%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT039+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 06:24:21 AM UTC 2026 % Result : Theorem 71.63s 71.97s % Output : Proof 0.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : MGT039+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.02 % Command : run_zenon %s %d % 0.05/0.30 % Computer : n012.cluster.edu % 0.05/0.30 % Model : x86_64 x86_64 % 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.05/0.30 % Memory : 8046.5625MB % 0.05/0.30 % OS : Linux 6.8.0-71-generic % 0.05/0.31 % CPULimit : 300 % 0.05/0.31 % WCLimit : 300 % 0.05/0.31 % DateTime : Mon Sep 7 12:55:56 UTC 2026 % 0.05/0.31 % CPUTime : % 71.63/71.97 (* PROOF-FOUND *) % 71.63/71.97 % SZS status Theorem % 71.63/71.97 (* BEGIN-PROOF *) % 71.63/71.97 % SZS output start Proof % 71.63/71.97 Theorem prove_t8 : (forall P : zenon_U, (((observational_period P)/\(slow_change P))->(selection_favors (efficient_producers) (first_movers) P))). % 71.63/71.97 Proof. % 71.63/71.97 assert (zenon_L1_ : forall (zenon_TT_z : zenon_U) (zenon_TE_ba : zenon_U), (in_environment zenon_TE_ba zenon_TT_z) -> (environment zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))) -> (greater zenon_TT_z (critical_point zenon_TE_ba)) -> False). % 71.63/71.97 do 2 intro. intros zenon_H13 zenon_H14 zenon_H15 zenon_H16 zenon_H17 zenon_H18. % 71.63/71.97 elim (classic ((~((end_time zenon_TE_ba) = zenon_TT_z))/\(~(greater (end_time zenon_TE_ba) zenon_TT_z)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 71.63/71.97 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 71.63/71.97 generalize (zenon_H15 zenon_TT_z). zenon_intro zenon_H1f. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 exact (zenon_H22 zenon_H13). % 71.63/71.97 generalize (mp_greater_or_equal (end_time zenon_TE_ba)). zenon_intro zenon_H24. % 71.63/71.97 generalize (zenon_H24 zenon_TT_z). zenon_intro zenon_H25. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H20; zenon_intro zenon_H26 ]. % 71.63/71.97 exact (zenon_H28 zenon_H20). % 71.63/71.97 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 71.63/71.97 exact (zenon_H1d zenon_H2a). % 71.63/71.97 exact (zenon_H1e zenon_H29). % 71.63/71.97 cut ((greater zenon_TT_z (critical_point zenon_TE_ba)) = (greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H17. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H18. % 71.63/71.97 cut (((critical_point zenon_TE_ba) = (critical_point zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 71.63/71.97 cut ((zenon_TT_z = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 71.63/71.97 congruence. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 71.63/71.97 apply zenon_H2e. zenon_intro zenon_H29. % 71.63/71.97 elim (classic ((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba)) = (zenon_TT_z = (end_time zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H2c. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H2f. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = zenon_TT_z)); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 71.63/71.97 congruence. % 71.63/71.97 exact (zenon_H1e zenon_H29). % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 apply zenon_H2d. zenon_intro zenon_H2a. % 71.63/71.97 generalize (zenon_H16 (end_time zenon_TE_ba)). zenon_intro zenon_H31. % 71.63/71.97 generalize (zenon_H31 zenon_TT_z). zenon_intro zenon_H32. % 71.63/71.97 generalize (zenon_H32 (critical_point zenon_TE_ba)). zenon_intro zenon_H33. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H1d | zenon_intro zenon_H34 ]. % 71.63/71.97 exact (zenon_H1d zenon_H2a). % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 71.63/71.97 exact (zenon_H36 zenon_H18). % 71.63/71.97 exact (zenon_H17 zenon_H35). % 71.63/71.97 apply zenon_H2b. apply refl_equal. % 71.63/71.97 (* end of lemma zenon_L1_ *) % 71.63/71.97 assert (zenon_L2_ : forall (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (exists T : zenon_U, ((in_environment zenon_TE_ba T)/\(greater T (critical_point zenon_TE_ba)))) -> (~(greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))) -> (environment zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> False). % 71.63/71.97 do 1 intro. intros zenon_H16 zenon_H37 zenon_H17 zenon_H14 zenon_H15. % 71.63/71.97 elim zenon_H37. zenon_intro zenon_TT_z. zenon_intro zenon_H38. % 71.63/71.97 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H13. zenon_intro zenon_H18. % 71.63/71.97 apply (zenon_L1_ zenon_TT_z zenon_TE_ba); trivial. % 71.63/71.97 (* end of lemma zenon_L2_ *) % 71.63/71.97 assert (zenon_L3_ : forall (zenon_TE_ba : zenon_U) (zenon_TP_ci : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (observational_period zenon_TP_ci) -> (slow_change zenon_TP_ci) -> (environment zenon_TE_ba) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (~(greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H39 zenon_H3a zenon_H14 zenon_H3b zenon_H17 zenon_H15. % 71.63/71.97 generalize (mp4_critical_point zenon_TP_ci). zenon_intro zenon_H3d. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 71.63/71.97 exact (zenon_H41 zenon_H39). % 71.63/71.97 exact (zenon_H40 zenon_H3a). % 71.63/71.97 generalize (zenon_H3e zenon_TE_ba). zenon_intro zenon_H42. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H43 | zenon_intro zenon_H37 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H23 | zenon_intro zenon_H44 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 exact (zenon_H44 zenon_H3b). % 71.63/71.97 apply (zenon_L2_ zenon_TE_ba); trivial. % 71.63/71.97 (* end of lemma zenon_L3_ *) % 71.63/71.97 assert (zenon_L4_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (environment zenon_TE_ba) -> (~(greater (end_time zenon_TE_ba) (start_time zenon_TE_ba))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (slow_change zenon_TP_ci) -> (observational_period zenon_TP_ci) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H14 zenon_H45 zenon_H15 zenon_H3b zenon_H3a zenon_H39. % 71.63/71.97 generalize (mp_time_of_critical_point zenon_TE_ba). zenon_intro zenon_H46. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H23 | zenon_intro zenon_H47 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 generalize (mp_greater_or_equal (critical_point zenon_TE_ba)). zenon_intro zenon_H48. % 71.63/71.97 generalize (zenon_H48 (start_time zenon_TE_ba)). zenon_intro zenon_H49. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H4c; zenon_intro zenon_H4b | zenon_intro zenon_H47; zenon_intro zenon_H4a ]. % 71.63/71.97 exact (zenon_H4c zenon_H47). % 71.63/71.97 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 71.63/71.97 elim (classic ((~((end_time zenon_TE_ba) = (critical_point zenon_TE_ba)))/\(~(greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 71.63/71.97 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H17. % 71.63/71.97 apply (zenon_L3_ zenon_TE_ba zenon_TP_ci); trivial. % 71.63/71.97 cut ((greater (critical_point zenon_TE_ba) (start_time zenon_TE_ba)) = (greater (end_time zenon_TE_ba) (start_time zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H45. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H4e. % 71.63/71.97 cut (((start_time zenon_TE_ba) = (start_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 71.63/71.97 cut (((critical_point zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 71.63/71.97 congruence. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 71.63/71.97 apply zenon_H55. zenon_intro zenon_H56. % 71.63/71.97 elim (classic ((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba)) = ((critical_point zenon_TE_ba) = (end_time zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H53. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H2f. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (critical_point zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 71.63/71.97 congruence. % 71.63/71.97 exact (zenon_H51 zenon_H56). % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 apply zenon_H54. zenon_intro zenon_H35. % 71.63/71.97 generalize (zenon_H16 (end_time zenon_TE_ba)). zenon_intro zenon_H31. % 71.63/71.97 generalize (zenon_H31 (critical_point zenon_TE_ba)). zenon_intro zenon_H57. % 71.63/71.97 generalize (zenon_H57 (start_time zenon_TE_ba)). zenon_intro zenon_H58. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H17 | zenon_intro zenon_H59 ]. % 71.63/71.97 exact (zenon_H17 zenon_H35). % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 71.63/71.97 exact (zenon_H5b zenon_H4e). % 71.63/71.97 exact (zenon_H45 zenon_H5a). % 71.63/71.97 apply zenon_H52. apply refl_equal. % 71.63/71.97 elim (classic (greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))); [ zenon_intro zenon_H35 | zenon_intro zenon_H17 ]. % 71.63/71.97 cut ((greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba)) = (greater (end_time zenon_TE_ba) (start_time zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H45. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H35. % 71.63/71.97 cut (((critical_point zenon_TE_ba) = (start_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 71.63/71.97 congruence. % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 exact (zenon_H5c zenon_H4d). % 71.63/71.97 apply (zenon_L3_ zenon_TE_ba zenon_TP_ci); trivial. % 71.63/71.97 (* end of lemma zenon_L4_ *) % 71.63/71.97 assert (zenon_L5_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (environment zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (slow_change zenon_TP_ci) -> (observational_period zenon_TP_ci) -> (~(greater_or_equal (end_time zenon_TE_ba) (start_time zenon_TE_ba))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H14 zenon_H15 zenon_H3b zenon_H3a zenon_H39 zenon_H5d. % 71.63/71.97 generalize (mp_greater_or_equal (end_time zenon_TE_ba)). zenon_intro zenon_H24. % 71.63/71.97 generalize (zenon_H24 (start_time zenon_TE_ba)). zenon_intro zenon_H5e. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H5d; zenon_intro zenon_H61 | zenon_intro zenon_H60; zenon_intro zenon_H5f ]. % 71.63/71.97 apply (zenon_notor_s _ _ zenon_H61). zenon_intro zenon_H45. zenon_intro zenon_H62. % 71.63/71.97 apply (zenon_L4_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H5d zenon_H60). % 71.63/71.97 (* end of lemma zenon_L5_ *) % 71.63/71.97 assert (zenon_L6_ : forall (zenon_TE_ba : zenon_U), (~(greater_or_equal (end_time zenon_TE_ba) (end_time zenon_TE_ba))) -> False). % 71.63/71.97 do 1 intro. intros zenon_H63. % 71.63/71.97 generalize (mp_greater_or_equal (end_time zenon_TE_ba)). zenon_intro zenon_H24. % 71.63/71.97 generalize (zenon_H24 (end_time zenon_TE_ba)). zenon_intro zenon_H64. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_H64); [ zenon_intro zenon_H63; zenon_intro zenon_H67 | zenon_intro zenon_H66; zenon_intro zenon_H65 ]. % 71.63/71.97 apply (zenon_notor_s _ _ zenon_H67). zenon_intro zenon_H68. zenon_intro zenon_H30. % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 exact (zenon_H63 zenon_H66). % 71.63/71.97 (* end of lemma zenon_L6_ *) % 71.63/71.97 assert (zenon_L7_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((greater_or_equal T (start_time zenon_TE_ba))/\(greater_or_equal (end_time zenon_TE_ba) T)))->(in_environment zenon_TE_ba T))) -> (environment zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (slow_change zenon_TP_ci) -> (observational_period zenon_TP_ci) -> (~(in_environment zenon_TE_ba (end_time zenon_TE_ba))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H69 zenon_H14 zenon_H15 zenon_H3b zenon_H3a zenon_H39 zenon_H6a. % 71.63/71.97 generalize (zenon_H69 (end_time zenon_TE_ba)). zenon_intro zenon_H6b. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H23 | zenon_intro zenon_H6e ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H5d | zenon_intro zenon_H63 ]. % 71.63/71.97 apply (zenon_L5_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_L6_ zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H6a zenon_H6c). % 71.63/71.97 (* end of lemma zenon_L7_ *) % 71.63/71.97 assert (zenon_L8_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (environment zenon_TE_ba) -> (~(greater (end_time zenon_TE_ba) (appear (efficient_producers) zenon_TE_ba))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (slow_change zenon_TP_ci) -> (observational_period zenon_TP_ci) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H14 zenon_H6f zenon_H15 zenon_H3b zenon_H3a zenon_H39. % 71.63/71.97 generalize (mp_critical_point_after_EP zenon_TE_ba). zenon_intro zenon_H70. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H23 | zenon_intro zenon_H71 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 generalize (mp_greater_or_equal (critical_point zenon_TE_ba)). zenon_intro zenon_H48. % 71.63/71.97 generalize (zenon_H48 (appear (efficient_producers) zenon_TE_ba)). zenon_intro zenon_H72. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H75; zenon_intro zenon_H74 | zenon_intro zenon_H71; zenon_intro zenon_H73 ]. % 71.63/71.97 exact (zenon_H75 zenon_H71). % 71.63/71.97 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 71.63/71.97 elim (classic ((~((end_time zenon_TE_ba) = (critical_point zenon_TE_ba)))/\(~(greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))))); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 71.63/71.97 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H17. % 71.63/71.97 apply (zenon_L3_ zenon_TE_ba zenon_TP_ci); trivial. % 71.63/71.97 cut ((greater (critical_point zenon_TE_ba) (appear (efficient_producers) zenon_TE_ba)) = (greater (end_time zenon_TE_ba) (appear (efficient_producers) zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H6f. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H77. % 71.63/71.97 cut (((appear (efficient_producers) zenon_TE_ba) = (appear (efficient_producers) zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 71.63/71.97 cut (((critical_point zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 71.63/71.97 congruence. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 71.63/71.97 apply zenon_H55. zenon_intro zenon_H56. % 71.63/71.97 elim (classic ((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba)) = ((critical_point zenon_TE_ba) = (end_time zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H53. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H2f. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (critical_point zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 71.63/71.97 congruence. % 71.63/71.97 exact (zenon_H51 zenon_H56). % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 apply zenon_H54. zenon_intro zenon_H35. % 71.63/71.97 generalize (zenon_H16 (end_time zenon_TE_ba)). zenon_intro zenon_H31. % 71.63/71.97 generalize (zenon_H31 (critical_point zenon_TE_ba)). zenon_intro zenon_H57. % 71.63/71.97 generalize (zenon_H57 (appear (efficient_producers) zenon_TE_ba)). zenon_intro zenon_H79. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H17 | zenon_intro zenon_H7a ]. % 71.63/71.97 exact (zenon_H17 zenon_H35). % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 71.63/71.97 exact (zenon_H7c zenon_H77). % 71.63/71.97 exact (zenon_H6f zenon_H7b). % 71.63/71.97 apply zenon_H78. apply refl_equal. % 71.63/71.97 elim (classic (greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba))); [ zenon_intro zenon_H35 | zenon_intro zenon_H17 ]. % 71.63/71.97 cut ((greater (end_time zenon_TE_ba) (critical_point zenon_TE_ba)) = (greater (end_time zenon_TE_ba) (appear (efficient_producers) zenon_TE_ba))). % 71.63/71.97 intro zenon_D_pnotp. % 71.63/71.97 apply zenon_H6f. % 71.63/71.97 rewrite <- zenon_D_pnotp. % 71.63/71.97 exact zenon_H35. % 71.63/71.97 cut (((critical_point zenon_TE_ba) = (appear (efficient_producers) zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 71.63/71.97 cut (((end_time zenon_TE_ba) = (end_time zenon_TE_ba))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 71.63/71.97 congruence. % 71.63/71.97 apply zenon_H30. apply refl_equal. % 71.63/71.97 exact (zenon_H7d zenon_H76). % 71.63/71.97 apply (zenon_L3_ zenon_TE_ba zenon_TP_ci); trivial. % 71.63/71.97 (* end of lemma zenon_L8_ *) % 71.63/71.97 assert (zenon_L9_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((in_environment zenon_TE_ba T)/\(greater_or_equal T (appear (efficient_producers) zenon_TE_ba))))->(greater (cardinality_at_time (efficient_producers) T) (zero)))) -> (environment zenon_TE_ba) -> (in_environment zenon_TE_ba (end_time zenon_TE_ba)) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (slow_change zenon_TP_ci) -> (observational_period zenon_TP_ci) -> (~(greater (cardinality_at_time (efficient_producers) (end_time zenon_TE_ba)) (zero))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H7e zenon_H14 zenon_H6c zenon_H15 zenon_H3b zenon_H3a zenon_H39 zenon_H7f. % 71.63/71.97 generalize (zenon_H7e (end_time zenon_TE_ba)). zenon_intro zenon_H80. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H23 | zenon_intro zenon_H83 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H6a | zenon_intro zenon_H84 ]. % 71.63/71.97 exact (zenon_H6a zenon_H6c). % 71.63/71.97 generalize (mp_greater_or_equal (end_time zenon_TE_ba)). zenon_intro zenon_H24. % 71.63/71.97 generalize (zenon_H24 (appear (efficient_producers) zenon_TE_ba)). zenon_intro zenon_H85. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_H85); [ zenon_intro zenon_H84; zenon_intro zenon_H88 | zenon_intro zenon_H87; zenon_intro zenon_H86 ]. % 71.63/71.97 apply (zenon_notor_s _ _ zenon_H88). zenon_intro zenon_H6f. zenon_intro zenon_H89. % 71.63/71.97 apply (zenon_L8_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H84 zenon_H87). % 71.63/71.97 exact (zenon_H7f zenon_H81). % 71.63/71.97 (* end of lemma zenon_L9_ *) % 71.63/71.97 assert (zenon_L10_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((in_environment zenon_TE_ba T)/\((greater (cardinality_at_time (first_movers) T) (zero))/\(greater (cardinality_at_time (efficient_producers) T) (zero)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_ba T))) -> (environment zenon_TE_ba) -> (in_environment zenon_TE_ba (end_time zenon_TE_ba)) -> (greater (cardinality_at_time (first_movers) (end_time zenon_TE_ba)) (zero)) -> (observational_period zenon_TP_ci) -> (slow_change zenon_TP_ci) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (~(subpopulations (first_movers) (efficient_producers) zenon_TE_ba (end_time zenon_TE_ba))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H8a zenon_H14 zenon_H6c zenon_H8b zenon_H39 zenon_H3a zenon_H3b zenon_H15 zenon_H8c. % 71.63/71.97 generalize (zenon_H8a (end_time zenon_TE_ba)). zenon_intro zenon_H8d. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H8d); [ zenon_intro zenon_H8f | zenon_intro zenon_H8e ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H8f); [ zenon_intro zenon_H23 | zenon_intro zenon_H90 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H90); [ zenon_intro zenon_H6a | zenon_intro zenon_H91 ]. % 71.63/71.97 exact (zenon_H6a zenon_H6c). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H92 | zenon_intro zenon_H7f ]. % 71.63/71.97 exact (zenon_H92 zenon_H8b). % 71.63/71.97 generalize (t6 zenon_TE_ba). zenon_intro zenon_H7e. % 71.63/71.97 apply (zenon_L9_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H8c zenon_H8e). % 71.63/71.97 (* end of lemma zenon_L10_ *) % 71.63/71.97 assert (zenon_L11_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (exists T : zenon_U, ((in_environment zenon_TE_ba T)/\(greater T (critical_point zenon_TE_ba)))) -> (forall Tc : zenon_U, (((environment zenon_TE_ba)/\(Tc = (critical_point zenon_TE_ba)))->((~(greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc)))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) zenon_TE_ba T)/\(greater T Tc))->(greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) -> (environment zenon_TE_ba) -> (~(greater (growth_rate (efficient_producers) (end_time zenon_TE_ba)) (growth_rate (first_movers) (end_time zenon_TE_ba)))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (slow_change zenon_TP_ci) -> (observational_period zenon_TP_ci) -> (greater (cardinality_at_time (first_movers) (end_time zenon_TE_ba)) (zero)) -> (in_environment zenon_TE_ba (end_time zenon_TE_ba)) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((in_environment zenon_TE_ba T)/\((greater (cardinality_at_time (first_movers) T) (zero))/\(greater (cardinality_at_time (efficient_producers) T) (zero)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_ba T))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H37 zenon_H93 zenon_H14 zenon_H94 zenon_H15 zenon_H3b zenon_H3a zenon_H39 zenon_H8b zenon_H6c zenon_H8a. % 71.63/71.97 elim zenon_H37. zenon_intro zenon_TT_z. zenon_intro zenon_H38. % 71.63/71.97 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H13. zenon_intro zenon_H18. % 71.63/71.97 generalize (zenon_H93 (critical_point zenon_TE_ba)). zenon_intro zenon_H95. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H23 | zenon_intro zenon_H2b ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply zenon_H2b. apply refl_equal. % 71.63/71.97 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98. % 71.63/71.97 generalize (zenon_H98 (end_time zenon_TE_ba)). zenon_intro zenon_H9a. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9c | zenon_intro zenon_H9b ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H9c); [ zenon_intro zenon_H8c | zenon_intro zenon_H17 ]. % 71.63/71.97 apply (zenon_L10_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_L1_ zenon_TT_z zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H94 zenon_H9b). % 71.63/71.97 (* end of lemma zenon_L11_ *) % 71.63/71.97 assert (zenon_L12_ : forall (zenon_TP_ci : zenon_U) (zenon_TE_ba : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater_or_equal (cardinality_at_time (first_movers) (end_time zenon_TE_ba)) (zero)) -> (~((cardinality_at_time (first_movers) (end_time zenon_TE_ba)) = (zero))) -> (~(selection_favors (efficient_producers) (first_movers) (end_time zenon_TE_ba))) -> (forall Tc : zenon_U, (((environment zenon_TE_ba)/\(Tc = (critical_point zenon_TE_ba)))->((~(greater (growth_rate (efficient_producers) Tc) (growth_rate (first_movers) Tc)))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) zenon_TE_ba T)/\(greater T Tc))->(greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((in_environment zenon_TE_ba T)/\((greater (cardinality_at_time (first_movers) T) (zero))/\(greater (cardinality_at_time (efficient_producers) T) (zero)))))->(subpopulations (first_movers) (efficient_producers) zenon_TE_ba T))) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_ba T)/\(greater (growth_rate (efficient_producers) T) (growth_rate (first_movers) T))))->(selection_favors (efficient_producers) (first_movers) T))) -> (observational_period zenon_TP_ci) -> (slow_change zenon_TP_ci) -> (in_environment zenon_TP_ci zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\(in_environment zenon_TE_ba T))->(greater_or_equal (end_time zenon_TE_ba) T))) -> (environment zenon_TE_ba) -> (forall T : zenon_U, (((environment zenon_TE_ba)/\((greater_or_equal T (start_time zenon_TE_ba))/\(greater_or_equal (end_time zenon_TE_ba) T)))->(in_environment zenon_TE_ba T))) -> False). % 71.63/71.97 do 2 intro. intros zenon_H16 zenon_H9d zenon_H9e zenon_H9f zenon_H93 zenon_H8a zenon_Ha0 zenon_H39 zenon_H3a zenon_H3b zenon_H15 zenon_H14 zenon_H69. % 71.63/71.97 generalize (mp_greater_or_equal (cardinality_at_time (first_movers) (end_time zenon_TE_ba))). zenon_intro zenon_Ha1. % 71.63/71.97 generalize (zenon_Ha1 (zero)). zenon_intro zenon_Ha2. % 71.63/71.97 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha5; zenon_intro zenon_Ha4 | zenon_intro zenon_H9d; zenon_intro zenon_Ha3 ]. % 71.63/71.97 exact (zenon_Ha5 zenon_H9d). % 71.63/71.97 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha6 ]. % 71.63/71.97 generalize (zenon_H69 (end_time zenon_TE_ba)). zenon_intro zenon_H6b. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H23 | zenon_intro zenon_H6e ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H5d | zenon_intro zenon_H63 ]. % 71.63/71.97 apply (zenon_L5_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_L6_ zenon_TE_ba); trivial. % 71.63/71.97 generalize (zenon_Ha0 (end_time zenon_TE_ba)). zenon_intro zenon_Ha7. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_H23 | zenon_intro zenon_Haa ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_H8c | zenon_intro zenon_H94 ]. % 71.63/71.97 apply (zenon_L10_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 generalize (mp4_critical_point zenon_TP_ci). zenon_intro zenon_H3d. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 71.63/71.97 exact (zenon_H41 zenon_H39). % 71.63/71.97 exact (zenon_H40 zenon_H3a). % 71.63/71.97 generalize (zenon_H3e zenon_TE_ba). zenon_intro zenon_H42. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H43 | zenon_intro zenon_H37 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H23 | zenon_intro zenon_H44 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 exact (zenon_H44 zenon_H3b). % 71.63/71.97 apply (zenon_L11_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H9f zenon_Ha8). % 71.63/71.97 exact (zenon_H9e zenon_Ha6). % 71.63/71.97 (* end of lemma zenon_L12_ *) % 71.63/71.97 apply NNPP. intro zenon_G. % 71.63/71.97 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z))))))); [ zenon_intro zenon_H16 | zenon_intro zenon_Hab ]. % 71.63/71.97 apply (zenon_notallex_s (fun P : zenon_U => (((observational_period P)/\(slow_change P))->(selection_favors (efficient_producers) (first_movers) P))) zenon_G); [ zenon_intro zenon_Hac; idtac ]. % 71.63/71.97 elim zenon_Hac. zenon_intro zenon_TP_ci. zenon_intro zenon_Had. % 71.63/71.97 apply (zenon_notimply_s _ _ zenon_Had). zenon_intro zenon_Haf. zenon_intro zenon_Hae. % 71.63/71.97 apply (zenon_and_s _ _ zenon_Haf). zenon_intro zenon_H39. zenon_intro zenon_H3a. % 71.63/71.97 generalize (mp3_favoured_trategy zenon_TP_ci). zenon_intro zenon_Hb0. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H41 | zenon_intro zenon_Hb3 ]. % 71.63/71.97 exact (zenon_H41 zenon_H39). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb5 | zenon_intro zenon_Hb4 ]. % 71.63/71.97 exact (zenon_Hb5 mp_organizational_sets1). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hb6 ]. % 71.63/71.97 exact (zenon_Hb7 mp_organizational_sets2). % 71.63/71.97 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(in_environment zenon_TP_ci E))->(selection_favors (efficient_producers) (first_movers) (end_time E)))) zenon_Hb6); [ zenon_intro zenon_Hb8; idtac ]. % 71.63/71.97 elim zenon_Hb8. zenon_intro zenon_TE_ba. zenon_intro zenon_Hb9. % 71.63/71.97 apply (zenon_notimply_s _ _ zenon_Hb9). zenon_intro zenon_Hba. zenon_intro zenon_H9f. % 71.63/71.97 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_H14. zenon_intro zenon_H3b. % 71.63/71.97 generalize (mp_environment_end_point zenon_TE_ba). zenon_intro zenon_H15. % 71.63/71.97 generalize (mp_time_in_environment zenon_TE_ba). zenon_intro zenon_H69. % 71.63/71.97 generalize (mp2_favour_members zenon_TE_ba). zenon_intro zenon_Hbb. % 71.63/71.97 generalize (zenon_Hbb (efficient_producers)). zenon_intro zenon_Hbc. % 71.63/71.97 generalize (mp1_high_growth_rates zenon_TE_ba). zenon_intro zenon_Hbd. % 71.63/71.97 generalize (zenon_Hbc (first_movers)). zenon_intro zenon_Hbe. % 71.63/71.97 generalize (zenon_Hbd (first_movers)). zenon_intro zenon_Hbf. % 71.63/71.97 generalize (mp_subpopulations zenon_TE_ba). zenon_intro zenon_Hc0. % 71.63/71.97 generalize (zenon_Hbf (efficient_producers)). zenon_intro zenon_Ha0. % 71.63/71.97 generalize (d1 zenon_TE_ba). zenon_intro zenon_H93. % 71.63/71.97 generalize (mp_contains_FM_and_EP zenon_TE_ba). zenon_intro zenon_H8a. % 71.63/71.97 generalize (zenon_Hbe (end_time zenon_TE_ba)). zenon_intro zenon_Hc1. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Ha8 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hc2); [ zenon_intro zenon_H23 | zenon_intro zenon_Hc3 ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc4 ]. % 71.63/71.97 generalize (zenon_Hc0 (end_time zenon_TE_ba)). zenon_intro zenon_Hc6. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H23 | zenon_intro zenon_H6a ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_L7_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 71.63/71.97 exact (zenon_Hc5 zenon_Hc9). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ]. % 71.63/71.97 generalize (zenon_Hc0 (end_time zenon_TE_ba)). zenon_intro zenon_Hc6. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H23 | zenon_intro zenon_H6a ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_L7_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 71.63/71.97 exact (zenon_Hcc zenon_Hca). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hcb); [ zenon_intro zenon_H7f | zenon_intro zenon_H9e ]. % 71.63/71.97 generalize (t6 zenon_TE_ba). zenon_intro zenon_H7e. % 71.63/71.97 generalize (zenon_H69 (end_time zenon_TE_ba)). zenon_intro zenon_H6b. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H23 | zenon_intro zenon_H6e ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H5d | zenon_intro zenon_H63 ]. % 71.63/71.97 apply (zenon_L5_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_L6_ zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_L9_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 generalize (mp_first_movers_exist zenon_TE_ba). zenon_intro zenon_Hcd. % 71.63/71.97 generalize (zenon_H69 (end_time zenon_TE_ba)). zenon_intro zenon_H6b. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H23 | zenon_intro zenon_H6e ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H5d | zenon_intro zenon_H63 ]. % 71.63/71.97 apply (zenon_L5_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 apply (zenon_L6_ zenon_TE_ba); trivial. % 71.63/71.97 generalize (zenon_Hcd (end_time zenon_TE_ba)). zenon_intro zenon_Hce. % 71.63/71.97 apply (zenon_imply_s _ _ zenon_Hce); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H9d ]. % 71.63/71.97 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_H23 | zenon_intro zenon_H6a ]. % 71.63/71.97 exact (zenon_H23 zenon_H14). % 71.63/71.97 exact (zenon_H6a zenon_H6c). % 71.63/71.97 apply (zenon_L12_ zenon_TP_ci zenon_TE_ba); trivial. % 71.63/71.97 exact (zenon_H9f zenon_Ha8). % 71.63/71.97 exact (zenon_Hae zenon_Hb1). % 71.63/71.97 apply zenon_Hab. zenon_intro zenon_Tx_hz. apply NNPP. zenon_intro zenon_Hd0. % 71.63/71.97 apply zenon_Hd0. zenon_intro zenon_Ty_ib. apply NNPP. zenon_intro zenon_Hd2. % 71.63/71.97 apply zenon_Hd2. zenon_intro zenon_Tz_id. apply NNPP. zenon_intro zenon_Hd4. % 71.63/71.97 apply (zenon_notimply_s _ _ zenon_Hd4). zenon_intro zenon_Hd6. zenon_intro zenon_Hd5. % 71.63/71.97 apply (zenon_notimply_s _ _ zenon_Hd5). zenon_intro zenon_Hd8. zenon_intro zenon_Hd7. % 0.07/72.01 generalize (mp_greater_transitivity zenon_Tx_hz). zenon_intro zenon_Hd9. % 0.07/72.01 generalize (zenon_Hd9 zenon_Ty_ib). zenon_intro zenon_Hda. % 0.07/72.01 generalize (zenon_Hda zenon_Tz_id). zenon_intro zenon_Hdb. % 0.07/72.01 apply (zenon_imply_s _ _ zenon_Hdb); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hdc ]. % 0.07/72.01 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_Hdf | zenon_intro zenon_Hde ]. % 0.07/72.01 exact (zenon_Hdf zenon_Hd6). % 0.07/72.01 exact (zenon_Hde zenon_Hd8). % 0.07/72.01 exact (zenon_Hd7 zenon_Hdc). % 0.07/72.01 Qed. % 0.07/72.01 % SZS output end Proof % 0.07/72.01 (* END-PROOF *) % 0.07/72.01 nodes searched: 6178547 % 0.07/72.01 max branch formulas: 25139 % 0.07/72.01 proof nodes created: 18748 % 0.07/72.01 formulas created: 2838072 % 0.07/72.01 %------------------------------------------------------------------------------