\/((critical_point zenon_TE_w) = (appear (efficient_producers) zenon_TE_w)))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H2e zenon_H1e zenon_H1f zenon_H2f. % 0.95/1.21 generalize (zenon_H2e (critical_point zenon_TE_w)). zenon_intro zenon_H30. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H25 | zenon_intro zenon_H20 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 generalize (mp_greater_or_equal (critical_point zenon_TE_w)). zenon_intro zenon_H27. % 0.95/1.21 generalize (zenon_H27 (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H33. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H35; zenon_intro zenon_H2f | zenon_intro zenon_H31; zenon_intro zenon_H34 ]. % 0.95/1.21 exact (zenon_H35 zenon_H31). % 0.95/1.21 exact (zenon_H2f zenon_H34). % 0.95/1.21 (* end of lemma zenon_L4_ *) % 0.95/1.21 assert (zenon_L5_ : forall (zenon_TE_w : zenon_U), (environment zenon_TE_w) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (~(greater_or_equal (critical_point zenon_TE_w) (appear (efficient_producers) zenon_TE_w))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H1e zenon_H1f zenon_H35. % 0.95/1.21 generalize (mp_greater_or_equal (critical_point zenon_TE_w)). zenon_intro zenon_H27. % 0.95/1.21 generalize (zenon_H27 (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H33. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H35; zenon_intro zenon_H2f | zenon_intro zenon_H31; zenon_intro zenon_H34 ]. % 0.95/1.21 generalize (mp_FM_and_EP_members_EP_appeared zenon_TE_w). zenon_intro zenon_H2e. % 0.95/1.21 apply (zenon_L4_ zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H35 zenon_H31). % 0.95/1.21 (* end of lemma zenon_L5_ *) % 0.95/1.21 assert (zenon_L6_ : forall (zenon_TE_w : zenon_U), (forall T : zenon_U, (((environment zenon_TE_w)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w (critical_point zenon_TE_w))/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w (critical_point zenon_TE_w))/\((greater_or_equal T (critical_point zenon_TE_w))/\(greater_or_equal (critical_point zenon_TE_w) T)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_w T))) -> (environment zenon_TE_w) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_w (critical_point zenon_TE_w)) -> ((critical_point zenon_TE_w) = (appear (efficient_producers) zenon_TE_w)) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (~(subpopulations (first_movers) (efficient_producers) zenon_TE_w (appear (efficient_producers) zenon_TE_w))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H36 zenon_H1e zenon_H22 zenon_H37 zenon_H1f zenon_H38. % 0.95/1.21 generalize (zenon_H36 (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H39. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H25 | zenon_intro zenon_H3c ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H20 | zenon_intro zenon_H3d ]. % 0.95/1.21 exact (zenon_H20 zenon_H22). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H20 | zenon_intro zenon_H3e ]. % 0.95/1.21 exact (zenon_H20 zenon_H22). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H3f | zenon_intro zenon_H35 ]. % 0.95/1.21 generalize (mp_greater_or_equal (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H17. % 0.95/1.21 generalize (zenon_H17 (critical_point zenon_TE_w)). zenon_intro zenon_H40. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H40); [ zenon_intro zenon_H3f; zenon_intro zenon_H43 | zenon_intro zenon_H42; zenon_intro zenon_H41 ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 0.95/1.21 apply zenon_H44. apply sym_equal. exact zenon_H37. % 0.95/1.21 exact (zenon_H3f zenon_H42). % 0.95/1.21 apply (zenon_L5_ zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H38 zenon_H3a). % 0.95/1.21 (* end of lemma zenon_L6_ *) % 0.95/1.21 assert (zenon_L7_ : forall (zenon_TE_w : zenon_U), (forall T2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_w)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w (critical_point zenon_TE_w))/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w T2)/\((greater_or_equal T (critical_point zenon_TE_w))/\(greater_or_equal T2 T)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_w T)))) -> (~(subpopulations (first_movers) (efficient_producers) zenon_TE_w (appear (efficient_producers) zenon_TE_w))) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> ((critical_point zenon_TE_w) = (appear (efficient_producers) zenon_TE_w)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_w (critical_point zenon_TE_w)) -> (environment zenon_TE_w) -> False). % 0.95/1.21 do 1 intro. intros zenon_H46 zenon_H38 zenon_H1f zenon_H37 zenon_H22 zenon_H1e. % 0.95/1.21 generalize (zenon_H46 (critical_point zenon_TE_w)). zenon_intro zenon_H36. % 0.95/1.21 apply (zenon_L6_ zenon_TE_w); trivial. % 0.95/1.21 (* end of lemma zenon_L7_ *) % 0.95/1.21 assert (zenon_L8_ : forall (zenon_TE_w : zenon_U) (zenon_TT_cv : zenon_U), (greater zenon_TT_cv (appear (efficient_producers) zenon_TE_w)) -> (~(greater_or_equal zenon_TT_cv (appear (efficient_producers) zenon_TE_w))) -> False). % 0.95/1.21 do 2 intro. intros zenon_H47 zenon_H48. % 0.95/1.21 generalize (mp_greater_or_equal zenon_TT_cv). zenon_intro zenon_H4a. % 0.95/1.21 generalize (zenon_H4a (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H4b. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H48; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.95/1.21 exact (zenon_H50 zenon_H47). % 0.95/1.21 exact (zenon_H48 zenon_H4d). % 0.95/1.21 (* end of lemma zenon_L8_ *) % 0.95/1.21 assert (zenon_L9_ : forall (zenon_TT_cv : zenon_U) (zenon_TE_w : zenon_U), (greater (critical_point zenon_TE_w) zenon_TT_cv) -> (~(greater_or_equal (critical_point zenon_TE_w) zenon_TT_cv)) -> False). % 0.95/1.21 do 2 intro. intros zenon_H51 zenon_H52. % 0.95/1.21 generalize (mp_greater_or_equal (critical_point zenon_TE_w)). zenon_intro zenon_H27. % 0.95/1.21 generalize (zenon_H27 zenon_TT_cv). zenon_intro zenon_H53. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H53); [ zenon_intro zenon_H52; zenon_intro zenon_H56 | zenon_intro zenon_H55; zenon_intro zenon_H54 ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 0.95/1.21 exact (zenon_H58 zenon_H51). % 0.95/1.21 exact (zenon_H52 zenon_H55). % 0.95/1.21 (* end of lemma zenon_L9_ *) % 0.95/1.21 assert (zenon_L10_ : forall (zenon_TT_cv : zenon_U) (zenon_TE_w : zenon_U), (~(subpopulations (first_movers) (efficient_producers) zenon_TE_w zenon_TT_cv)) -> (greater (critical_point zenon_TE_w) zenon_TT_cv) -> (greater zenon_TT_cv (appear (efficient_producers) zenon_TE_w)) -> (forall T : zenon_U, (((environment zenon_TE_w)/\((in_environment zenon_TE_w (critical_point zenon_TE_w))/\((greater_or_equal T (appear (efficient_producers) zenon_TE_w))/\(greater (critical_point zenon_TE_w) T))))->(in_environment zenon_TE_w T))) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (environment zenon_TE_w) -> False). % 0.95/1.21 do 2 intro. intros zenon_H59 zenon_H51 zenon_H47 zenon_H5a zenon_H1f zenon_H1e. % 0.95/1.21 generalize (a10 zenon_TE_w). zenon_intro zenon_H5b. % 0.95/1.21 generalize (zenon_H5b (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H5c. % 0.95/1.21 generalize (zenon_H5c (critical_point zenon_TE_w)). zenon_intro zenon_H5d. % 0.95/1.21 generalize (zenon_H5d zenon_TT_cv). zenon_intro zenon_H5e. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H25 | zenon_intro zenon_H61 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H38 | zenon_intro zenon_H62 ]. % 0.95/1.21 generalize (mp_FM_and_EP_when_EP_appears zenon_TE_w). zenon_intro zenon_H63. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H64 | zenon_intro zenon_H3a ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H25 | zenon_intro zenon_H65 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 generalize (mp_FM_and_EP_members_EP_appeared zenon_TE_w). zenon_intro zenon_H2e. % 0.95/1.21 generalize (zenon_H5a (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H66. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H25 | zenon_intro zenon_H69 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H24 | zenon_intro zenon_H6a ]. % 0.95/1.21 exact (zenon_H24 zenon_H1f). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H15 | zenon_intro zenon_H6b ]. % 0.95/1.21 apply (zenon_L1_ zenon_TE_w); trivial. % 0.95/1.21 generalize (zenon_H2e (critical_point zenon_TE_w)). zenon_intro zenon_H30. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H25 | zenon_intro zenon_H20 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 generalize (mp_greater_or_equal (critical_point zenon_TE_w)). zenon_intro zenon_H27. % 0.95/1.21 generalize (zenon_H27 (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H33. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H35; zenon_intro zenon_H2f | zenon_intro zenon_H31; zenon_intro zenon_H34 ]. % 0.95/1.21 exact (zenon_H35 zenon_H31). % 0.95/1.21 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H6c | zenon_intro zenon_H37 ]. % 0.95/1.21 exact (zenon_H6b zenon_H6c). % 0.95/1.21 generalize (zenon_H5b (critical_point zenon_TE_w)). zenon_intro zenon_H46. % 0.95/1.21 generalize (zenon_H46 (critical_point zenon_TE_w)). zenon_intro zenon_H36. % 0.95/1.21 generalize (zenon_H36 (critical_point zenon_TE_w)). zenon_intro zenon_H6d. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H6e | zenon_intro zenon_H22 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H25 | zenon_intro zenon_H6f ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H20 | zenon_intro zenon_H70 ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H20 | zenon_intro zenon_H71 ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H26 | zenon_intro zenon_H26 ]. % 0.95/1.21 apply (zenon_L3_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_L3_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_L7_ zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H65 zenon_H67). % 0.95/1.21 exact (zenon_H38 zenon_H3a). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H20 | zenon_intro zenon_H72 ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H48 | zenon_intro zenon_H52 ]. % 0.95/1.21 apply (zenon_L8_ zenon_TE_w zenon_TT_cv); trivial. % 0.95/1.21 apply (zenon_L9_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H59 zenon_H5f). % 0.95/1.21 (* end of lemma zenon_L10_ *) % 0.95/1.21 assert (zenon_L11_ : forall (zenon_TE_w : zenon_U), (greater_or_equal (difference (growth_rate (first_movers) (critical_point zenon_TE_w)) (growth_rate (efficient_producers) (critical_point zenon_TE_w))) (zero)) -> (~((greater (difference (growth_rate (first_movers) (critical_point zenon_TE_w)) (growth_rate (efficient_producers) (critical_point zenon_TE_w))) (zero))\/((difference (growth_rate (first_movers) (critical_point zenon_TE_w)) (growth_rate (efficient_producers) (critical_point zenon_TE_w))) = (zero)))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H73 zenon_H74. % 0.95/1.21 generalize (mp_greater_or_equal (difference (growth_rate (first_movers) (critical_point zenon_TE_w)) (growth_rate (efficient_producers) (critical_point zenon_TE_w)))). zenon_intro zenon_H75. % 0.95/1.21 generalize (zenon_H75 (zero)). zenon_intro zenon_H76. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H78; zenon_intro zenon_H74 | zenon_intro zenon_H73; zenon_intro zenon_H77 ]. % 0.95/1.21 exact (zenon_H78 zenon_H73). % 0.95/1.21 exact (zenon_H74 zenon_H77). % 0.95/1.21 (* end of lemma zenon_L11_ *) % 0.95/1.21 assert (zenon_L12_ : forall (zenon_TE_w : zenon_U), (environment zenon_TE_w) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (forall Tc : zenon_U, (((environment zenon_TE_w)/\(Tc = (critical_point zenon_TE_w)))->((~(greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc)))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) zenon_TE_w T)/\(greater T Tc))->(greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) -> (~(greater_or_equal (difference (growth_rate (first_movers) (critical_point zenon_TE_w)) (growth_rate (efficient_producers) (critical_point zenon_TE_w))) (zero))) -> False). % 0.95/1.21 do 1 intro. intros zenon_H1e zenon_H1f zenon_H79 zenon_H78. % 0.95/1.21 generalize (mp_greater_or_equal (difference (growth_rate (first_movers) (critical_point zenon_TE_w)) (growth_rate (efficient_producers) (critical_point zenon_TE_w)))). zenon_intro zenon_H75. % 0.95/1.21 generalize (zenon_H75 (zero)). zenon_intro zenon_H76. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H76); [ zenon_intro zenon_H78; zenon_intro zenon_H74 | zenon_intro zenon_H73; zenon_intro zenon_H77 ]. % 0.95/1.21 generalize (mp_relationship_of_growth_rates zenon_TE_w). zenon_intro zenon_H7a. % 0.95/1.21 generalize (zenon_H7a (critical_point zenon_TE_w)). zenon_intro zenon_H7b. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7c | zenon_intro zenon_H73 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H25 | zenon_intro zenon_H7d ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H7d); [ zenon_intro zenon_H20 | zenon_intro zenon_H7e ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply zenon_H7e. zenon_intro zenon_H7f. % 0.95/1.21 generalize (zenon_H79 (critical_point zenon_TE_w)). zenon_intro zenon_H80. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H25 | zenon_intro zenon_H2c ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply zenon_H2c. apply refl_equal. % 0.95/1.21 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83. % 0.95/1.21 generalize (mp_negative_growth_rate_difference (critical_point zenon_TE_w)). zenon_intro zenon_H85. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H85); [ zenon_intro zenon_H87; zenon_intro zenon_H84 | zenon_intro zenon_H7f; zenon_intro zenon_H86 ]. % 0.95/1.21 exact (zenon_H87 zenon_H7f). % 0.95/1.21 exact (zenon_H84 zenon_H86). % 0.95/1.21 apply (zenon_L11_ zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H78 zenon_H73). % 0.95/1.21 (* end of lemma zenon_L12_ *) % 0.95/1.21 assert (zenon_L13_ : forall (zenon_TE_w : zenon_U) (zenon_TT_cv : zenon_U), (zenon_TT_cv = (appear (efficient_producers) zenon_TE_w)) -> ((critical_point zenon_TE_w) = (appear (efficient_producers) zenon_TE_w)) -> (~(greater_or_equal zenon_TT_cv (critical_point zenon_TE_w))) -> False). % 0.95/1.21 do 2 intro. intros zenon_H88 zenon_H37 zenon_H89. % 0.95/1.21 generalize (mp_greater_or_equal zenon_TT_cv). zenon_intro zenon_H4a. % 0.95/1.21 generalize (zenon_H4a (critical_point zenon_TE_w)). zenon_intro zenon_H8a. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H8a); [ zenon_intro zenon_H89; zenon_intro zenon_H8d | zenon_intro zenon_H8c; zenon_intro zenon_H8b ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 0.95/1.21 cut ((zenon_TT_cv = (appear (efficient_producers) zenon_TE_w)) = (zenon_TT_cv = (critical_point zenon_TE_w))). % 0.95/1.21 intro zenon_D_pnotp. % 0.95/1.21 apply zenon_H8e. % 0.95/1.21 rewrite <- zenon_D_pnotp. % 0.95/1.21 exact zenon_H88. % 0.95/1.21 cut (((appear (efficient_producers) zenon_TE_w) = (critical_point zenon_TE_w))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 0.95/1.21 cut ((zenon_TT_cv = zenon_TT_cv)); [idtac | apply NNPP; zenon_intro zenon_H90]. % 0.95/1.21 congruence. % 0.95/1.21 apply zenon_H90. apply refl_equal. % 0.95/1.21 apply zenon_H44. apply sym_equal. exact zenon_H37. % 0.95/1.21 exact (zenon_H89 zenon_H8c). % 0.95/1.21 (* end of lemma zenon_L13_ *) % 0.95/1.21 assert (zenon_L14_ : forall (zenon_TE_w : zenon_U) (zenon_TT_cv : zenon_U), (zenon_TT_cv = (appear (efficient_producers) zenon_TE_w)) -> (~(greater_or_equal zenon_TT_cv (appear (efficient_producers) zenon_TE_w))) -> False). % 0.95/1.21 do 2 intro. intros zenon_H88 zenon_H48. % 0.95/1.21 generalize (mp_greater_or_equal zenon_TT_cv). zenon_intro zenon_H4a. % 0.95/1.21 generalize (zenon_H4a (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H4b. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H48; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.95/1.21 exact (zenon_H4f zenon_H88). % 0.95/1.21 exact (zenon_H48 zenon_H4d). % 0.95/1.21 (* end of lemma zenon_L14_ *) % 0.95/1.21 assert (zenon_L15_ : forall (zenon_TT_cv : zenon_U) (zenon_TE_w : zenon_U), (forall T2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_w)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w (appear (efficient_producers) zenon_TE_w))/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w T2)/\((greater_or_equal T (appear (efficient_producers) zenon_TE_w))/\(greater_or_equal T2 T)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_w T)))) -> (~(subpopulations (first_movers) (efficient_producers) zenon_TE_w zenon_TT_cv)) -> (greater (critical_point zenon_TE_w) zenon_TT_cv) -> (zenon_TT_cv = (appear (efficient_producers) zenon_TE_w)) -> (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_w)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w T1)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_w T2)/\((greater_or_equal T T1)/\(greater_or_equal T2 T)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_w T))))) -> (forall T : zenon_U, (((environment zenon_TE_w)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_w T))->(greater_or_equal T (appear (efficient_producers) zenon_TE_w)))) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (forall T : zenon_U, (((environment zenon_TE_w)/\((in_environment zenon_TE_w (critical_point zenon_TE_w))/\((greater_or_equal T (appear (efficient_producers) zenon_TE_w))/\(greater (critical_point zenon_TE_w) T))))->(in_environment zenon_TE_w T))) -> (environment zenon_TE_w) -> False). % 0.95/1.21 do 2 intro. intros zenon_H5c zenon_H59 zenon_H51 zenon_H88 zenon_H5b zenon_H2e zenon_H1f zenon_H5a zenon_H1e. % 0.95/1.21 generalize (zenon_H5c (critical_point zenon_TE_w)). zenon_intro zenon_H5d. % 0.95/1.21 generalize (zenon_H5d zenon_TT_cv). zenon_intro zenon_H5e. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H25 | zenon_intro zenon_H61 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H38 | zenon_intro zenon_H62 ]. % 0.95/1.21 generalize (mp_FM_and_EP_when_EP_appears zenon_TE_w). zenon_intro zenon_H63. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H64 | zenon_intro zenon_H3a ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H25 | zenon_intro zenon_H65 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 generalize (zenon_H5a (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H66. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H25 | zenon_intro zenon_H69 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H24 | zenon_intro zenon_H6a ]. % 0.95/1.21 exact (zenon_H24 zenon_H1f). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H15 | zenon_intro zenon_H6b ]. % 0.95/1.21 apply (zenon_L1_ zenon_TE_w); trivial. % 0.95/1.21 generalize (zenon_H2e (critical_point zenon_TE_w)). zenon_intro zenon_H30. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H25 | zenon_intro zenon_H20 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 generalize (mp_greater_or_equal (critical_point zenon_TE_w)). zenon_intro zenon_H27. % 0.95/1.21 generalize (zenon_H27 (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H33. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H35; zenon_intro zenon_H2f | zenon_intro zenon_H31; zenon_intro zenon_H34 ]. % 0.95/1.21 exact (zenon_H35 zenon_H31). % 0.95/1.21 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H6c | zenon_intro zenon_H37 ]. % 0.95/1.21 exact (zenon_H6b zenon_H6c). % 0.95/1.21 generalize (zenon_H5b (critical_point zenon_TE_w)). zenon_intro zenon_H46. % 0.95/1.21 generalize (zenon_H46 (critical_point zenon_TE_w)). zenon_intro zenon_H36. % 0.95/1.21 generalize (zenon_H36 zenon_TT_cv). zenon_intro zenon_H91. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H92 | zenon_intro zenon_H5f ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H92); [ zenon_intro zenon_H25 | zenon_intro zenon_H93 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H20 | zenon_intro zenon_H94 ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H94); [ zenon_intro zenon_H20 | zenon_intro zenon_H95 ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H95); [ zenon_intro zenon_H89 | zenon_intro zenon_H52 ]. % 0.95/1.21 apply (zenon_L13_ zenon_TE_w zenon_TT_cv); trivial. % 0.95/1.21 apply (zenon_L9_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H59 zenon_H5f). % 0.95/1.21 exact (zenon_H65 zenon_H67). % 0.95/1.21 exact (zenon_H38 zenon_H3a). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H20 | zenon_intro zenon_H72 ]. % 0.95/1.21 apply (zenon_L2_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H48 | zenon_intro zenon_H52 ]. % 0.95/1.21 apply (zenon_L14_ zenon_TE_w zenon_TT_cv); trivial. % 0.95/1.21 apply (zenon_L9_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_H59 zenon_H5f). % 0.95/1.21 (* end of lemma zenon_L15_ *) % 0.95/1.21 assert (zenon_L16_ : forall (zenon_TT_cv : zenon_U) (zenon_TE_w : zenon_U), (environment zenon_TE_w) -> (forall T : zenon_U, (((environment zenon_TE_w)/\((in_environment zenon_TE_w (critical_point zenon_TE_w))/\((greater_or_equal T (appear (efficient_producers) zenon_TE_w))/\(greater (critical_point zenon_TE_w) T))))->(in_environment zenon_TE_w T))) -> (in_environment zenon_TE_w (critical_point zenon_TE_w)) -> (zenon_TT_cv = (appear (efficient_producers) zenon_TE_w)) -> (greater (critical_point zenon_TE_w) zenon_TT_cv) -> (~(subpopulations (first_movers) (efficient_producers) zenon_TE_w zenon_TT_cv)) -> False). % 0.95/1.21 do 2 intro. intros zenon_H1e zenon_H5a zenon_H1f zenon_H88 zenon_H51 zenon_H59. % 0.95/1.21 generalize (a10 zenon_TE_w). zenon_intro zenon_H5b. % 0.95/1.21 generalize (mp_FM_and_EP_members_EP_appeared zenon_TE_w). zenon_intro zenon_H2e. % 0.95/1.21 generalize (zenon_H5b (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H5c. % 0.95/1.21 apply (zenon_L15_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 (* end of lemma zenon_L16_ *) % 0.95/1.21 apply NNPP. intro zenon_G. % 0.95/1.21 apply (zenon_notallex_s (fun E : zenon_U => (forall T : zenon_U, (((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)))) zenon_G); [ zenon_intro zenon_H96; idtac ]. % 0.95/1.21 elim zenon_H96. zenon_intro zenon_TE_w. zenon_intro zenon_H97. % 0.95/1.21 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_w)/\((in_environment zenon_TE_w (critical_point zenon_TE_w))/\((greater_or_equal T (appear (efficient_producers) zenon_TE_w))/\(greater (critical_point zenon_TE_w) T))))->(selection_favors (first_movers) (efficient_producers) T))) zenon_H97); [ zenon_intro zenon_H98; idtac ]. % 0.95/1.21 elim zenon_H98. zenon_intro zenon_TT_cv. zenon_intro zenon_H99. % 0.95/1.21 apply (zenon_notimply_s _ _ zenon_H99). zenon_intro zenon_H9b. zenon_intro zenon_H9a. % 0.95/1.21 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H1e. zenon_intro zenon_H9c. % 0.95/1.21 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H1f. zenon_intro zenon_H9d. % 0.95/1.21 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H4d. zenon_intro zenon_H51. % 0.95/1.21 generalize (mp_greater_or_equal zenon_TT_cv). zenon_intro zenon_H4a. % 0.95/1.21 generalize (zenon_H4a (appear (efficient_producers) zenon_TE_w)). zenon_intro zenon_H4b. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H48; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ]. % 0.95/1.21 exact (zenon_H48 zenon_H4d). % 0.95/1.21 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H47 | zenon_intro zenon_H88 ]. % 0.95/1.21 generalize (mp_critical_time_points zenon_TE_w). zenon_intro zenon_H5a. % 0.95/1.21 generalize (mp1_high_growth_rates zenon_TE_w). zenon_intro zenon_H9e. % 0.95/1.21 generalize (zenon_H9e (efficient_producers)). zenon_intro zenon_H9f. % 0.95/1.21 generalize (zenon_H9f (first_movers)). zenon_intro zenon_Ha0. % 0.95/1.21 generalize (zenon_Ha0 zenon_TT_cv). zenon_intro zenon_Ha1. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha2 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Ha3); [ zenon_intro zenon_H25 | zenon_intro zenon_Ha4 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ]. % 0.95/1.21 generalize (mp_symmetry_of_subpopulations zenon_TE_w). zenon_intro zenon_Ha7. % 0.95/1.21 generalize (zenon_Ha7 zenon_TT_cv). zenon_intro zenon_Ha8. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H25 | zenon_intro zenon_H59 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L10_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_Ha6 zenon_Ha9). % 0.95/1.21 generalize (mp_positive_growth_rate_difference zenon_TT_cv). zenon_intro zenon_Hab. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_Hab); [ zenon_intro zenon_Hae; zenon_intro zenon_Ha5 | zenon_intro zenon_Had; zenon_intro zenon_Hac ]. % 0.95/1.21 generalize (d1 zenon_TE_w). zenon_intro zenon_H79. % 0.95/1.21 generalize (mp_decreasing_function zenon_TE_w). zenon_intro zenon_Haf. % 0.95/1.21 generalize (zenon_Haf zenon_TT_cv). zenon_intro zenon_Hb0. % 0.95/1.21 generalize (zenon_Hb0 (critical_point zenon_TE_w)). zenon_intro zenon_Hb1. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_H25 | zenon_intro zenon_Hb4 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_H24 | zenon_intro zenon_Hb5 ]. % 0.95/1.21 exact (zenon_H24 zenon_H1f). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 0.95/1.21 apply (zenon_L12_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb6); [ zenon_intro zenon_H48 | zenon_intro zenon_H58 ]. % 0.95/1.21 apply (zenon_L8_ zenon_TE_w zenon_TT_cv); trivial. % 0.95/1.21 exact (zenon_H58 zenon_H51). % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Had ]. % 0.95/1.21 generalize (mp_difference_between_founding_rates zenon_TT_cv). zenon_intro zenon_Hb8. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ]. % 0.95/1.21 generalize (a12 zenon_TE_w). zenon_intro zenon_Hbd. % 0.95/1.21 generalize (zenon_Hbd zenon_TT_cv). zenon_intro zenon_Hbe. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_Haa | zenon_intro zenon_Hbf ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H25 | zenon_intro zenon_H59 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L10_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_Hbc zenon_Hbf). % 0.95/1.21 apply zenon_Hbb. zenon_intro zenon_Hc0. % 0.95/1.21 generalize (l3 zenon_TE_w). zenon_intro zenon_Hc1. % 0.95/1.21 generalize (zenon_Hc1 zenon_TT_cv). zenon_intro zenon_Hc2. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hc2); [ zenon_intro zenon_Haa | zenon_intro zenon_Hc3 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H25 | zenon_intro zenon_H59 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L10_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_Hc3 zenon_Hc0). % 0.95/1.21 exact (zenon_Hb7 zenon_Hb9). % 0.95/1.21 exact (zenon_Hae zenon_Had). % 0.95/1.21 exact (zenon_Ha5 zenon_Hac). % 0.95/1.21 exact (zenon_H9a zenon_Ha2). % 0.95/1.21 generalize (mp_critical_time_points zenon_TE_w). zenon_intro zenon_H5a. % 0.95/1.21 generalize (mp1_high_growth_rates zenon_TE_w). zenon_intro zenon_H9e. % 0.95/1.21 generalize (zenon_H9e (efficient_producers)). zenon_intro zenon_H9f. % 0.95/1.21 generalize (zenon_H9f (first_movers)). zenon_intro zenon_Ha0. % 0.95/1.21 generalize (zenon_Ha0 zenon_TT_cv). zenon_intro zenon_Ha1. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha2 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Ha3); [ zenon_intro zenon_H25 | zenon_intro zenon_Ha4 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ]. % 0.95/1.21 generalize (mp_symmetry_of_subpopulations zenon_TE_w). zenon_intro zenon_Ha7. % 0.95/1.21 generalize (zenon_Ha7 zenon_TT_cv). zenon_intro zenon_Ha8. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H25 | zenon_intro zenon_H59 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L16_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_Ha6 zenon_Ha9). % 0.95/1.21 generalize (mp_positive_growth_rate_difference zenon_TT_cv). zenon_intro zenon_Hab. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_Hab); [ zenon_intro zenon_Hae; zenon_intro zenon_Ha5 | zenon_intro zenon_Had; zenon_intro zenon_Hac ]. % 0.95/1.21 generalize (mp_decreasing_function zenon_TE_w). zenon_intro zenon_Haf. % 0.95/1.21 generalize (d1 zenon_TE_w). zenon_intro zenon_H79. % 0.95/1.21 generalize (zenon_Haf zenon_TT_cv). zenon_intro zenon_Hb0. % 0.95/1.21 generalize (zenon_Hb0 (critical_point zenon_TE_w)). zenon_intro zenon_Hb1. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_H25 | zenon_intro zenon_Hb4 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_H24 | zenon_intro zenon_Hb5 ]. % 0.95/1.21 exact (zenon_H24 zenon_H1f). % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 0.95/1.21 apply (zenon_L12_ zenon_TE_w); trivial. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hb6); [ zenon_intro zenon_H48 | zenon_intro zenon_H58 ]. % 0.95/1.21 apply (zenon_L14_ zenon_TE_w zenon_TT_cv); trivial. % 0.95/1.21 exact (zenon_H58 zenon_H51). % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Had ]. % 0.95/1.21 generalize (mp_difference_between_founding_rates zenon_TT_cv). zenon_intro zenon_Hb8. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbb ]. % 0.95/1.21 generalize (a12 zenon_TE_w). zenon_intro zenon_Hbd. % 0.95/1.21 generalize (zenon_Hbd zenon_TT_cv). zenon_intro zenon_Hbe. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_Haa | zenon_intro zenon_Hbf ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H25 | zenon_intro zenon_H59 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L16_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_Hbc zenon_Hbf). % 0.95/1.21 apply zenon_Hbb. zenon_intro zenon_Hc0. % 0.95/1.21 generalize (l3 zenon_TE_w). zenon_intro zenon_Hc1. % 0.95/1.21 generalize (zenon_Hc1 zenon_TT_cv). zenon_intro zenon_Hc2. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_Hc2); [ zenon_intro zenon_Haa | zenon_intro zenon_Hc3 ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H25 | zenon_intro zenon_H59 ]. % 0.95/1.21 exact (zenon_H25 zenon_H1e). % 0.95/1.21 apply (zenon_L16_ zenon_TT_cv zenon_TE_w); trivial. % 0.95/1.21 exact (zenon_Hc3 zenon_Hc0). % 0.95/1.21 exact (zenon_Hb7 zenon_Hb9). % 0.95/1.21 exact (zenon_Hae zenon_Had). % 0.95/1.21 exact (zenon_Ha5 zenon_Hac). % 0.95/1.21 exact (zenon_H9a zenon_Ha2). % 0.95/1.21 Qed. % 0.95/1.21 % SZS output end Proof % 0.95/1.21 (* END-PROOF *) % 0.95/1.21 nodes searched: 23163 % 0.95/1.21 max branch formulas: 2763 % 0.95/1.21 proof nodes created: 2157 % 0.95/1.21 formulas created: 62789 % 0.95/1.21 %------------------------------------------------------------------------------