%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT055+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 06:24:24 AM UTC 2026 % Result : Theorem 3.43s 3.77s % Output : Proof 3.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT055+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n019.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 13:26:22 UTC 2026 % 0.09/0.35 % CPUTime : % 3.43/3.77 (* PROOF-FOUND *) % 3.43/3.77 % SZS status Theorem % 3.43/3.77 (* BEGIN-PROOF *) % 3.43/3.77 % SZS output start Proof % 3.43/3.77 Theorem lemma_8 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization X)/\((has_endowment X)/\(((age X T0) = (zero))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (eta))/\((smaller_or_equal (age X T2) (sigma))/\((greater (age X T3) (sigma))/\((greater (sigma) (eta))/\(greater (eta) (zero))))))))))->((greater (hazard_of_mortality X T3) (hazard_of_mortality X T2))/\((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))). % 3.43/3.77 Proof. % 3.43/3.77 assert (zenon_L1_ : (~((eta) = (eta))) -> False). % 3.43/3.77 do 0 intro. intros zenon_Hf. % 3.43/3.77 apply zenon_Hf. apply refl_equal. % 3.43/3.77 (* end of lemma zenon_L1_ *) % 3.43/3.77 assert (zenon_L2_ : forall (zenon_TT3_v : zenon_U) (zenon_TX_w : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((greater (age zenon_TX_w zenon_TT3_v) (eta))->(~(has_immunity zenon_TX_w zenon_TT3_v))) -> (has_immunity zenon_TX_w zenon_TT3_v) -> (greater (age zenon_TX_w zenon_TT3_v) (sigma)) -> (greater (sigma) (eta)) -> False). % 3.43/3.77 do 2 intro. intros zenon_H10 zenon_H11 zenon_H12 zenon_H13 zenon_H14. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H11); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 3.43/3.77 elim (classic ((~((age zenon_TX_w zenon_TT3_v) = (sigma)))/\(~(greater (age zenon_TX_w zenon_TT3_v) (sigma))))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 3.43/3.77 exact (zenon_H1b zenon_H13). % 3.43/3.77 cut ((greater (sigma) (eta)) = (greater (age zenon_TX_w zenon_TT3_v) (eta))). % 3.43/3.77 intro zenon_D_pnotp. % 3.43/3.77 apply zenon_H18. % 3.43/3.77 rewrite <- zenon_D_pnotp. % 3.43/3.77 exact zenon_H14. % 3.43/3.77 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 3.43/3.77 cut (((sigma) = (age zenon_TX_w zenon_TT3_v))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 3.43/3.77 congruence. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 3.43/3.77 apply zenon_H1f. zenon_intro zenon_H20. % 3.43/3.77 elim (classic ((age zenon_TX_w zenon_TT3_v) = (age zenon_TX_w zenon_TT3_v))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT3_v) = (age zenon_TX_w zenon_TT3_v)) = ((sigma) = (age zenon_TX_w zenon_TT3_v))). % 3.43/3.77 intro zenon_D_pnotp. % 3.43/3.77 apply zenon_H1d. % 3.43/3.77 rewrite <- zenon_D_pnotp. % 3.43/3.77 exact zenon_H21. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT3_v) = (age zenon_TX_w zenon_TT3_v))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT3_v) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 3.43/3.77 congruence. % 3.43/3.77 exact (zenon_H1c zenon_H20). % 3.43/3.77 apply zenon_H22. apply refl_equal. % 3.43/3.77 apply zenon_H22. apply refl_equal. % 3.43/3.77 apply zenon_H1e. zenon_intro zenon_H13. % 3.43/3.77 generalize (zenon_H10 (age zenon_TX_w zenon_TT3_v)). zenon_intro zenon_H23. % 3.43/3.77 generalize (zenon_H23 (sigma)). zenon_intro zenon_H24. % 3.43/3.77 generalize (zenon_H24 (eta)). zenon_intro zenon_H25. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H1b | zenon_intro zenon_H26 ]. % 3.43/3.77 exact (zenon_H1b zenon_H13). % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 3.43/3.77 exact (zenon_H28 zenon_H14). % 3.43/3.77 exact (zenon_H18 zenon_H27). % 3.43/3.77 apply zenon_Hf. apply refl_equal. % 3.43/3.77 exact (zenon_H17 zenon_H12). % 3.43/3.77 (* end of lemma zenon_L2_ *) % 3.43/3.77 assert (zenon_L3_ : forall (zenon_TT3_v : zenon_U) (zenon_TX_w : 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, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> (has_immunity zenon_TX_w zenon_TT3_v) -> (greater (age zenon_TX_w zenon_TT3_v) (sigma)) -> (greater (sigma) (eta)) -> False). % 3.43/3.77 do 2 intro. intros zenon_H10 zenon_H29 zenon_H12 zenon_H13 zenon_H14. % 3.43/3.77 generalize (zenon_H29 zenon_TT3_v). zenon_intro zenon_H2a. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H11. % 3.43/3.77 apply (zenon_L2_ zenon_TT3_v zenon_TX_w); trivial. % 3.43/3.77 (* end of lemma zenon_L3_ *) % 3.43/3.77 assert (zenon_L4_ : forall (zenon_TT2_bz : zenon_U) (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_w)/\((age zenon_TX_w T0) = (zero)))->((greater (age zenon_TX_w T) (sigma))<->(dissimilar zenon_TX_w T0 T))))) -> (is_aligned zenon_TX_w zenon_TT0_ca) -> (~(is_aligned zenon_TX_w zenon_TT2_bz)) -> (~(greater (age zenon_TX_w zenon_TT2_bz) (sigma))) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> (organization zenon_TX_w) -> False). % 3.43/3.77 do 3 intro. intros zenon_H2e zenon_H2f zenon_H30 zenon_H31 zenon_H32 zenon_H2c. % 3.43/3.77 generalize (zenon_H2e zenon_TT0_ca). zenon_intro zenon_H35. % 3.43/3.77 generalize (zenon_H35 zenon_TT2_bz). zenon_intro zenon_H36. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 exact (zenon_H39 zenon_H32). % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H31; zenon_intro zenon_H3d | zenon_intro zenon_H3c; zenon_intro zenon_H3b ]. % 3.43/3.77 generalize (definition_2 zenon_TX_w). zenon_intro zenon_H3e. % 3.43/3.77 generalize (zenon_H3e zenon_TT0_ca). zenon_intro zenon_H3f. % 3.43/3.77 generalize (zenon_H3f zenon_TT2_bz). zenon_intro zenon_H40. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H40); [ zenon_intro zenon_H3d; zenon_intro zenon_H42 | zenon_intro zenon_H3b; zenon_intro zenon_H41 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H3a | zenon_intro zenon_H43 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply zenon_H43. zenon_intro zenon_H44. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H46; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H45 ]. % 3.43/3.77 exact (zenon_H46 zenon_H2f). % 3.43/3.77 exact (zenon_H30 zenon_H45). % 3.43/3.77 exact (zenon_H3d zenon_H3b). % 3.43/3.77 exact (zenon_H31 zenon_H3c). % 3.43/3.77 (* end of lemma zenon_L4_ *) % 3.43/3.77 assert (zenon_L5_ : forall (zenon_TT0_ca : zenon_U) (zenon_TT3_v : zenon_U) (zenon_TX_w : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_w)/\((age zenon_TX_w T0) = (zero)))->((greater (age zenon_TX_w T) (sigma))<->(dissimilar zenon_TX_w T0 T))))) -> (greater (age zenon_TX_w zenon_TT3_v) (sigma)) -> (is_aligned zenon_TX_w zenon_TT3_v) -> (is_aligned zenon_TX_w zenon_TT0_ca) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> (organization zenon_TX_w) -> False). % 3.43/3.77 do 3 intro. intros zenon_H2e zenon_H13 zenon_H47 zenon_H2f zenon_H32 zenon_H2c. % 3.43/3.77 generalize (zenon_H2e zenon_TT0_ca). zenon_intro zenon_H35. % 3.43/3.77 generalize (zenon_H35 zenon_TT3_v). zenon_intro zenon_H48. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H38 | zenon_intro zenon_H49 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 exact (zenon_H39 zenon_H32). % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H1b; zenon_intro zenon_H4b | zenon_intro zenon_H13; zenon_intro zenon_H4a ]. % 3.43/3.77 exact (zenon_H1b zenon_H13). % 3.43/3.77 generalize (definition_2 zenon_TX_w). zenon_intro zenon_H3e. % 3.43/3.77 generalize (zenon_H3e zenon_TT0_ca). zenon_intro zenon_H3f. % 3.43/3.77 generalize (zenon_H3f zenon_TT3_v). zenon_intro zenon_H4c. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4b; zenon_intro zenon_H4e | zenon_intro zenon_H4a; zenon_intro zenon_H4d ]. % 3.43/3.77 exact (zenon_H4b zenon_H4a). % 3.43/3.77 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H2c. zenon_intro zenon_H4f. % 3.43/3.77 apply (zenon_notequiv_s _ _ zenon_H4f); [ zenon_intro zenon_H46; zenon_intro zenon_H47 | zenon_intro zenon_H2f; zenon_intro zenon_H50 ]. % 3.43/3.77 exact (zenon_H46 zenon_H2f). % 3.43/3.77 exact (zenon_H50 zenon_H47). % 3.43/3.77 (* end of lemma zenon_L5_ *) % 3.43/3.77 assert (zenon_L6_ : forall (zenon_TT3_v : zenon_U) (zenon_TT0_ca : zenon_U) (zenon_TT2_bz : zenon_U) (zenon_TX_w : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (age zenon_TX_w zenon_TT2_bz) (eta)) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> (~(greater (hazard_of_mortality zenon_TX_w zenon_TT3_v) (hazard_of_mortality zenon_TX_w zenon_TT2_bz))) -> (greater (sigma) (age zenon_TX_w zenon_TT2_bz)) -> (greater (sigma) (eta)) -> (greater (age zenon_TX_w zenon_TT3_v) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> False). % 3.43/3.77 do 4 intro. intros zenon_H10 zenon_H51 zenon_H32 zenon_H52 zenon_H53 zenon_H14 zenon_H13 zenon_H29. % 3.43/3.77 generalize (assumption_13 zenon_TX_w). zenon_intro zenon_H54. % 3.43/3.77 generalize (zenon_H29 zenon_TT2_bz). zenon_intro zenon_H55. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H2c. zenon_intro zenon_H56. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 3.43/3.77 exact (zenon_H5a zenon_H51). % 3.43/3.77 generalize (zenon_H54 zenon_TT0_ca). zenon_intro zenon_H5b. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H38 | zenon_intro zenon_H2f ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 exact (zenon_H39 zenon_H32). % 3.43/3.77 generalize (assumption_16 zenon_TX_w). zenon_intro zenon_H5c. % 3.43/3.77 generalize (assumption_15 zenon_TX_w). zenon_intro zenon_H2e. % 3.43/3.77 generalize (zenon_H5c zenon_TT3_v). zenon_intro zenon_H5d. % 3.43/3.77 generalize (zenon_H5d zenon_TT2_bz). zenon_intro zenon_H5e. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H3a | zenon_intro zenon_H61 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 3.43/3.77 apply zenon_H63. zenon_intro zenon_H12. % 3.43/3.77 apply (zenon_L3_ zenon_TT3_v zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 3.43/3.77 exact (zenon_H65 zenon_H59). % 3.43/3.77 generalize (assumption_14 zenon_TX_w). zenon_intro zenon_H66. % 3.43/3.77 generalize (zenon_H66 zenon_TT2_bz). zenon_intro zenon_H67. % 3.43/3.77 generalize (zenon_H67 zenon_TT3_v). zenon_intro zenon_H68. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H3a | zenon_intro zenon_H6b ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H30 | zenon_intro zenon_H6c ]. % 3.43/3.77 generalize (meaning_postulate_greater_strict (age zenon_TX_w zenon_TT2_bz)). zenon_intro zenon_H6d. % 3.43/3.77 generalize (zenon_H6d (sigma)). zenon_intro zenon_H6e. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H31 | zenon_intro zenon_H6f ]. % 3.43/3.77 apply (zenon_L4_ zenon_TT2_bz zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 exact (zenon_H6f zenon_H53). % 3.43/3.77 apply zenon_H6c. zenon_intro zenon_H47. % 3.43/3.77 apply (zenon_L5_ zenon_TT0_ca zenon_TT3_v zenon_TX_w); trivial. % 3.43/3.77 exact (zenon_H64 zenon_H69). % 3.43/3.77 exact (zenon_H52 zenon_H5f). % 3.43/3.77 (* end of lemma zenon_L6_ *) % 3.43/3.77 assert (zenon_L7_ : forall (zenon_TT1_ek : zenon_U) (zenon_TX_w : zenon_U), (greater (eta) (age zenon_TX_w zenon_TT1_ek)) -> (~(smaller_or_equal (age zenon_TX_w zenon_TT1_ek) (eta))) -> False). % 3.43/3.77 do 2 intro. intros zenon_H70 zenon_H71. % 3.43/3.77 generalize (definition_smaller_or_equal (age zenon_TX_w zenon_TT1_ek)). zenon_intro zenon_H73. % 3.43/3.77 generalize (zenon_H73 (eta)). zenon_intro zenon_H74. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H71; zenon_intro zenon_H77 | zenon_intro zenon_H76; zenon_intro zenon_H75 ]. % 3.43/3.77 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78. % 3.43/3.77 generalize (definition_smaller (age zenon_TX_w zenon_TT1_ek)). zenon_intro zenon_H7a. % 3.43/3.77 generalize (zenon_H7a (eta)). zenon_intro zenon_H7b. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H7b); [ zenon_intro zenon_H79; zenon_intro zenon_H7d | zenon_intro zenon_H7c; zenon_intro zenon_H70 ]. % 3.43/3.77 exact (zenon_H7d zenon_H70). % 3.43/3.77 exact (zenon_H79 zenon_H7c). % 3.43/3.77 exact (zenon_H71 zenon_H76). % 3.43/3.77 (* end of lemma zenon_L7_ *) % 3.43/3.77 assert (zenon_L8_ : forall (zenon_TT2_bz : zenon_U) (zenon_TT1_ek : zenon_U) (zenon_TX_w : zenon_U), (organization zenon_TX_w) -> (has_immunity zenon_TX_w zenon_TT1_ek) -> (~(has_immunity zenon_TX_w zenon_TT2_bz)) -> (~(greater (hazard_of_mortality zenon_TX_w zenon_TT2_bz) (hazard_of_mortality zenon_TX_w zenon_TT1_ek))) -> False). % 3.43/3.77 do 3 intro. intros zenon_H2c zenon_H7e zenon_H59 zenon_H7f. % 3.43/3.77 generalize (assumption_3 zenon_TX_w). zenon_intro zenon_H80. % 3.43/3.77 generalize (zenon_H80 zenon_TT1_ek). zenon_intro zenon_H81. % 3.43/3.77 generalize (zenon_H81 zenon_TT2_bz). zenon_intro zenon_H82. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H84); [ zenon_intro zenon_H3a | zenon_intro zenon_H85 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H86 | zenon_intro zenon_H65 ]. % 3.43/3.77 exact (zenon_H86 zenon_H7e). % 3.43/3.77 exact (zenon_H65 zenon_H59). % 3.43/3.77 exact (zenon_H7f zenon_H83). % 3.43/3.77 (* end of lemma zenon_L8_ *) % 3.43/3.77 assert (zenon_L9_ : forall (zenon_TT2_bz : zenon_U) (zenon_TT1_ek : zenon_U) (zenon_TX_w : zenon_U), (greater (eta) (age zenon_TX_w zenon_TT1_ek)) -> (~(greater (hazard_of_mortality zenon_TX_w zenon_TT2_bz) (hazard_of_mortality zenon_TX_w zenon_TT1_ek))) -> (forall T : zenon_U, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> (greater (age zenon_TX_w zenon_TT2_bz) (eta)) -> False). % 3.43/3.77 do 3 intro. intros zenon_H70 zenon_H7f zenon_H29 zenon_H51. % 3.43/3.77 generalize (zenon_H29 zenon_TT2_bz). zenon_intro zenon_H55. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H2c. zenon_intro zenon_H56. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 3.43/3.77 exact (zenon_H5a zenon_H51). % 3.43/3.77 generalize (zenon_H29 zenon_TT1_ek). zenon_intro zenon_H87. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H2c. zenon_intro zenon_H88. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7e ]. % 3.43/3.77 apply (zenon_L7_ zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L8_ zenon_TT2_bz zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 (* end of lemma zenon_L9_ *) % 3.43/3.77 assert (zenon_L10_ : forall (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), (~(greater (eta) (age zenon_TX_w zenon_TT0_ca))) -> (greater (eta) (zero)) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> False). % 3.43/3.77 do 2 intro. intros zenon_H8b zenon_H8c zenon_H32. % 3.43/3.77 elim (classic ((zero) = (age zenon_TX_w zenon_TT0_ca))); [ zenon_intro zenon_H8d | zenon_intro zenon_H8e ]. % 3.43/3.77 cut ((greater (eta) (zero)) = (greater (eta) (age zenon_TX_w zenon_TT0_ca))). % 3.43/3.77 intro zenon_D_pnotp. % 3.43/3.77 apply zenon_H8b. % 3.43/3.77 rewrite <- zenon_D_pnotp. % 3.43/3.77 exact zenon_H8c. % 3.43/3.77 cut (((zero) = (age zenon_TX_w zenon_TT0_ca))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 3.43/3.77 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 3.43/3.77 congruence. % 3.43/3.77 apply zenon_Hf. apply refl_equal. % 3.43/3.77 exact (zenon_H8e zenon_H8d). % 3.43/3.77 apply zenon_H8e. apply sym_equal. exact zenon_H32. % 3.43/3.77 (* end of lemma zenon_L10_ *) % 3.43/3.77 assert (zenon_L11_ : forall (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> (greater (eta) (zero)) -> (~(smaller_or_equal (age zenon_TX_w zenon_TT0_ca) (eta))) -> False). % 3.43/3.77 do 2 intro. intros zenon_H32 zenon_H8c zenon_H8f. % 3.43/3.77 generalize (definition_smaller_or_equal (age zenon_TX_w zenon_TT0_ca)). zenon_intro zenon_H90. % 3.43/3.77 generalize (zenon_H90 (eta)). zenon_intro zenon_H91. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H91); [ zenon_intro zenon_H8f; zenon_intro zenon_H94 | zenon_intro zenon_H93; zenon_intro zenon_H92 ]. % 3.43/3.77 apply (zenon_notor_s _ _ zenon_H94). zenon_intro zenon_H96. zenon_intro zenon_H95. % 3.43/3.77 generalize (definition_smaller (age zenon_TX_w zenon_TT0_ca)). zenon_intro zenon_H97. % 3.43/3.77 generalize (zenon_H97 (eta)). zenon_intro zenon_H98. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H98); [ zenon_intro zenon_H96; zenon_intro zenon_H8b | zenon_intro zenon_H9a; zenon_intro zenon_H99 ]. % 3.43/3.77 apply (zenon_L10_ zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 exact (zenon_H96 zenon_H9a). % 3.43/3.77 exact (zenon_H8f zenon_H93). % 3.43/3.77 (* end of lemma zenon_L11_ *) % 3.43/3.77 assert (zenon_L12_ : forall (zenon_TT1_ek : zenon_U) (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), (forall T : zenon_U, (((organization zenon_TX_w)/\((has_immunity zenon_TX_w zenon_TT0_ca)/\(has_immunity zenon_TX_w T)))->((hazard_of_mortality zenon_TX_w zenon_TT0_ca) = (hazard_of_mortality zenon_TX_w T)))) -> (organization zenon_TX_w) -> (has_immunity zenon_TX_w zenon_TT0_ca) -> (has_immunity zenon_TX_w zenon_TT1_ek) -> (~((hazard_of_mortality zenon_TX_w zenon_TT1_ek) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca))) -> False). % 3.43/3.77 do 3 intro. intros zenon_H9b zenon_H2c zenon_H9c zenon_H7e zenon_H9d. % 3.43/3.77 generalize (zenon_H9b zenon_TT1_ek). zenon_intro zenon_H9e. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H9e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9f ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Ha0); [ zenon_intro zenon_H3a | zenon_intro zenon_Ha1 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H86 ]. % 3.43/3.77 exact (zenon_Ha2 zenon_H9c). % 3.43/3.77 exact (zenon_H86 zenon_H7e). % 3.43/3.77 apply zenon_H9d. apply sym_equal. exact zenon_H9f. % 3.43/3.77 (* end of lemma zenon_L12_ *) % 3.43/3.77 assert (zenon_L13_ : forall (zenon_TT1_ek : zenon_U) (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), (organization zenon_TX_w) -> (has_immunity zenon_TX_w zenon_TT0_ca) -> (has_immunity zenon_TX_w zenon_TT1_ek) -> (~((hazard_of_mortality zenon_TX_w zenon_TT1_ek) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca))) -> False). % 3.43/3.77 do 3 intro. intros zenon_H2c zenon_H9c zenon_H7e zenon_H9d. % 3.43/3.77 generalize (assumption_2 zenon_TX_w). zenon_intro zenon_Ha3. % 3.43/3.77 generalize (zenon_Ha3 zenon_TT0_ca). zenon_intro zenon_H9b. % 3.43/3.77 apply (zenon_L12_ zenon_TT1_ek zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 (* end of lemma zenon_L13_ *) % 3.43/3.77 assert (zenon_L14_ : forall (zenon_TT0_ca : zenon_U) (zenon_TT1_ek : zenon_U) (zenon_TX_w : zenon_U), (greater (eta) (age zenon_TX_w zenon_TT1_ek)) -> (~((hazard_of_mortality zenon_TX_w zenon_TT1_ek) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca))) -> (forall T : zenon_U, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> (greater (eta) (zero)) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> False). % 3.43/3.77 do 3 intro. intros zenon_H70 zenon_H9d zenon_H29 zenon_H8c zenon_H32. % 3.43/3.77 generalize (zenon_H29 zenon_TT0_ca). zenon_intro zenon_Ha4. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Ha4). zenon_intro zenon_H2c. zenon_intro zenon_Ha5. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Ha5). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H8f | zenon_intro zenon_H9c ]. % 3.43/3.77 apply (zenon_L11_ zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 generalize (zenon_H29 zenon_TT1_ek). zenon_intro zenon_H87. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H2c. zenon_intro zenon_H88. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7e ]. % 3.43/3.77 apply (zenon_L7_ zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L13_ zenon_TT1_ek zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 (* end of lemma zenon_L14_ *) % 3.43/3.77 assert (zenon_L15_ : forall (zenon_TT1_ek : zenon_U) (zenon_TX_w : zenon_U), ((age zenon_TX_w zenon_TT1_ek) = (eta)) -> (~(smaller_or_equal (age zenon_TX_w zenon_TT1_ek) (eta))) -> False). % 3.43/3.77 do 2 intro. intros zenon_Ha8 zenon_H71. % 3.43/3.77 generalize (definition_smaller_or_equal (age zenon_TX_w zenon_TT1_ek)). zenon_intro zenon_H73. % 3.43/3.77 generalize (zenon_H73 (eta)). zenon_intro zenon_H74. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H71; zenon_intro zenon_H77 | zenon_intro zenon_H76; zenon_intro zenon_H75 ]. % 3.43/3.77 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78. % 3.43/3.77 exact (zenon_H78 zenon_Ha8). % 3.43/3.77 exact (zenon_H71 zenon_H76). % 3.43/3.77 (* end of lemma zenon_L15_ *) % 3.43/3.77 assert (zenon_L16_ : forall (zenon_TT2_bz : zenon_U) (zenon_TT1_ek : zenon_U) (zenon_TX_w : zenon_U), ((age zenon_TX_w zenon_TT1_ek) = (eta)) -> (~(greater (hazard_of_mortality zenon_TX_w zenon_TT2_bz) (hazard_of_mortality zenon_TX_w zenon_TT1_ek))) -> (forall T : zenon_U, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> (greater (age zenon_TX_w zenon_TT2_bz) (eta)) -> False). % 3.43/3.77 do 3 intro. intros zenon_Ha8 zenon_H7f zenon_H29 zenon_H51. % 3.43/3.77 generalize (zenon_H29 zenon_TT2_bz). zenon_intro zenon_H55. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H2c. zenon_intro zenon_H56. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 3.43/3.77 exact (zenon_H5a zenon_H51). % 3.43/3.77 generalize (zenon_H29 zenon_TT1_ek). zenon_intro zenon_H87. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H2c. zenon_intro zenon_H88. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7e ]. % 3.43/3.77 apply (zenon_L15_ zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L8_ zenon_TT2_bz zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 (* end of lemma zenon_L16_ *) % 3.43/3.77 assert (zenon_L17_ : forall (zenon_TT1_ek : zenon_U) (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> (greater (eta) (zero)) -> (~((hazard_of_mortality zenon_TX_w zenon_TT1_ek) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca))) -> (forall T : zenon_U, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> ((age zenon_TX_w zenon_TT1_ek) = (eta)) -> False). % 3.43/3.77 do 3 intro. intros zenon_H32 zenon_H8c zenon_H9d zenon_H29 zenon_Ha8. % 3.43/3.77 generalize (zenon_H29 zenon_TT1_ek). zenon_intro zenon_H87. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H2c. zenon_intro zenon_H88. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7e ]. % 3.43/3.77 apply (zenon_L15_ zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 generalize (zenon_H29 zenon_TT0_ca). zenon_intro zenon_Ha4. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Ha4). zenon_intro zenon_H2c. zenon_intro zenon_Ha5. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Ha5). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H8f | zenon_intro zenon_H9c ]. % 3.43/3.77 apply (zenon_L11_ zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L13_ zenon_TT1_ek zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 (* end of lemma zenon_L17_ *) % 3.43/3.77 assert (zenon_L18_ : (~((sigma) = (sigma))) -> False). % 3.43/3.77 do 0 intro. intros zenon_Ha9. % 3.43/3.77 apply zenon_Ha9. apply refl_equal. % 3.43/3.77 (* end of lemma zenon_L18_ *) % 3.43/3.77 assert (zenon_L19_ : forall (zenon_TT2_bz : zenon_U) (zenon_TT0_ca : zenon_U) (zenon_TX_w : zenon_U), (organization zenon_TX_w) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> (~(is_aligned zenon_TX_w zenon_TT2_bz)) -> (is_aligned zenon_TX_w zenon_TT0_ca) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_w)/\((age zenon_TX_w T0) = (zero)))->((greater (age zenon_TX_w T) (sigma))<->(dissimilar zenon_TX_w T0 T))))) -> (~(greater (sigma) (sigma))) -> ((age zenon_TX_w zenon_TT2_bz) = (sigma)) -> False). % 3.43/3.77 do 3 intro. intros zenon_H2c zenon_H32 zenon_H30 zenon_H2f zenon_H2e zenon_Haa zenon_Hab. % 3.43/3.77 elim (classic ((sigma) = (age zenon_TX_w zenon_TT2_bz))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 3.43/3.77 elim (classic (greater (age zenon_TX_w zenon_TT2_bz) (sigma))); [ zenon_intro zenon_H3c | zenon_intro zenon_H31 ]. % 3.43/3.77 cut ((greater (age zenon_TX_w zenon_TT2_bz) (sigma)) = (greater (sigma) (sigma))). % 3.43/3.77 intro zenon_D_pnotp. % 3.43/3.77 apply zenon_Haa. % 3.43/3.77 rewrite <- zenon_D_pnotp. % 3.43/3.77 exact zenon_H3c. % 3.43/3.77 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT2_bz) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 3.43/3.77 congruence. % 3.43/3.77 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_Haf | zenon_intro zenon_Ha9 ]. % 3.43/3.77 cut (((sigma) = (sigma)) = ((age zenon_TX_w zenon_TT2_bz) = (sigma))). % 3.43/3.77 intro zenon_D_pnotp. % 3.43/3.77 apply zenon_Hae. % 3.43/3.77 rewrite <- zenon_D_pnotp. % 3.43/3.77 exact zenon_Haf. % 3.43/3.77 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 3.43/3.77 cut (((sigma) = (age zenon_TX_w zenon_TT2_bz))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.43/3.77 congruence. % 3.43/3.77 exact (zenon_Had zenon_Hac). % 3.43/3.77 apply zenon_Ha9. apply refl_equal. % 3.43/3.77 apply zenon_Ha9. apply refl_equal. % 3.43/3.77 apply zenon_Ha9. apply refl_equal. % 3.43/3.77 apply (zenon_L4_ zenon_TT2_bz zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 elim (classic ((age zenon_TX_w zenon_TT2_bz) = (age zenon_TX_w zenon_TT2_bz))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ]. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT2_bz) = (age zenon_TX_w zenon_TT2_bz)) = ((sigma) = (age zenon_TX_w zenon_TT2_bz))). % 3.43/3.77 intro zenon_D_pnotp. % 3.43/3.77 apply zenon_Had. % 3.43/3.77 rewrite <- zenon_D_pnotp. % 3.43/3.77 exact zenon_Hb0. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT2_bz) = (age zenon_TX_w zenon_TT2_bz))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 3.43/3.77 cut (((age zenon_TX_w zenon_TT2_bz) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 3.43/3.77 congruence. % 3.43/3.77 exact (zenon_Hae zenon_Hab). % 3.43/3.77 apply zenon_Hb1. apply refl_equal. % 3.43/3.77 apply zenon_Hb1. apply refl_equal. % 3.43/3.77 (* end of lemma zenon_L19_ *) % 3.43/3.77 assert (zenon_L20_ : forall (zenon_TT0_ca : zenon_U) (zenon_TT3_v : zenon_U) (zenon_TT2_bz : zenon_U) (zenon_TX_w : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (age zenon_TX_w zenon_TT2_bz) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_w zenon_TT3_v) (hazard_of_mortality zenon_TX_w zenon_TT2_bz))) -> ((age zenon_TX_w zenon_TT2_bz) = (sigma)) -> (greater (sigma) (eta)) -> (greater (age zenon_TX_w zenon_TT3_v) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_w)/\(((smaller_or_equal (age zenon_TX_w T) (eta))->(has_immunity zenon_TX_w T))/\((greater (age zenon_TX_w T) (eta))->(~(has_immunity zenon_TX_w T)))))) -> ((age zenon_TX_w zenon_TT0_ca) = (zero)) -> False). % 3.43/3.77 do 4 intro. intros zenon_H10 zenon_H51 zenon_H52 zenon_Hab zenon_H14 zenon_H13 zenon_H29 zenon_H32. % 3.43/3.77 generalize (assumption_13 zenon_TX_w). zenon_intro zenon_H54. % 3.43/3.77 generalize (zenon_H29 zenon_TT2_bz). zenon_intro zenon_H55. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H2c. zenon_intro zenon_H56. % 3.43/3.77 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 3.43/3.77 exact (zenon_H5a zenon_H51). % 3.43/3.77 generalize (assumption_16 zenon_TX_w). zenon_intro zenon_H5c. % 3.43/3.77 generalize (zenon_H54 zenon_TT0_ca). zenon_intro zenon_H5b. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H38 | zenon_intro zenon_H2f ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 exact (zenon_H39 zenon_H32). % 3.43/3.77 generalize (assumption_15 zenon_TX_w). zenon_intro zenon_H2e. % 3.43/3.77 generalize (zenon_H5c zenon_TT3_v). zenon_intro zenon_H5d. % 3.43/3.77 generalize (zenon_H5d zenon_TT2_bz). zenon_intro zenon_H5e. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H3a | zenon_intro zenon_H61 ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 3.43/3.77 apply zenon_H63. zenon_intro zenon_H12. % 3.43/3.77 apply (zenon_L3_ zenon_TT3_v zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 3.43/3.77 exact (zenon_H65 zenon_H59). % 3.43/3.77 generalize (assumption_14 zenon_TX_w). zenon_intro zenon_H66. % 3.43/3.77 generalize (zenon_H66 zenon_TT2_bz). zenon_intro zenon_H67. % 3.43/3.77 generalize (zenon_H67 zenon_TT3_v). zenon_intro zenon_H68. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H3a | zenon_intro zenon_H6b ]. % 3.43/3.77 exact (zenon_H3a zenon_H2c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H30 | zenon_intro zenon_H6c ]. % 3.43/3.77 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hb2. % 3.43/3.77 generalize (zenon_Hb2 (sigma)). zenon_intro zenon_Hb3. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_Haa | zenon_intro zenon_Haa ]. % 3.43/3.77 apply (zenon_L19_ zenon_TT2_bz zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L19_ zenon_TT2_bz zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 apply zenon_H6c. zenon_intro zenon_H47. % 3.43/3.77 apply (zenon_L5_ zenon_TT0_ca zenon_TT3_v zenon_TX_w); trivial. % 3.43/3.77 exact (zenon_H64 zenon_H69). % 3.43/3.77 exact (zenon_H52 zenon_H5f). % 3.43/3.77 (* end of lemma zenon_L20_ *) % 3.43/3.77 apply NNPP. intro zenon_G. % 3.43/3.77 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_H10 | zenon_intro zenon_Hb4 ]. % 3.43/3.77 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization X)/\((has_endowment X)/\(((age X T0) = (zero))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (eta))/\((smaller_or_equal (age X T2) (sigma))/\((greater (age X T3) (sigma))/\((greater (sigma) (eta))/\(greater (eta) (zero))))))))))->((greater (hazard_of_mortality X T3) (hazard_of_mortality X T2))/\((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))) zenon_G); [ zenon_intro zenon_Hb5; idtac ]. % 3.43/3.77 elim zenon_Hb5. zenon_intro zenon_TX_w. zenon_intro zenon_Hb6. % 3.43/3.77 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_w)/\((has_endowment zenon_TX_w)/\(((age zenon_TX_w T0) = (zero))/\((smaller_or_equal (age zenon_TX_w T1) (eta))/\((greater (age zenon_TX_w T2) (eta))/\((smaller_or_equal (age zenon_TX_w T2) (sigma))/\((greater (age zenon_TX_w T3) (sigma))/\((greater (sigma) (eta))/\(greater (eta) (zero))))))))))->((greater (hazard_of_mortality zenon_TX_w T3) (hazard_of_mortality zenon_TX_w T2))/\((greater (hazard_of_mortality zenon_TX_w T2) (hazard_of_mortality zenon_TX_w T1))/\((hazard_of_mortality zenon_TX_w T1) = (hazard_of_mortality zenon_TX_w T0))))))))) zenon_Hb6); [ zenon_intro zenon_Hb7; idtac ]. % 3.43/3.77 elim zenon_Hb7. zenon_intro zenon_TT0_ca. zenon_intro zenon_Hb8. % 3.43/3.77 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_w)/\((has_endowment zenon_TX_w)/\(((age zenon_TX_w zenon_TT0_ca) = (zero))/\((smaller_or_equal (age zenon_TX_w T1) (eta))/\((greater (age zenon_TX_w T2) (eta))/\((smaller_or_equal (age zenon_TX_w T2) (sigma))/\((greater (age zenon_TX_w T3) (sigma))/\((greater (sigma) (eta))/\(greater (eta) (zero))))))))))->((greater (hazard_of_mortality zenon_TX_w T3) (hazard_of_mortality zenon_TX_w T2))/\((greater (hazard_of_mortality zenon_TX_w T2) (hazard_of_mortality zenon_TX_w T1))/\((hazard_of_mortality zenon_TX_w T1) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca)))))))) zenon_Hb8); [ zenon_intro zenon_Hb9; idtac ]. % 3.43/3.77 elim zenon_Hb9. zenon_intro zenon_TT1_ek. zenon_intro zenon_Hba. % 3.43/3.77 apply (zenon_notallex_s (fun T2 : zenon_U => (forall T3 : zenon_U, (((organization zenon_TX_w)/\((has_endowment zenon_TX_w)/\(((age zenon_TX_w zenon_TT0_ca) = (zero))/\((smaller_or_equal (age zenon_TX_w zenon_TT1_ek) (eta))/\((greater (age zenon_TX_w T2) (eta))/\((smaller_or_equal (age zenon_TX_w T2) (sigma))/\((greater (age zenon_TX_w T3) (sigma))/\((greater (sigma) (eta))/\(greater (eta) (zero))))))))))->((greater (hazard_of_mortality zenon_TX_w T3) (hazard_of_mortality zenon_TX_w T2))/\((greater (hazard_of_mortality zenon_TX_w T2) (hazard_of_mortality zenon_TX_w zenon_TT1_ek))/\((hazard_of_mortality zenon_TX_w zenon_TT1_ek) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca))))))) zenon_Hba); [ zenon_intro zenon_Hbb; idtac ]. % 3.43/3.77 elim zenon_Hbb. zenon_intro zenon_TT2_bz. zenon_intro zenon_Hbc. % 3.43/3.77 apply (zenon_notallex_s (fun T3 : zenon_U => (((organization zenon_TX_w)/\((has_endowment zenon_TX_w)/\(((age zenon_TX_w zenon_TT0_ca) = (zero))/\((smaller_or_equal (age zenon_TX_w zenon_TT1_ek) (eta))/\((greater (age zenon_TX_w zenon_TT2_bz) (eta))/\((smaller_or_equal (age zenon_TX_w zenon_TT2_bz) (sigma))/\((greater (age zenon_TX_w T3) (sigma))/\((greater (sigma) (eta))/\(greater (eta) (zero))))))))))->((greater (hazard_of_mortality zenon_TX_w T3) (hazard_of_mortality zenon_TX_w zenon_TT2_bz))/\((greater (hazard_of_mortality zenon_TX_w zenon_TT2_bz) (hazard_of_mortality zenon_TX_w zenon_TT1_ek))/\((hazard_of_mortality zenon_TX_w zenon_TT1_ek) = (hazard_of_mortality zenon_TX_w zenon_TT0_ca)))))) zenon_Hbc); [ zenon_intro zenon_Hbd; idtac ]. % 3.43/3.77 elim zenon_Hbd. zenon_intro zenon_TT3_v. zenon_intro zenon_Hbe. % 3.43/3.77 apply (zenon_notimply_s _ _ zenon_Hbe). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H2c. zenon_intro zenon_Hc1. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hc3. zenon_intro zenon_Hc2. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H32. zenon_intro zenon_Hc4. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H76. zenon_intro zenon_Hc5. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H51. zenon_intro zenon_Hc6. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H13. zenon_intro zenon_Hc9. % 3.43/3.77 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H14. zenon_intro zenon_H8c. % 3.43/3.77 generalize (definition_1 zenon_TX_w). zenon_intro zenon_Hca. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_Hca); [ zenon_intro zenon_Hcc; zenon_intro zenon_Hcb | zenon_intro zenon_Hc3; zenon_intro zenon_H29 ]. % 3.43/3.77 exact (zenon_Hcc zenon_Hc3). % 3.43/3.77 generalize (definition_smaller_or_equal (age zenon_TX_w zenon_TT1_ek)). zenon_intro zenon_H73. % 3.43/3.77 generalize (zenon_H73 (eta)). zenon_intro zenon_H74. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H71; zenon_intro zenon_H77 | zenon_intro zenon_H76; zenon_intro zenon_H75 ]. % 3.43/3.77 exact (zenon_H71 zenon_H76). % 3.43/3.77 generalize (definition_smaller_or_equal (age zenon_TX_w zenon_TT2_bz)). zenon_intro zenon_Hcd. % 3.43/3.77 generalize (zenon_Hcd (sigma)). zenon_intro zenon_Hce. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_Hce); [ zenon_intro zenon_Hd1; zenon_intro zenon_Hd0 | zenon_intro zenon_Hc8; zenon_intro zenon_Hcf ]. % 3.43/3.77 exact (zenon_Hd1 zenon_Hc8). % 3.43/3.77 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hab ]. % 3.43/3.77 generalize (definition_smaller (age zenon_TX_w zenon_TT2_bz)). zenon_intro zenon_Hd3. % 3.43/3.77 generalize (zenon_Hd3 (sigma)). zenon_intro zenon_Hd4. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd5; zenon_intro zenon_H6f | zenon_intro zenon_Hd2; zenon_intro zenon_H53 ]. % 3.43/3.77 exact (zenon_Hd5 zenon_Hd2). % 3.43/3.77 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha8 ]. % 3.43/3.77 generalize (definition_smaller (age zenon_TX_w zenon_TT1_ek)). zenon_intro zenon_H7a. % 3.43/3.77 generalize (zenon_H7a (eta)). zenon_intro zenon_H7b. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H7b); [ zenon_intro zenon_H79; zenon_intro zenon_H7d | zenon_intro zenon_H7c; zenon_intro zenon_H70 ]. % 3.43/3.77 exact (zenon_H79 zenon_H7c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_H52 | zenon_intro zenon_Hd6 ]. % 3.43/3.77 apply (zenon_L6_ zenon_TT3_v zenon_TT0_ca zenon_TT2_bz zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_H7f | zenon_intro zenon_H9d ]. % 3.43/3.77 apply (zenon_L9_ zenon_TT2_bz zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L14_ zenon_TT0_ca zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_H52 | zenon_intro zenon_Hd6 ]. % 3.43/3.77 apply (zenon_L6_ zenon_TT3_v zenon_TT0_ca zenon_TT2_bz zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_H7f | zenon_intro zenon_H9d ]. % 3.43/3.77 apply (zenon_L16_ zenon_TT2_bz zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L17_ zenon_TT1_ek zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H7c | zenon_intro zenon_Ha8 ]. % 3.43/3.77 generalize (definition_smaller (age zenon_TX_w zenon_TT1_ek)). zenon_intro zenon_H7a. % 3.43/3.77 generalize (zenon_H7a (eta)). zenon_intro zenon_H7b. % 3.43/3.77 apply (zenon_equiv_s _ _ zenon_H7b); [ zenon_intro zenon_H79; zenon_intro zenon_H7d | zenon_intro zenon_H7c; zenon_intro zenon_H70 ]. % 3.43/3.77 exact (zenon_H79 zenon_H7c). % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_H52 | zenon_intro zenon_Hd6 ]. % 3.43/3.77 apply (zenon_L20_ zenon_TT0_ca zenon_TT3_v zenon_TT2_bz zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_H7f | zenon_intro zenon_H9d ]. % 3.43/3.77 apply (zenon_L9_ zenon_TT2_bz zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L14_ zenon_TT0_ca zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_H52 | zenon_intro zenon_Hd6 ]. % 3.43/3.77 apply (zenon_L20_ zenon_TT0_ca zenon_TT3_v zenon_TT2_bz zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_H7f | zenon_intro zenon_H9d ]. % 3.43/3.77 apply (zenon_L16_ zenon_TT2_bz zenon_TT1_ek zenon_TX_w); trivial. % 3.43/3.77 apply (zenon_L17_ zenon_TT1_ek zenon_TT0_ca zenon_TX_w); trivial. % 3.43/3.77 apply zenon_Hb4. zenon_intro zenon_Tx_ih. apply NNPP. zenon_intro zenon_Hd8. % 3.43/3.77 apply zenon_Hd8. zenon_intro zenon_Ty_ij. apply NNPP. zenon_intro zenon_Hda. % 3.43/3.77 apply zenon_Hda. zenon_intro zenon_Tz_il. apply NNPP. zenon_intro zenon_Hdc. % 3.43/3.77 apply (zenon_notimply_s _ _ zenon_Hdc). zenon_intro zenon_Hde. zenon_intro zenon_Hdd. % 3.43/3.77 apply (zenon_notimply_s _ _ zenon_Hdd). zenon_intro zenon_He0. zenon_intro zenon_Hdf. % 3.43/3.77 generalize (meaning_postulate_greater_transitive zenon_Tx_ih). zenon_intro zenon_He1. % 3.43/3.77 generalize (zenon_He1 zenon_Ty_ij). zenon_intro zenon_He2. % 3.43/3.77 generalize (zenon_He2 zenon_Tz_il). zenon_intro zenon_He3. % 3.43/3.77 apply (zenon_imply_s _ _ zenon_He3); [ zenon_intro zenon_He5 | zenon_intro zenon_He4 ]. % 3.43/3.77 apply (zenon_notand_s _ _ zenon_He5); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 3.43/3.77 exact (zenon_He7 zenon_Hde). % 3.43/3.77 exact (zenon_He6 zenon_He0). % 3.43/3.77 exact (zenon_Hdf zenon_He4). % 3.43/3.77 Qed. % 3.43/3.77 % SZS output end Proof % 3.43/3.77 (* END-PROOF *) % 3.43/3.77 nodes searched: 124004 % 3.43/3.77 max branch formulas: 1957 % 3.43/3.77 proof nodes created: 1073 % 3.43/3.77 formulas created: 50342 % 3.43/3.77 %------------------------------------------------------------------------------