%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT025+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 06:24:19 AM UTC 2026 % Result : Theorem 0.20s 0.53s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT025+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.11/0.36 % Computer : n010.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Mon Sep 7 12:10:11 UTC 2026 % 0.11/0.36 % CPUTime : % 0.20/0.53 (* PROOF-FOUND *) % 0.20/0.53 % SZS status Theorem % 0.20/0.53 (* BEGIN-PROOF *) % 0.20/0.53 % SZS output start Proof % 0.20/0.53 Theorem prove_l7 : (forall E : zenon_U, (forall T : zenon_U, (((environment E)/\((subpopulations (first_movers) (efficient_producers) E T)/\(constant (number_of_organizations E T))))->((((growth_rate (first_movers) T) = (zero))/\((growth_rate (efficient_producers) T) = (zero)))\/(((greater (growth_rate (first_movers) T) (zero))/\(greater (zero) (growth_rate (efficient_producers) T)))\/((greater (growth_rate (efficient_producers) T) (zero))/\(greater (zero) (growth_rate (first_movers) T)))))))). % 0.20/0.53 Proof. % 0.20/0.53 assert (zenon_L1_ : forall (zenon_TT_l : zenon_U) (zenon_TE_m : zenon_U), (~(subpopulation (first_movers) zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H8 zenon_H9 zenon_Ha. % 0.20/0.53 generalize (mp_subpopulations zenon_TE_m). zenon_intro zenon_Hd. % 0.20/0.53 generalize (zenon_Hd zenon_TT_l). zenon_intro zenon_He. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 exact (zenon_H11 zenon_H9). % 0.20/0.53 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.20/0.53 exact (zenon_H8 zenon_H14). % 0.20/0.53 (* end of lemma zenon_L1_ *) % 0.20/0.53 assert (zenon_L2_ : forall (zenon_TT_l : zenon_U), ((greater (cardinality_at_time (first_movers) zenon_TT_l) (zero))/\(greater (cardinality_at_time (efficient_producers) zenon_TT_l) (zero))) -> (~(greater (cardinality_at_time (first_movers) zenon_TT_l) (zero))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H15 zenon_H16. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.20/0.53 exact (zenon_H16 zenon_H18). % 0.20/0.53 (* end of lemma zenon_L2_ *) % 0.20/0.53 assert (zenon_L3_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (~(greater (cardinality_at_time (first_movers) zenon_TT_l) (zero))) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H16 zenon_H19 zenon_Ha. % 0.20/0.53 generalize (mp_non_zero_producers zenon_TE_m). zenon_intro zenon_H1a. % 0.20/0.53 generalize (zenon_H1a zenon_TT_l). zenon_intro zenon_H1b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1c | zenon_intro zenon_H15 ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 exact (zenon_H1d zenon_H19). % 0.20/0.53 apply (zenon_L2_ zenon_TT_l); trivial. % 0.20/0.53 (* end of lemma zenon_L3_ *) % 0.20/0.53 assert (zenon_L4_ : forall (zenon_TT_l : zenon_U) (zenon_TE_m : zenon_U), (~(subpopulation (efficient_producers) zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H1e zenon_H9 zenon_Ha. % 0.20/0.53 generalize (mp_subpopulations zenon_TE_m). zenon_intro zenon_Hd. % 0.20/0.53 generalize (zenon_Hd zenon_TT_l). zenon_intro zenon_He. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 exact (zenon_H11 zenon_H9). % 0.20/0.53 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.20/0.53 exact (zenon_H1e zenon_H13). % 0.20/0.53 (* end of lemma zenon_L4_ *) % 0.20/0.53 assert (zenon_L5_ : forall (zenon_TT_l : zenon_U), ((greater (cardinality_at_time (first_movers) zenon_TT_l) (zero))/\(greater (cardinality_at_time (efficient_producers) zenon_TT_l) (zero))) -> (~(greater (cardinality_at_time (efficient_producers) zenon_TT_l) (zero))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H15 zenon_H1f. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.20/0.53 exact (zenon_H1f zenon_H17). % 0.20/0.53 (* end of lemma zenon_L5_ *) % 0.20/0.53 assert (zenon_L6_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (~(greater (cardinality_at_time (efficient_producers) zenon_TT_l) (zero))) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H1f zenon_H19 zenon_Ha. % 0.20/0.53 generalize (mp_non_zero_producers zenon_TE_m). zenon_intro zenon_H1a. % 0.20/0.53 generalize (zenon_H1a zenon_TT_l). zenon_intro zenon_H1b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1c | zenon_intro zenon_H15 ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 exact (zenon_H1d zenon_H19). % 0.20/0.53 apply (zenon_L5_ zenon_TT_l); trivial. % 0.20/0.53 (* end of lemma zenon_L6_ *) % 0.20/0.53 assert (zenon_L7_ : (~((first_movers) = (first_movers))) -> False). % 0.20/0.53 do 0 intro. intros zenon_H20. % 0.20/0.53 apply zenon_H20. apply refl_equal. % 0.20/0.53 (* end of lemma zenon_L7_ *) % 0.20/0.53 assert (zenon_L8_ : forall (zenon_TT_l : zenon_U), (~((greater (cardinality_at_time (first_movers) zenon_TT_l) (zero))->(((first_movers) = (efficient_producers))\/((first_movers) = (first_movers))))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H21. % 0.20/0.53 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H18. zenon_intro zenon_H22. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H23. zenon_intro zenon_H20. % 0.20/0.53 apply zenon_H20. apply refl_equal. % 0.20/0.53 (* end of lemma zenon_L8_ *) % 0.20/0.53 assert (zenon_L9_ : forall (zenon_TT_l : zenon_U) (zenon_TE_m : zenon_U), (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (~((number_of_organizations zenon_TE_m zenon_TT_l) = (sum (cardinality_at_time (first_movers) zenon_TT_l) (cardinality_at_time (efficient_producers) zenon_TT_l)))) -> False). % 0.20/0.53 do 2 intro. intros zenon_Ha zenon_H9 zenon_H24. % 0.20/0.53 generalize (mp_only_members zenon_TE_m). zenon_intro zenon_H25. % 0.20/0.53 generalize (zenon_H25 (first_movers)). zenon_intro zenon_H26. % 0.20/0.53 generalize (zenon_H26 zenon_TT_l). zenon_intro zenon_H27. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H29); [ zenon_intro zenon_H12 | zenon_intro zenon_H2a ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H8 | zenon_intro zenon_H21 ]. % 0.20/0.53 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 apply (zenon_L8_ zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H24 zenon_H28). % 0.20/0.53 (* end of lemma zenon_L9_ *) % 0.20/0.53 assert (zenon_L10_ : forall (zenon_TT_l : zenon_U), ((constant (cardinality_at_time (first_movers) zenon_TT_l))/\(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H2b zenon_H2c. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.20/0.53 exact (zenon_H2c zenon_H2e). % 0.20/0.53 (* end of lemma zenon_L10_ *) % 0.20/0.53 assert (zenon_L11_ : forall (zenon_TT_l : zenon_U), ((increases (cardinality_at_time (first_movers) zenon_TT_l))/\(decreases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(increases (cardinality_at_time (first_movers) zenon_TT_l))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H2f zenon_H30. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.20/0.53 exact (zenon_H30 zenon_H32). % 0.20/0.53 (* end of lemma zenon_L11_ *) % 0.20/0.53 assert (zenon_L12_ : forall (zenon_TT_l : zenon_U), ((decreases (cardinality_at_time (first_movers) zenon_TT_l))/\(increases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(increases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H33 zenon_H34. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.20/0.53 exact (zenon_H34 zenon_H35). % 0.20/0.53 (* end of lemma zenon_L12_ *) % 0.20/0.53 assert (zenon_L13_ : forall (zenon_TT_l : zenon_U) (zenon_TE_m : zenon_U), (forall B : zenon_U, (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum B C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant B)/\(constant C))\/(((increases B)/\(decreases C))\/((decreases B)/\(increases C))))))) -> (~(increases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(increases (cardinality_at_time (first_movers) zenon_TT_l))) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H37 zenon_H34 zenon_H30 zenon_H2c zenon_H38 zenon_H9 zenon_Ha. % 0.20/0.53 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.53 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.53 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 exact (zenon_H3d zenon_H38). % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.53 apply (zenon_L10_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.53 apply (zenon_L11_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L12_ zenon_TT_l); trivial. % 0.20/0.53 (* end of lemma zenon_L13_ *) % 0.20/0.53 assert (zenon_L14_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> (~(increases (cardinality_at_time (first_movers) zenon_TT_l))) -> (forall B : zenon_U, (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum B C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant B)/\(constant C))\/(((increases B)/\(decreases C))\/((decreases B)/\(increases C))))))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H3f zenon_H40 zenon_Ha zenon_H9 zenon_H38 zenon_H2c zenon_H30 zenon_H37. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H34 | zenon_intro zenon_H45 ]. % 0.20/0.53 apply (zenon_L13_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 exact (zenon_H40 zenon_H45). % 0.20/0.53 (* end of lemma zenon_L14_ *) % 0.20/0.53 assert (zenon_L15_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~((growth_rate (first_movers) zenon_TT_l) = (zero))) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H46 zenon_H47 zenon_H40 zenon_H38 zenon_H19 zenon_H9 zenon_Ha zenon_H48. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H30 | zenon_intro zenon_H4e ]. % 0.20/0.53 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.53 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.53 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.53 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.53 exact (zenon_H11 zenon_H9). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.53 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L14_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H48 zenon_H4e). % 0.20/0.53 exact (zenon_H47 zenon_H4d). % 0.20/0.53 (* end of lemma zenon_L15_ *) % 0.20/0.53 assert (zenon_L16_ : forall (zenon_TT_l : zenon_U), ((decreases (cardinality_at_time (first_movers) zenon_TT_l))/\(increases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(decreases (cardinality_at_time (first_movers) zenon_TT_l))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H33 zenon_H55. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.20/0.53 exact (zenon_H55 zenon_H36). % 0.20/0.53 (* end of lemma zenon_L16_ *) % 0.20/0.53 assert (zenon_L17_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), ((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> ((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H4c zenon_H48 zenon_Ha zenon_H9 zenon_H38 zenon_H2c zenon_H56 zenon_H4b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H30 | zenon_intro zenon_H4e ]. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H55 | zenon_intro zenon_H57 ]. % 0.20/0.53 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.53 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.53 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.53 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 exact (zenon_H3d zenon_H38). % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.53 apply (zenon_L10_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.53 apply (zenon_L11_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L16_ zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H56 zenon_H57). % 0.20/0.53 exact (zenon_H48 zenon_H4e). % 0.20/0.53 (* end of lemma zenon_L17_ *) % 0.20/0.53 assert (zenon_L18_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~((growth_rate (first_movers) zenon_TT_l) = (zero))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H46 zenon_H47 zenon_H56 zenon_H38 zenon_H9 zenon_Ha zenon_H48. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 0.20/0.53 apply (zenon_L17_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H47 zenon_H4d). % 0.20/0.53 (* end of lemma zenon_L18_ *) % 0.20/0.53 assert (zenon_L19_ : forall (zenon_TT_l : zenon_U), ((increases (cardinality_at_time (first_movers) zenon_TT_l))/\(decreases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(decreases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H2f zenon_H58. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.20/0.53 exact (zenon_H58 zenon_H31). % 0.20/0.53 (* end of lemma zenon_L19_ *) % 0.20/0.53 assert (zenon_L20_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum (cardinality_at_time (first_movers) zenon_TT_l) C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant (cardinality_at_time (first_movers) zenon_TT_l))/\(constant C))\/(((increases (cardinality_at_time (first_movers) zenon_TT_l))/\(decreases C))\/((decreases (cardinality_at_time (first_movers) zenon_TT_l))/\(increases C)))))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H3f zenon_H40 zenon_H39 zenon_Ha zenon_H9 zenon_H38 zenon_H2c zenon_H59. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H34 | zenon_intro zenon_H45 ]. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H58 | zenon_intro zenon_H5a ]. % 0.20/0.53 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.53 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 exact (zenon_H3d zenon_H38). % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.53 apply (zenon_L10_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.53 apply (zenon_L19_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L12_ zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H59 zenon_H5a). % 0.20/0.53 exact (zenon_H40 zenon_H45). % 0.20/0.53 (* end of lemma zenon_L20_ *) % 0.20/0.53 assert (zenon_L21_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~((growth_rate (first_movers) zenon_TT_l) = (zero))) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H46 zenon_H47 zenon_H40 zenon_H38 zenon_H59 zenon_H19 zenon_H9 zenon_Ha. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 0.20/0.53 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.53 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.53 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.53 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.53 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.53 exact (zenon_H11 zenon_H9). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.53 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L20_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H47 zenon_H4d). % 0.20/0.53 (* end of lemma zenon_L21_ *) % 0.20/0.53 assert (zenon_L22_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> (~(decreases (cardinality_at_time (first_movers) zenon_TT_l))) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H3f zenon_H59 zenon_H55 zenon_H2c zenon_H38 zenon_H9 zenon_Ha. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H58 | zenon_intro zenon_H5a ]. % 0.20/0.53 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.53 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.53 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.53 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 exact (zenon_H3d zenon_H38). % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.53 apply (zenon_L10_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.53 apply (zenon_L19_ zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L16_ zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H59 zenon_H5a). % 0.20/0.53 (* end of lemma zenon_L22_ *) % 0.20/0.53 assert (zenon_L23_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (forall E : zenon_U, (forall T : zenon_U, (((environment E)/\((in_environment E T)/\((subpopulation (efficient_producers) E T)/\(greater (cardinality_at_time (efficient_producers) T) (zero)))))->(((constant (cardinality_at_time (efficient_producers) T))->((growth_rate (efficient_producers) T) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) T))->(greater (growth_rate (efficient_producers) T) (zero)))/\((decreases (cardinality_at_time (efficient_producers) T))->(greater (zero) (growth_rate (efficient_producers) T)))))))) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> (~(decreases (cardinality_at_time (first_movers) zenon_TT_l))) -> (~(constant (cardinality_at_time (first_movers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> False). % 0.20/0.53 do 2 intro. intros zenon_H4f zenon_H59 zenon_H55 zenon_H2c zenon_H38 zenon_H19 zenon_H9 zenon_Ha. % 0.20/0.53 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.53 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.53 exact (zenon_H12 zenon_Ha). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.53 exact (zenon_H11 zenon_H9). % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.53 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.53 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 apply (zenon_L22_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 (* end of lemma zenon_L23_ *) % 0.20/0.53 assert (zenon_L24_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~((growth_rate (first_movers) zenon_TT_l) = (zero))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H46 zenon_H47 zenon_Ha zenon_H9 zenon_H19 zenon_H38 zenon_H59 zenon_H56. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H55 | zenon_intro zenon_H57 ]. % 0.20/0.53 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.53 apply (zenon_L23_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.53 exact (zenon_H56 zenon_H57). % 0.20/0.53 exact (zenon_H47 zenon_H4d). % 0.20/0.53 (* end of lemma zenon_L24_ *) % 0.20/0.53 assert (zenon_L25_ : forall (zenon_TT_l : zenon_U), ((constant (cardinality_at_time (first_movers) zenon_TT_l))/\(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H2b zenon_H5b. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.20/0.53 exact (zenon_H5b zenon_H2d). % 0.20/0.53 (* end of lemma zenon_L25_ *) % 0.20/0.53 assert (zenon_L26_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> ((number_of_organizations zenon_TE_m zenon_TT_l) = (sum (cardinality_at_time (first_movers) zenon_TT_l) (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(increases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (forall B : zenon_U, (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum B C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant B)/\(constant C))\/(((increases B)/\(decreases C))\/((decreases B)/\(increases C))))))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H46 zenon_H48 zenon_H28 zenon_H38 zenon_H5b zenon_H34 zenon_H37. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.20/0.53 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H30 | zenon_intro zenon_H4e ]. % 0.20/0.53 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.54 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.54 exact (zenon_H24 zenon_H28). % 0.20/0.54 exact (zenon_H3d zenon_H38). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.54 apply (zenon_L25_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.54 apply (zenon_L11_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L12_ zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H48 zenon_H4e). % 0.20/0.54 (* end of lemma zenon_L26_ *) % 0.20/0.54 assert (zenon_L27_ : forall (zenon_TT_l : zenon_U) (zenon_TE_m : zenon_U), (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (forall B : zenon_U, (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum B C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant B)/\(constant C))\/(((increases B)/\(decreases C))\/((decreases B)/\(increases C))))))) -> (~(increases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> ((number_of_organizations zenon_TE_m zenon_TT_l) = (sum (cardinality_at_time (first_movers) zenon_TT_l) (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> False). % 0.20/0.54 do 2 intro. intros zenon_Ha zenon_H9 zenon_H19 zenon_H37 zenon_H34 zenon_H5b zenon_H38 zenon_H28 zenon_H48. % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L26_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 (* end of lemma zenon_L27_ *) % 0.20/0.54 assert (zenon_L28_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~((growth_rate (efficient_producers) zenon_TT_l) = (zero))) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H3f zenon_H62 zenon_H48 zenon_H38 zenon_H19 zenon_H9 zenon_Ha zenon_H40. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H5b | zenon_intro zenon_H63 ]. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H34 | zenon_intro zenon_H45 ]. % 0.20/0.54 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.54 generalize (mp_only_members zenon_TE_m). zenon_intro zenon_H25. % 0.20/0.54 generalize (zenon_H25 (first_movers)). zenon_intro zenon_H26. % 0.20/0.54 generalize (zenon_H26 zenon_TT_l). zenon_intro zenon_H27. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H29); [ zenon_intro zenon_H12 | zenon_intro zenon_H2a ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H8 | zenon_intro zenon_H21 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L8_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L27_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 exact (zenon_H40 zenon_H45). % 0.20/0.54 exact (zenon_H62 zenon_H63). % 0.20/0.54 (* end of lemma zenon_L28_ *) % 0.20/0.54 assert (zenon_L29_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> (forall B : zenon_U, (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum B C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant B)/\(constant C))\/(((increases B)/\(decreases C))\/((decreases B)/\(increases C))))))) -> (~(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H46 zenon_H48 zenon_H37 zenon_H5b zenon_H38 zenon_H9 zenon_Ha zenon_H56. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H30 | zenon_intro zenon_H4e ]. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H55 | zenon_intro zenon_H57 ]. % 0.20/0.54 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.54 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.54 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 exact (zenon_H3d zenon_H38). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.54 apply (zenon_L25_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.54 apply (zenon_L11_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L16_ zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H56 zenon_H57). % 0.20/0.54 exact (zenon_H48 zenon_H4e). % 0.20/0.54 (* end of lemma zenon_L29_ *) % 0.20/0.54 assert (zenon_L30_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~((growth_rate (efficient_producers) zenon_TT_l) = (zero))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(greater (growth_rate (first_movers) zenon_TT_l) (zero))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H3f zenon_H62 zenon_Ha zenon_H9 zenon_H19 zenon_H56 zenon_H38 zenon_H48. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H5b | zenon_intro zenon_H63 ]. % 0.20/0.54 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L29_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H62 zenon_H63). % 0.20/0.54 (* end of lemma zenon_L30_ *) % 0.20/0.54 assert (zenon_L31_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), ((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> ((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H44 zenon_H40 zenon_Ha zenon_H9 zenon_H38 zenon_H5b zenon_H59 zenon_H43. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H34 | zenon_intro zenon_H45 ]. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H58 | zenon_intro zenon_H5a ]. % 0.20/0.54 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.54 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.54 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.54 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 exact (zenon_H3d zenon_H38). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.54 apply (zenon_L25_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.54 apply (zenon_L19_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L12_ zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H59 zenon_H5a). % 0.20/0.54 exact (zenon_H40 zenon_H45). % 0.20/0.54 (* end of lemma zenon_L31_ *) % 0.20/0.54 assert (zenon_L32_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~((growth_rate (efficient_producers) zenon_TT_l) = (zero))) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> (~(greater (growth_rate (efficient_producers) zenon_TT_l) (zero))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H3f zenon_H62 zenon_H59 zenon_H38 zenon_H9 zenon_Ha zenon_H40. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H5b | zenon_intro zenon_H63 ]. % 0.20/0.54 apply (zenon_L31_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H62 zenon_H63). % 0.20/0.54 (* end of lemma zenon_L32_ *) % 0.20/0.54 assert (zenon_L33_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (first_movers) zenon_TT_l))->((growth_rate (first_movers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (growth_rate (first_movers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (first_movers) zenon_TT_l))->(greater (zero) (growth_rate (first_movers) zenon_TT_l))))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> (environment zenon_TE_m) -> (in_environment zenon_TE_m zenon_TT_l) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (~(constant (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (~(decreases (cardinality_at_time (efficient_producers) zenon_TT_l))) -> (forall B : zenon_U, (forall C : zenon_U, ((((number_of_organizations zenon_TE_m zenon_TT_l) = (sum B C))/\(constant (number_of_organizations zenon_TE_m zenon_TT_l)))->(((constant B)/\(constant C))\/(((increases B)/\(decreases C))\/((decreases B)/\(increases C))))))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H46 zenon_H56 zenon_Ha zenon_H9 zenon_H38 zenon_H5b zenon_H58 zenon_H37. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H55 | zenon_intro zenon_H57 ]. % 0.20/0.54 generalize (zenon_H37 (cardinality_at_time (first_movers) zenon_TT_l)). zenon_intro zenon_H39. % 0.20/0.54 generalize (zenon_H39 (cardinality_at_time (efficient_producers) zenon_TT_l)). zenon_intro zenon_H3a. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H24 | zenon_intro zenon_H3d ]. % 0.20/0.54 apply (zenon_L9_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 exact (zenon_H3d zenon_H38). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3e ]. % 0.20/0.54 apply (zenon_L25_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H2f | zenon_intro zenon_H33 ]. % 0.20/0.54 apply (zenon_L19_ zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L16_ zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H56 zenon_H57). % 0.20/0.54 (* end of lemma zenon_L33_ *) % 0.20/0.54 assert (zenon_L34_ : forall (zenon_TE_m : zenon_U) (zenon_TT_l : zenon_U), (((constant (cardinality_at_time (efficient_producers) zenon_TT_l))->((growth_rate (efficient_producers) zenon_TT_l) = (zero)))/\(((increases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (growth_rate (efficient_producers) zenon_TT_l) (zero)))/\((decreases (cardinality_at_time (efficient_producers) zenon_TT_l))->(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))))) -> (~((growth_rate (efficient_producers) zenon_TT_l) = (zero))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_l))) -> (constant (number_of_organizations zenon_TE_m zenon_TT_l)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_m zenon_TT_l) -> (in_environment zenon_TE_m zenon_TT_l) -> (environment zenon_TE_m) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_l))) -> False). % 0.20/0.54 do 2 intro. intros zenon_H3f zenon_H62 zenon_H56 zenon_H38 zenon_H19 zenon_H9 zenon_Ha zenon_H59. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H5b | zenon_intro zenon_H63 ]. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H58 | zenon_intro zenon_H5a ]. % 0.20/0.54 generalize (mp_abc_sum_increase (number_of_organizations zenon_TE_m zenon_TT_l)). zenon_intro zenon_H37. % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L33_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 exact (zenon_H59 zenon_H5a). % 0.20/0.54 exact (zenon_H62 zenon_H63). % 0.20/0.54 (* end of lemma zenon_L34_ *) % 0.20/0.54 apply NNPP. intro zenon_G. % 0.20/0.54 apply (zenon_notallex_s (fun E : zenon_U => (forall T : zenon_U, (((environment E)/\((subpopulations (first_movers) (efficient_producers) E T)/\(constant (number_of_organizations E T))))->((((growth_rate (first_movers) T) = (zero))/\((growth_rate (efficient_producers) T) = (zero)))\/(((greater (growth_rate (first_movers) T) (zero))/\(greater (zero) (growth_rate (efficient_producers) T)))\/((greater (growth_rate (efficient_producers) T) (zero))/\(greater (zero) (growth_rate (first_movers) T)))))))) zenon_G); [ zenon_intro zenon_H64; idtac ]. % 0.20/0.54 elim zenon_H64. zenon_intro zenon_TE_m. zenon_intro zenon_H65. % 0.20/0.54 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_m)/\((subpopulations (first_movers) (efficient_producers) zenon_TE_m T)/\(constant (number_of_organizations zenon_TE_m T))))->((((growth_rate (first_movers) T) = (zero))/\((growth_rate (efficient_producers) T) = (zero)))\/(((greater (growth_rate (first_movers) T) (zero))/\(greater (zero) (growth_rate (efficient_producers) T)))\/((greater (growth_rate (efficient_producers) T) (zero))/\(greater (zero) (growth_rate (first_movers) T))))))) zenon_H65); [ zenon_intro zenon_H66; idtac ]. % 0.20/0.54 elim zenon_H66. zenon_intro zenon_TT_l. zenon_intro zenon_H67. % 0.20/0.54 apply (zenon_notimply_s _ _ zenon_H67). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_Ha. zenon_intro zenon_H6e. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H19. zenon_intro zenon_H38. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H47 | zenon_intro zenon_H62 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H48 | zenon_intro zenon_H59 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H40 | zenon_intro zenon_H56 ]. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L15_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L18_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H40 | zenon_intro zenon_H56 ]. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L21_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (first_movers)). zenon_intro zenon_H5c. % 0.20/0.54 generalize (zenon_H5c zenon_TE_m). zenon_intro zenon_H5d. % 0.20/0.54 generalize (zenon_H5d zenon_TT_l). zenon_intro zenon_H5e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5f | zenon_intro zenon_H46 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H12 | zenon_intro zenon_H60 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H11 | zenon_intro zenon_H61 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H8 | zenon_intro zenon_H16 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L24_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H48 | zenon_intro zenon_H59 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H40 | zenon_intro zenon_H56 ]. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.54 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.54 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.54 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L28_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.54 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.54 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.54 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L30_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H40 | zenon_intro zenon_H56 ]. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.54 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.54 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.54 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L32_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 generalize (mp_time_point_occur zenon_TE_m). zenon_intro zenon_H6f. % 0.20/0.54 generalize (zenon_H6f zenon_TT_l). zenon_intro zenon_H70. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H1c | zenon_intro zenon_H9 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H12 | zenon_intro zenon_H1d ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 exact (zenon_H1d zenon_H19). % 0.20/0.54 generalize (mp_growth_rate (efficient_producers)). zenon_intro zenon_H4f. % 0.20/0.54 generalize (zenon_H4f zenon_TE_m). zenon_intro zenon_H50. % 0.20/0.54 generalize (zenon_H50 zenon_TT_l). zenon_intro zenon_H51. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H3f ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H53 ]. % 0.20/0.54 exact (zenon_H12 zenon_Ha). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H11 | zenon_intro zenon_H54 ]. % 0.20/0.54 exact (zenon_H11 zenon_H9). % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.20/0.54 apply (zenon_L4_ zenon_TT_l zenon_TE_m); trivial. % 0.20/0.54 apply (zenon_L6_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 apply (zenon_L34_ zenon_TE_m zenon_TT_l); trivial. % 0.20/0.54 Qed. % 0.20/0.54 % SZS output end Proof % 0.20/0.54 (* END-PROOF *) % 0.20/0.54 nodes searched: 9144 % 0.20/0.54 max branch formulas: 1038 % 0.20/0.54 proof nodes created: 1473 % 0.20/0.54 formulas created: 21662 % 0.20/0.54 %------------------------------------------------------------------------------